[{"data":1,"prerenderedAt":132915},["ShallowReactive",2],{"post-\u002Fblog\u002F2026\u002F0012-shu-xue-yu-hua-jia":3,"i-ci:tag":-1,"i-mingcute:time-line":-1},{"post":4,"nextPost":193,"prevPost":203},{"id":5,"title":6,"body":7,"description":189,"draft":190,"enableCodeHighlight":190,"enableCodeHightlight":190,"enableComment":191,"enableD2":190,"enableKatex":190,"extension":192,"image":186,"important":190,"location":193,"meta":194,"navigation":191,"ogImage":193,"path":195,"seo":196,"stem":197,"summary":198,"tags":199,"time":201,"__hash__":202},"blog\u002Fblog\u002F2026\u002F0012-shu-xue-yu-hua-jia.md","数学与画家",{"type":8,"value":9,"toc":185},"minimark",[10,23,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99,102,105,108,111,114,117,120,123,126,129,132,135,138,141,144,147,150,153,156,159,162,165,168,171,174,177,180],[11,12,13,14,22],"p",{},"前段时间，OpenAI 声称，他们用内部尚未正式发布的模型产出了七百多篇论文，「AI 接替数学家」的叙事于是再一次被推到台前。市场是狂热还是炒作，我已经疲于争论。那七百篇论文是否名副其实，也先放在一边。真正让我想写点东西的，",[15,16,21],"a",{"href":17,"rel":18,"target":20},"https:\u002F\u002Fx.com\u002FNoe1017_Monad\u002Fstatus\u002F2112008540592410951",[19],"nofollow","_blank","是 Twitter 上一条获得不少认同的帖子","。它把数学结构说成人类为了迁就自己那点脑容量而被迫发明的拐杖，把 AI 说成不需要几何直观、可以直接站在高维展开式里往下看的怪物。最后一句尤其漂亮：我们终于拿到了上帝账本里的答案，却发现上帝算账根本不用微积分，他老人家是直接拿计算器硬按出来的。",[24,25,26],"blockquote",{},[11,27,28,29,32,33,35,36,38,39,41,42,44,45,47,48,50,51,53],{},"所谓优雅的数学结构，本质上是人类为了迁就自己那点可怜的脑容量，被迫发明出来的拐杖。  ",[30,31],"br",{},"\n一个顶尖人类数学家的工作内存，撑死也就同时追踪五六个变量的交互。  ",[30,34],{},"\n当你在算一个偏微分方程或者组合不等式时，一旦展开到三阶以上，几十个交叉项涌出来，人脑就直接宕机了。  ",[30,37],{},"\n所以人类数学家极其厌恶展开高阶项，一旦看到高阶项发散，人类的本能反应是此路不通，赶紧退回来找对称性、找不变量、搞同调代数或者几何直观，试图不展开式子就把问题绕过去。  ",[30,40],{},"\n但 AI 没有这个生理缺陷。  ",[30,43],{},"\n对于上万个并发的 Agent 来说，同时追踪一万个五阶交叉项的系数变化，跟我们算 1+1 一样轻松。  ",[30,46],{},"\n在它的视野里，根本不需要什么几何直观，它直接站在高维的代数展开式里往下看，人类觉得像乱麻一样的百项高阶余项，在它眼里就是一张明明白白的线性方程组。  ",[30,49],{},"\n既然把式子硬展开到第七阶，再凑几个待定系数就能让所有讨厌的发散项精准归零，它为什么要费劲去帮你发明一个人类能看懂的新概念？  ",[30,52],{},"\n这 700 个结果背后最无奈的黑色幽默：我们终于拿到了上帝账本里的答案，却发现上帝算账根本不用微积分，他老人家是直接拿计算器硬按出来的。",[11,55,56],{},"这套论证值得认真对待，恰恰因为它错得很有代表性：它把人类的工作记忆、数学的审美偏好、AI 的暴力计算串成了一条看似严密的因果链。但这条链中间有一个关键的偷换——它把「人类因为认知限制而偏爱结构」偷换成了「结构只是认知限制的产物」。前者是发生学上的事实，后者是一个关于数学本体的判断。两者之间隔着一整个哲学鸿沟。",[11,58,59],{},"画家这个比喻，也许比「拐杖」更接近真相。画家画不出世界上的每一个光子，所以他发明了透视、明暗和构图。但这些都长在真实的结构上：透视是射影几何，明暗是光的传播，构图是视觉心理。一个能逐像素渲染世界的渲染器，仍然跑在同一套射影几何上。暴力计算并没有绕开结构。它把结构执行到了人眼跟不上的规模。数学里的「硬展开」也一样。",[11,61,62],{},"它对人类工作记忆的描述大体成立，对数学的判断则基本错了。结构就是数学本身，拐杖之说站不住。AI 同样依赖结构，只不过那种结构人读不懂。问题在于「能不能翻译」，美丑反而次要。而翻译，恰恰是当前 AI 数学产出链条上最缺失的一环。",[11,64,65],{},"先承认其中合理的部分。人类的工作记忆确实窄得可怜。Miller 在 1956 年给出著名的 7±2，后来 Cowan 又把它修正到 4±1 左右。数字有争议，但「窄」这个结论没有被推翻。数学家偏爱对称性、不变量、同调，厌恶把式子硬展开，很大程度上确实是认知经济学的产物：找不变量，本质上是把高维信息压缩成一两个人类握得住的符号。AI 在大规模符号展开和并行系数追踪上的优势也是真实的。AlphaTensor 找矩阵乘法算法、各种组合搜索里那些看似暴力、实则依赖结构化搜索空间的路线，确实绕开了人类偏好的那条美学路径。",[11,67,68],{},"问题出在下一步。从「人类因为认知限制而偏爱结构」推到「结构只是认知限制的产物」，这是一个发生学谬误。一个东西因为什么被发明出来，并不等于它是什么。望远镜是因为人眼太弱才被造出来的，但这不意味着望远镜里的木星卫星是人类的幻觉。十进制是因为人有十根手指才流行的，但这也不意味着素数分布依赖于手指的数量。数学结构也一样：它可能是因为人脑太窄才被优先发现的，但一旦被发现，它说的就是对象本身的事，与人类脑容量无关。",[11,70,71],{},"把 Galois 群说成「人类算不动五次方程，所以编个借口说它不可解」，是一种误解。它本身是一个定理：一个方程能用根式解，当且仅当它的 Galois 群可解。五次一般方程对应的对称群 S5 不是可解群，所以没有根式解。这个结论与人类的工作记忆无关。就算人类有无限的工作记忆，S5 依然不是可解群，这个定理依然成立。同样，Noether 定理把连续对称性和守恒律绑在一起。把它说成「人类看不懂，所以画个对称性的图安慰自己」，也是一种误解。它说的是物理世界的一条结构事实：如果世界没有这种对称性，相应的守恒律就不存在。同调群也常被误解成「空间太复杂，人类算不动，所以发明一个符号糊弄过去」。它探测的是空间的洞，而它作为不变量能被计算，本身依赖链复形这一整套结构。",[11,73,74],{},"此外，它的说服力有很大一部分来自修辞。「可怜的脑容量」「拐杖」「硬按」——这些词先把你放在一个需要被怜悯的位置，再让你接受结论。把修辞剥掉，论证的核心其实只有一句：人脑窄，AI 不窄，所以结构是拐杖。而这句话恰恰是跳步的。",[11,76,77],{},"退一步说，就算 AI 真的把式子硬展开到第七阶，把所有发散项精准归零，它拿到的只是一张针对这个特例的系数表，换一个情形就未必管用。它能告诉你「这里可以归零」，但不能告诉你「为什么这里必然可以归零」。前者是答案，后者才是数学。打个比方：给你七百个点，你总可以找到一个不超过 699 次的多项式，让它精确穿过每一个点。但这只是插值，够不上理解。它在七百个点之外没有任何预测力。硬展开加待定系数，本质上就是高维版本的插值——你用一个足够大的展开式，把眼前的项全部按住，然后宣布问题解决了。可数学要的是「为什么会这样，以及换一个情形会怎样」。「按住」远远不够。",[11,79,80],{},"照这个逻辑，AI 不需要几何直观，可以直接站在高维的代数展开式里往下看。这个画面假设存在一个「没有直观」的视角。但任何计算都发生在某种表示里，而表示本身就是一种结构。Transformer 的注意力是内容相关的路由，等变网络把对称性硬编码进架构，神经算子学的是函数空间之间的映射——这些做法都把结构写进了模型，只是藏得比较深。没有免费午餐定理早就说过，不存在对所有问题都最优的通用学习器。每一个能学的模型，都带着自己的归纳偏置。所谓「不需要直观的 AI」，只是把直观藏进了架构里，让人看不见而已。",[11,82,83],{},"AlphaTensor 常被拿来当例子，但它恰恰站在这个论证的反面。DeepMind 并没有枚举所有可能的算法。它在张量分解的结构化空间里做强化学习搜索。它能找到 Strassen 式的算法，正是因为搜索空间被结构约束过。把 AlphaTensor 说成「暴力硬算」的证据，是对它的误读。",[11,85,86],{},"更有意思的是，AI 自己的前沿正在往结构走，纯暴力那条路反而越走越窄。等变网络、神经算子、状态空间模型、注意力机制，都是在把某种先验写进模型。为什么？因为纯暴力在高维会指数爆炸。这个领域最聪明的一批人，正在用工程手段重新发明数学家一百年前就熟悉的那些东西：对称性、局部性、可分解性。AI 的研究者自己正在沿着那条路径追赶，「绕开审美」的预言并没有发生。",[11,88,89],{},"技术细节上也站不住。「高阶项发散」常被当作「项太多、人脑装不下」的同义词。但在很多场合，发散属于表示问题，跟项数多少关系不大：这个展开本身是一个渐近级数，并不收敛。渐近级数在前几项可以给出极好的近似，但继续展开不会逼近真值。你需要的是重求和、解析延拓，或者换一个表示。数学家看到发散就后退，是因为他们知道「继续展开」不会自动收敛。这时候该做的是换一种表示，把项数堆得更高没有用。AI 就算把发散项凑没了，也可能只找到一种形式上的消去，并未得到收敛的表示。",[11,91,92],{},"即便并行 Agent 真的能同时追踪一万个五阶交叉项，代价也不是零。算力、内存、通信都会随着项数组合爆炸。「并行」被当成了免费的午餐。更关键的是，这个天花板背后还有复杂性理论：在普遍接受的复杂性假设下，有些问题是内在难解的——问题本身的复杂度摆在那里，跟聪明与否关系不大。「人脑太小」和「问题太难」被混为一谈了。就算给一个无限工作记忆的理想智能体，它也会撞上指数爆炸。人类偏爱结构，既因为脑子小，也因为问题本身硬。",[11,94,95],{},"所以，AI 可以使用一种人读不懂的结构。硬展开同样有结构，只不过这种结构被执行到了人跟不上的规模。一个逐像素渲染的渲染器，算得比任何画家都细，却始终跑在射影几何上，把透视算到了人眼看不见的精度。AI 的硬展开也一样：它把代数结构展开到了人脑装不下的长度，却始终在代数结构之内。",[11,97,98],{},"「上帝拿计算器硬按」假设答案先于结构存在。它背后是一个很朴素的柏拉图式画面：答案早就躺在那里，结构只是人类够不着时用的梯子。但数学的实践不是这样。很多答案是在结构被发明出来之后才成为「答案」的。",[11,100,101],{},"一个猜想在 n=5 成立、在 n=6 崩掉，硬算给你两个数。结构告诉你边界在哪里，以及为什么边界在那里。两个数可以和无穷多个故事相容，结构帮你挑出正确的那个。更一般地，硬算只能处理有限多个情形。即使你在计算机上验证费马大定理到 n 等于十亿，也不构成对所有的 n 的证明。Wiles 的证明之所以成立，靠的是模形式这座桥，把问题接到了另一个世界。计算量的大小并非关键。",[11,103,104],{},"知道一个命题为真，和知道它为什么为真，不是一回事。前者是证明，后者是理解。硬算可以给你前者，未必给你后者。而且，硬算能证明的通常只是有限多个特例。一旦命题是全称的，你就需要结构、归纳或者某种不变量，才能跨过「有限」到「所有」的鸿沟。七百个结果里可能有一些本身就是关于有限对象的定理，本身就有价值。但如果它们大多是硬展开出来的特例，那么它们更像是一批精确的数值事实，未必是可迁移的定理。另外，「七百篇论文」和「七百个结果」不是一回事。前者可能包含大量增量工作，后者才是数学意义上的成果。这个区分本身就值得追问，但先放在一边。",[11,106,107],{},"数学史上早有「先有黑箱，后有理解」的先例。四色定理 1976 年由机器辅助证明，当时吵得很厉害。后来人类花了很多年去简化、去压缩，形式化验证也完成了，但「机器证明算不算理解」这个问题并没有完全消失。Kepler 猜想被 Hales 用大规模计算机辅助证明，后来又有 Flyspeck 项目做形式化验证。模式很清楚：先拿到一个可验证但不可读的答案，再花一代人把它翻译成人类握得住的结构。翻译可能失败，也可能要几代人，但「现在翻译不出来」从来不足以让人停下来。",[11,109,110],{},"而且，人类数学自己也早就遇到过不可读的问题。有限单群分类定理的证明上万页，散落在几百篇文章里，据说至今没有人从头到尾读完。这是人类自己造出来的黑箱。区别只在于规模：人类数学在二十世纪就已经开始生产超出个体阅读能力的结果，AI 只是把这个趋势推得更远。",[11,112,113],{},"黑箱当然有价值。它可以被引用、被使用、被当作下一步的踏脚石。但它的价值有一个天花板：验证成本无法摊销。一个你理解了的定理，可以在一段话里教给别人，可以在新问题里直接调用。一个你不理解的黑箱，每用一次都要重新跑一遍、重新信一遍。理解之所以重要，是因为它把验证成本压缩成了可复用的结构。没有理解，知识就不能以低成本累积。",[11,115,116],{},"把这种思路推到极端：也许黑箱就是数学的新常态。也许未来的数学单位会从定理变成证书。数学家追求的东西，也会从「看懂」转向「可验证、可组合、可规模化」。这是一个严肃的可能性，我不打算轻易否定它。但它比「AI 算得更快」是一个大得多的主张：它改变的是数学知识的定义，速度倒在其次。而且，就算走到那一步，信任基础设施本身仍然是结构：证书格式、证明助理、可复现性标准、社区共识。黑箱的未来并未取消结构，只不过把结构挪到了另一个地方。",[11,118,119],{},"至于审美，AI 正在用一个丑但有效的答案挑战「美是数学的先验判据」这个前提。这个前提站不住。",[11,121,122],{},"数学史上「丑的真理」屡见不鲜。三次方程的求根公式在 16 世纪就撞上了 casus irreducibilis：三个实根，却必须经过复数才能算出来。当时的数学家觉得这近乎荒谬。非欧几何刚出来的时候，高斯不敢公开发表。Cantor 的无穷集合遭到 Kronecker 的激烈反对。Weierstrass 造出处处连续、处处不可导的函数，被当时的许多人视为病态。Banach-Tarski 分球悖论更是像在说「数学不该长这样」。后来的处理方式，是扩写美的定义，把这些东西留下来。复数变成了复平面上的几何，非欧几何变成了曲率，病态函数催生了测度论，也逼着拓扑学重新审视连续与收敛。分球悖论则逼着人们去追问选择公理到底意味着什么。丑的东西待得够久，人类就会给它找一套它配得上的语言。语言找到了，它就不丑了。",[11,124,125],{},"所以，美更像事后的评价。数学家说一个证明美，通常是在说：它把原本分散的东西统一了，没有多余的假设，并且揭示了机制。这些都是理解完成之后的判词，很难充当发现之前的门槛。历史上真正被审美直觉挡在门外的结果——比如 Galois 生前没能发表的手稿——事后看，那是审美的失败，数学本身并没有失败。",[11,127,128],{},"但也不要走到另一个极端，把审美说成纯粹的非理性。审美其实是一个关于「可压缩性」的启发式：一个漂亮的证明，往往更容易推广、更容易迁移、更容易在别的问题里复用。它当然会犯错，但命中率并不低。数学家对丑的警惕，除了对陌生的恐惧，还包含一种合理怀疑：这东西也许无法一般化。把审美当成纯粹的偏见，这太便宜了。",[11,130,131],{},"所以，「能不能翻译」比「美不美」更值得问。丑是可以忍受的，只要它能在可接受的成本内被压缩成一套可迁移的结构。丑而无法批量翻译，才是真正的问题。对 AI 那七百个结果，关键在翻译成本：把它们变成人类可读的结构要花多大代价，这个代价能不能被规模化地摊薄。如果每个结果都需要一位数学家花十年去反推，那七百个结果的边际价值就取决于翻译的规模化程度——而这恰恰是 AI 可能帮上忙的地方：让 AI 去搜「能压缩这七百个结果的统一框架」。丑不可怕，可怕的是丑得无法批量处理。",[11,133,134],{},"「地球灭亡之前，人类没法理解的事情肯定存在。」这句话我同意。Gödel 的不完备定理保证了真而不可证的东西存在，复杂性理论则告诉我们，一大批问题在可接受的资源内算不动。但这句话不能推出「所以现在别理解了」。",[11,136,137],{},"从「存在无法理解的东西」推不出「眼前这七百个就是无法理解的」。这是一个很基本的逻辑错误：存在量词不能这样实例化。而且，可理解域的边界是未知的，历史上每一次都被推得比预期远得多。Hilbert 纲领失败了，但失败本身催生了证明论和可计算性理论，也深刻改变了模型论的问题意识。数学的边界更像一片雾。你往前走，雾就退一点。",[11,139,140],{},"理解有许多层次。我们理解热力学，不需要追踪每一个分子。同样，我们理解一个函数，不需要它的封闭形式。七百个结果可能在细粒度上不可读，但在粗粒度上仍然可以被理解：它们可能共享某种对称性、某种生成机制、某种还没被命名的结构。放弃理解需要「已经证明这里推不动」。「现在看着像一团乱麻」还不够。前者是数学，后者是情绪。",[11,142,143],{},"另外，AI 的方法太有针对性，这是数学界最实在的批评之一。以前一个理论出来，不仅解决目标问题，还会带来一整套工具箱，影响其他领域。现在的 AI 方法往往只解决目标问题，然后就结束了。",[11,145,146],{},"这条批评有它的道理。人类数学的溢出效应是结构性的。Galois 理论本来是为了解五次方程，产出的群论和域扩张后来成了整个代数的主干。Riemann 为了理解素数分布把复分析引进数论，他的几何工作又养活了微分几何和拓扑。同调代数从拓扑里长出来，最后变成了交换代数、代数几何、表示论的通用语法。目标问题是钩子，工具箱才是本体。数学界评价一个工作，隐含的标准是「它留下了什么可复用的东西」。「它证明了什么」只是起点。",[11,148,149],{},"AI 目前的产出恰好踩在这个标准的反面。AlphaTensor 找矩阵乘法算法、组合搜索、符号回归凑公式，共同特征是：针对特定实例、依赖大规模搜索、结果的可迁移性有限。它优化的是「这个问题有没有解、解是什么」。「这类问题的结构长什么样」则被放在一边。一个只针对单点的工具，边际价值确实低，尤其当它消耗的算力还能拿去做别的事。",[11,151,152],{},"但针对性太强，是 AI 的局限，还是当前阶段的局限？历史上「针对性太强」的批评也落在过人类自己头上。数值分析早期被纯数学家看不起，觉得是工程凑数，后来它长出了稳定性、收敛阶、条件数这一整套理论。概率论被当成赌博工具几百年，Kolmogorov 公理化之后才翻身。针对性强的工具，如果被反复使用，往往会倒逼出一般理论。差别在于：人类工具的一般化是被使用者的需求驱动的，慢但稳。AI 工具的一般化目前没有人系统性地做，因为发论文的激励在「又刷了一个纪录」，不在「把这套方法抽象成可复用的框架」。",[11,154,155],{},"所以，真正缺的，是有人负责把针对性的方法一般化。「AI 方法针对性太强」只是表象。人类数学家有同行评议和长期声誉在逼他们想「这东西能不能推广」。AI 数学的产出链条里，这个环节目前是断的。如果哪天真有团队认真做「把七百个硬展开结果反推成一个统一框架」，而且做成了，那这条批评就自动消解了。但这件事的难度不比发现那七百个结果低，甚至更高：归纳一个框架，靠的是猜对抽象层级，算力反而次要。而这恰恰是目前最说不清楚 AI 能不能做好的部分。",[11,157,158],{},"翻译是一项制度功能，很难靠某位数学家的英雄行为完成。人类数学之所以能把计算变成结构，靠的是一整套同行评议、教科书、研讨会和长期声誉的机器，在逼着每一代人去问「这东西能不能推广」。个别天才只是其中一环。AI 数学现在缺的，正是这台机器，算力和聪明的模型都还在其次。真正的瓶颈在分工，认知带宽不是主要问题。",[11,160,161],{},"这套论证的力量来自三个漂亮的偷换，把动机当成定义，把事后的判词当成先验的门槛，把答案当成理解。",[11,163,164],{},"但挑战是真的，只是位置放错了：我们把计算翻译成结构的制度，没有跟上计算的速度。「AI 比人算得快」只是表面。",[11,166,167],{},"画家画不出世界上的每一个光子，所以他发明透视。但透视是射影几何，跟「眼睛不行」没有关系。",[11,169,170],{},"今天最强的渲染器可以逐像素地硬算，但它仍然跑在透视的数学上。硬算并没有取消结构。它把结构算到了人眼跟不上的地方。",[11,172,173],{},"上帝或许真的在用计算器。但账本不是给计算器看的。人类接下来要做的，是翻译账本，让计算器的结果变得可读。",[11,175,176],{},"所以说，AI 在未来会彻底取代数学研究的劳动吗？",[11,178,179],{},"我认为不会，而且在未来很长一段时间里，都不会，至少在 AGI 诞生之前永远不会。",[24,181,182],{},[11,183,184],{},"砸掉计算器解决不了问题。数学的下一份工作，也许要从「发现」转向「翻译」。",{"title":186,"searchDepth":187,"depth":187,"links":188},"",2,[],"前段时间，OpenAI 声称，他们用内部尚未正式发布的模型产出了七百多篇论文，「AI 接替数学家」的叙事于是再一次被推到台前。市场是狂热还是炒作，我已经疲于争论。那七百篇论文是否名副其实，也先放在一边。真正让我想写点东西的，是 Twitter 上一条获得不少认同的帖子。它把数学结构说成人类为了迁就自己那点脑容量而被迫发明的拐杖，把 AI 说成不需要几何直观、可以直接站在高维展开式里往下看的怪物。最后一句尤其漂亮：我们终于拿到了上帝账本里的答案，却发现上帝算账根本不用微积分，他老人家是直接拿计算器硬按出来的。",false,true,"md",null,{},"\u002Fblog\u002F2026\u002F0012-shu-xue-yu-hua-jia",{"title":6,"description":189},"blog\u002F2026\u002F0012-shu-xue-yu-hua-jia","结构本身就是定理，AI 也有结构，只是那种结构人读不懂。关键在于可翻译性，以及把计算翻译成结构的制度是否跟得上。硬算常给出有限情形的答案而非「为什么」，而把针对性的结果一般化、翻译成可复用结构的制度，在 AI 数学的产出链条里是断的。",[200],"thoughts","2026-10-25T16:52:45+08:00","MTXFn_wz9eNH537cFyhWDAYMtvfSTEdfulMeMndlEyU",{"id":204,"title":205,"body":206,"description":132904,"draft":190,"enableCodeHighlight":190,"enableCodeHightlight":190,"enableComment":191,"enableD2":190,"enableKatex":191,"extension":192,"image":186,"important":190,"location":193,"meta":132905,"navigation":191,"ogImage":193,"path":132906,"seo":132907,"stem":132908,"summary":132909,"tags":132910,"time":132913,"__hash__":132914},"blog\u002Fblog\u002F2026\u002F0011-about-the-f-divergence.md","f-散度族及其推论",{"type":8,"value":207,"toc":132843},[208,260,374,721,724,729,949,1113,1189,2508,2513,3353,4020,4457,4914,5400,5404,5726,5769,5773,5909,6087,6144,6687,6859,7344,7557,7561,8612,8947,9045,9049,9290,9563,9599,10069,10224,10753,10756,10760,10862,11166,11171,12136,12804,13616,14459,14591,15520,16071,16369,16710,17244,17550,18166,19278,20098,20641,20987,21240,21478,21509,21605,21609,21641,21644,21647,21664,21667,21671,21674,21762,21998,22538,22703,23247,23250,23540,23825,24386,24389,24687,25382,25746,25750,25912,26389,26661,27057,27768,27771,28208,28211,28648,28917,29881,30134,30775,31013,31181,31368,31778,32284,33002,33728,33784,34029,34290,34707,34711,34713,34880,34949,35589,35984,36376,36385,36731,37346,37350,37352,37484,37552,38080,38087,38460,38833,39786,40635,40639,40641,40822,41138,41677,41839,42247,42310,42787,43405,44317,44508,44934,44938,45022,45363,45808,46184,46393,46665,46851,47389,47930,48356,48359,49214,49303,49572,49576,49579,50148,50615,50825,50953,51494,51707,51716,52218,52686,52690,55109,55113,55408,55412,55668,56335,56339,57298,57989,58491,58495,58850,59176,59281,60014,60887,60891,61712,61747,61998,62164,63210,63863,63869,64135,64633,64826,67016,68030,68340,68615,69127,70815,71705,73475,74238,74241,74652,74655,74658,74662,74968,75306,76072,76075,76436,76468,76957,77020,77815,78193,78241,78245,79127,79433,80575,82269,82273,84092,84098,84242,84644,85188,86315,87256,87262,87730,88415,88822,88895,88934,89332,89661,89913,90659,90724,92005,92650,97156,97163,97167,97170,99082,99341,99510,99514,99518,99521,99924,100130,100920,101046,101558,101562,101978,102236,102696,103402,103406,103467,103599,103986,104334,105564,105568,105754,106109,106112,106590,106980,107492,107775,108196,108456,108460,108463,108797,108801,108805,111765,114824,114827,114831,114884,115131,115344,115470,115831,116106,116483,116604,116609,116613,117650,117653,117657,117660,117719,117722,117726,117916,117920,117923,118452,118807,118811,118814,119386,119506,119510,119558,119961,119964,119968,120033,120037,120040,120394,120397,120401,120482,120836,121112,121270,121507,121773,122096,122468,122878,123753,124285,124555,124558,124562,124566,124917,124922,125661,126114,126452,126454,127055,127217,127223,127569,128085,128091,128665,128907,128911,129504,129895,130315,130663,131136,131140,131398,131713,131819,132353,132356,132360,132363,132840],[11,209,210,211,259],{},"f-散度族是概率分布之间差异的一大类度量，它用一个凸函数 ",[212,213,217,239],"span",{"className":214,"translate":216},[215],"katex","no",[212,218,221],{"className":219},[220],"katex-mathml",[222,223,225],"math",{"xmlns":224},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[226,227,228,235],"semantics",{},[229,230,231],"mrow",{},[232,233,234],"mi",{},"f",[236,237,234],"annotation",{"encoding":238},"application\u002Fx-tex",[212,240,244],{"className":241,"ariaHidden":243},[242],"katex-html","true",[212,245,248,253],{"className":246},[247],"base",[212,249],{"className":250,"style":252},[251],"strut","height:0.8889em;vertical-align:-0.1944em;",[212,254,234],{"className":255,"style":258},[256,257],"mord","mathnormal","margin-right:0.1076em;"," 来统一描述 KL 散度、JS 散度、全变差、卡方散度等许多常见散度。可以把它理解为「散度」的通用模板。",[11,261,262,263,291,292,373],{},"用一个凸函数 ",[212,264,266,279],{"className":265,"translate":216},[215],[212,267,269],{"className":268},[220],[222,270,271],{"xmlns":224},[226,272,273,277],{},[229,274,275],{},[232,276,234],{},[236,278,234],{"encoding":238},[212,280,282],{"className":281,"ariaHidden":243},[242],[212,283,285,288],{"className":284},[247],[212,286],{"className":287,"style":252},[251],[212,289,234],{"className":290,"style":258},[256,257],"（满足 ",[212,293,295,327],{"className":294,"translate":216},[215],[212,296,298],{"className":297},[220],[222,299,300],{"xmlns":224},[226,301,302,324],{},[229,303,304,306,311,315,318,321],{},[232,305,234],{},[307,308,310],"mo",{"stretchy":309},"false","(",[312,313,314],"mn",{},"1",[307,316,317],{"stretchy":309},")",[307,319,320],{},"=",[312,322,323],{},"0",[236,325,326],{"encoding":238},"f(1)=0",[212,328,330,363],{"className":329,"ariaHidden":243},[242],[212,331,333,337,340,344,347,351,356,360],{"className":332},[247],[212,334],{"className":335,"style":336},[251],"height:1em;vertical-align:-0.25em;",[212,338,234],{"className":339,"style":258},[256,257],[212,341,310],{"className":342},[343],"mopen",[212,345,314],{"className":346},[256],[212,348,317],{"className":349},[350],"mclose",[212,352],{"className":353,"style":355},[354],"mspace","margin-right:0.2778em;",[212,357,320],{"className":358},[359],"mrel",[212,361],{"className":362,"style":355},[354],[212,364,366,370],{"className":365},[247],[212,367],{"className":368,"style":369},[251],"height:0.6444em;",[212,371,323],{"className":372},[256],"）定义的散度模板：",[212,375,378],{"className":376,"translate":216},[377],"katex-display",[212,379,381,458],{"className":380,"translate":216},[215],[212,382,384],{"className":383},[220],[222,385,387],{"xmlns":224,"display":386},"block",[226,388,389,455],{},[229,390,391,399,401,404,408,411,413,415,423],{},[392,393,394,397],"msub",{},[232,395,396],{},"D",[232,398,234],{},[307,400,310],{"stretchy":309},[232,402,403],{},"P",[232,405,407],{"mathvariant":406},"normal","∥",[232,409,410],{},"Q",[307,412,317],{"stretchy":309},[307,414,320],{},[392,416,417,421],{},[232,418,420],{"mathvariant":419},"double-struck","E",[232,422,410],{},[229,424,425,428,430,452],{},[307,426,427],{"fence":243},"[",[232,429,234],{},[229,431,432,434,450],{},[307,433,310],{"fence":243},[435,436,437,444],"mfrac",{},[229,438,439,442],{},[232,440,441],{},"d",[232,443,403],{},[229,445,446,448],{},[232,447,441],{},[232,449,410],{},[307,451,317],{"fence":243},[307,453,454],{"fence":243},"]",[236,456,457],{"encoding":238},"D_f(P\\|Q)\n=\\mathbb E_Q\\left[\nf\\left(\\frac{dP}{dQ}\\right)\\right]",[212,459,461,550],{"className":460,"ariaHidden":243},[242],[212,462,464,468,525,528,532,535,538,541,544,547],{"className":463},[247],[212,465],{"className":466,"style":467},[251],"height:1.0361em;vertical-align:-0.2861em;",[212,469,471,475],{"className":470},[256],[212,472,396],{"className":473,"style":474},[256,257],"margin-right:0.0278em;",[212,476,479],{"className":477},[478],"msupsub",[212,480,484,516],{"className":481},[482,483],"vlist-t","vlist-t2",[212,485,488,511],{"className":486},[487],"vlist-r",[212,489,493],{"className":490,"style":492},[491],"vlist","height:0.3361em;",[212,494,496,501],{"style":495},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[212,497],{"className":498,"style":500},[499],"pstrut","height:2.7em;",[212,502,508],{"className":503},[504,505,506,507],"sizing","reset-size6","size3","mtight",[212,509,234],{"className":510,"style":258},[256,257,507],[212,512,515],{"className":513},[514],"vlist-s","​",[212,517,519],{"className":518},[487],[212,520,523],{"className":521,"style":522},[491],"height:0.2861em;",[212,524],{},[212,526,310],{"className":527},[343],[212,529,403],{"className":530,"style":531},[256,257],"margin-right:0.1389em;",[212,533,407],{"className":534},[256],[212,536,410],{"className":537},[256,257],[212,539,317],{"className":540},[350],[212,542],{"className":543,"style":355},[354],[212,545,320],{"className":546},[359],[212,548],{"className":549,"style":355},[354],[212,551,553,557,600,604],{"className":552},[247],[212,554],{"className":555,"style":556},[251],"height:2.4em;vertical-align:-0.95em;",[212,558,560,564],{"className":559},[256],[212,561,420],{"className":562},[256,563],"mathbb",[212,565,567],{"className":566},[478],[212,568,570,592],{"className":569},[482,483],[212,571,573,589],{"className":572},[487],[212,574,577],{"className":575,"style":576},[491],"height:0.3283em;",[212,578,580,583],{"style":579},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[212,581],{"className":582,"style":500},[499],[212,584,586],{"className":585},[504,505,506,507],[212,587,410],{"className":588},[256,257,507],[212,590,515],{"className":591},[514],[212,593,595],{"className":594},[487],[212,596,598],{"className":597,"style":522},[491],[212,599],{},[212,601],{"className":602,"style":603},[354],"margin-right:0.1667em;",[212,605,608,617,620,623,715],{"className":606},[607],"minner",[212,609,613],{"className":610,"style":612},[343,611],"delimcenter","top:0em;",[212,614,427],{"className":615},[616,506],"delimsizing",[212,618,234],{"className":619,"style":258},[256,257],[212,621],{"className":622,"style":603},[354],[212,624,626,632,709],{"className":625},[607],[212,627,629],{"className":628,"style":612},[343,611],[212,630,310],{"className":631},[616,506],[212,633,635,639,706],{"className":634},[256],[212,636],{"className":637},[343,638],"nulldelimiter",[212,640,642],{"className":641},[435],[212,643,645,697],{"className":644},[482,483],[212,646,648,694],{"className":647},[487],[212,649,652,668,679],{"className":650,"style":651},[491],"height:1.3714em;",[212,653,655,659],{"style":654},"top:-2.314em;",[212,656],{"className":657,"style":658},[499],"height:3em;",[212,660,662,665],{"className":661},[256],[212,663,441],{"className":664},[256,257],[212,666,410],{"className":667},[256,257],[212,669,671,674],{"style":670},"top:-3.23em;",[212,672],{"className":673,"style":658},[499],[212,675],{"className":676,"style":678},[677],"frac-line","border-bottom-width:0.04em;",[212,680,682,685],{"style":681},"top:-3.677em;",[212,683],{"className":684,"style":658},[499],[212,686,688,691],{"className":687},[256],[212,689,441],{"className":690},[256,257],[212,692,403],{"className":693,"style":531},[256,257],[212,695,515],{"className":696},[514],[212,698,700],{"className":699},[487],[212,701,704],{"className":702,"style":703},[491],"height:0.8804em;",[212,705],{},[212,707],{"className":708},[350,638],[212,710,712],{"className":711,"style":612},[350,611],[212,713,317],{"className":714},[616,506],[212,716,718],{"className":717,"style":612},[350,611],[212,719,454],{"className":720},[616,506],[11,722,723],{},"它统一了 KL、JS、全变差、卡方、Hellinger 等众多散度，具有非负性、联合凸性、变分对偶表示和数据处理不等式等核心性质，是信息论和生成模型理论中的基础工具。",[725,726,728],"h2",{"id":727},"_1-定义","1. 定义",[11,730,731,732,777,778,835,836,865,866,894,895,948],{},"设 ",[212,733,735,754],{"className":734,"translate":216},[215],[212,736,738],{"className":737},[220],[222,739,740],{"xmlns":224},[226,741,742,751],{},[229,743,744,746,749],{},[232,745,403],{},[307,747,748],{"separator":243},",",[232,750,410],{},[236,752,753],{"encoding":238},"P,Q",[212,755,757],{"className":756,"ariaHidden":243},[242],[212,758,760,764,767,771,774],{"className":759},[247],[212,761],{"className":762,"style":763},[251],"height:0.8778em;vertical-align:-0.1944em;",[212,765,403],{"className":766,"style":531},[256,257],[212,768,748],{"className":769},[770],"mpunct",[212,772],{"className":773,"style":603},[354],[212,775,410],{"className":776},[256,257]," 是同一个可测空间 ",[212,779,781,806],{"className":780,"translate":216},[215],[212,782,784],{"className":783},[220],[222,785,786],{"xmlns":224},[226,787,788,803],{},[229,789,790,792,796,798,801],{},[307,791,310],{"stretchy":309},[232,793,795],{"mathvariant":794},"script","X",[307,797,748],{"separator":243},[232,799,800],{"mathvariant":794},"A",[307,802,317],{"stretchy":309},[236,804,805],{"encoding":238},"(\\mathcal X,\\mathcal A)",[212,807,809],{"className":808,"ariaHidden":243},[242],[212,810,812,815,818,823,826,829,832],{"className":811},[247],[212,813],{"className":814,"style":336},[251],[212,816,310],{"className":817},[343],[212,819,795],{"className":820,"style":822},[256,821],"mathcal","margin-right:0.1464em;",[212,824,748],{"className":825},[770],[212,827],{"className":828,"style":603},[354],[212,830,800],{"className":831},[256,821],[212,833,317],{"className":834},[350]," 上的两个概率分布，且 ",[212,837,839,852],{"className":838,"translate":216},[215],[212,840,842],{"className":841},[220],[222,843,844],{"xmlns":224},[226,845,846,850],{},[229,847,848],{},[232,849,403],{},[236,851,403],{"encoding":238},[212,853,855],{"className":854,"ariaHidden":243},[242],[212,856,858,862],{"className":857},[247],[212,859],{"className":860,"style":861},[251],"height:0.6833em;",[212,863,403],{"className":864,"style":531},[256,257]," 关于 ",[212,867,869,882],{"className":868,"translate":216},[215],[212,870,872],{"className":871},[220],[222,873,874],{"xmlns":224},[226,875,876,880],{},[229,877,878],{},[232,879,410],{},[236,881,410],{"encoding":238},[212,883,885],{"className":884,"ariaHidden":243},[242],[212,886,888,891],{"className":887},[247],[212,889],{"className":890,"style":763},[251],[212,892,410],{"className":893},[256,257]," 绝对连续（即 ",[212,896,898,917],{"className":897,"translate":216},[215],[212,899,901],{"className":900},[220],[222,902,903],{"xmlns":224},[226,904,905,914],{},[229,906,907,909,912],{},[232,908,403],{},[307,910,911],{},"≪",[232,913,410],{},[236,915,916],{"encoding":238},"P\\ll Q",[212,918,920,939],{"className":919,"ariaHidden":243},[242],[212,921,923,927,930,933,936],{"className":922},[247],[212,924],{"className":925,"style":926},[251],"height:0.7224em;vertical-align:-0.0391em;",[212,928,403],{"className":929,"style":531},[256,257],[212,931],{"className":932,"style":355},[354],[212,934,911],{"className":935},[359],[212,937],{"className":938,"style":355},[354],[212,940,942,945],{"className":941},[247],[212,943],{"className":944,"style":763},[251],[212,946,410],{"className":947},[256,257],"），记",[212,950,952],{"className":951,"translate":216},[377],[212,953,955,999],{"className":954,"translate":216},[215],[212,956,958],{"className":957},[220],[222,959,960],{"xmlns":224,"display":386},[226,961,962,996],{},[229,963,964,967,969,972,974,976,990,992,994],{},[232,965,966],{},"t",[307,968,310],{"stretchy":309},[232,970,971],{},"x",[307,973,317],{"stretchy":309},[307,975,320],{},[435,977,978,984],{},[229,979,980,982],{},[232,981,441],{},[232,983,403],{},[229,985,986,988],{},[232,987,441],{},[232,989,410],{},[307,991,310],{"stretchy":309},[232,993,971],{},[307,995,317],{"stretchy":309},[236,997,998],{"encoding":238},"t(x)=\\frac{dP}{dQ}(x)",[212,1000,1002,1029],{"className":1001,"ariaHidden":243},[242],[212,1003,1005,1008,1011,1014,1017,1020,1023,1026],{"className":1004},[247],[212,1006],{"className":1007,"style":336},[251],[212,1009,966],{"className":1010},[256,257],[212,1012,310],{"className":1013},[343],[212,1015,971],{"className":1016},[256,257],[212,1018,317],{"className":1019},[350],[212,1021],{"className":1022,"style":355},[354],[212,1024,320],{"className":1025},[359],[212,1027],{"className":1028,"style":355},[354],[212,1030,1032,1036,1104,1107,1110],{"className":1031},[247],[212,1033],{"className":1034,"style":1035},[251],"height:2.2519em;vertical-align:-0.8804em;",[212,1037,1039,1042,1101],{"className":1038},[256],[212,1040],{"className":1041},[343,638],[212,1043,1045],{"className":1044},[435],[212,1046,1048,1093],{"className":1047},[482,483],[212,1049,1051,1090],{"className":1050},[487],[212,1052,1054,1068,1076],{"className":1053,"style":651},[491],[212,1055,1056,1059],{"style":654},[212,1057],{"className":1058,"style":658},[499],[212,1060,1062,1065],{"className":1061},[256],[212,1063,441],{"className":1064},[256,257],[212,1066,410],{"className":1067},[256,257],[212,1069,1070,1073],{"style":670},[212,1071],{"className":1072,"style":658},[499],[212,1074],{"className":1075,"style":678},[677],[212,1077,1078,1081],{"style":681},[212,1079],{"className":1080,"style":658},[499],[212,1082,1084,1087],{"className":1083},[256],[212,1085,441],{"className":1086},[256,257],[212,1088,403],{"className":1089,"style":531},[256,257],[212,1091,515],{"className":1092},[514],[212,1094,1096],{"className":1095},[487],[212,1097,1099],{"className":1098,"style":703},[491],[212,1100],{},[212,1102],{"className":1103},[350,638],[212,1105,310],{"className":1106},[343],[212,1108,971],{"className":1109},[256,257],[212,1111,317],{"className":1112},[350],[11,1114,1115,1116,1188],{},"为 Radon–Nikodym 导数（在离散情形就是概率质量之比，在密度存在时就是密度之比 ",[212,1117,1119,1151],{"className":1118,"translate":216},[215],[212,1120,1122],{"className":1121},[220],[222,1123,1124],{"xmlns":224},[226,1125,1126,1148],{},[229,1127,1128,1130,1132,1134,1136,1139,1142,1144,1146],{},[232,1129,11],{},[307,1131,310],{"stretchy":309},[232,1133,971],{},[307,1135,317],{"stretchy":309},[232,1137,1138],{"mathvariant":406},"\u002F",[232,1140,1141],{},"q",[307,1143,310],{"stretchy":309},[232,1145,971],{},[307,1147,317],{"stretchy":309},[236,1149,1150],{"encoding":238},"p(x)\u002Fq(x)",[212,1152,1154],{"className":1153,"ariaHidden":243},[242],[212,1155,1157,1160,1163,1166,1169,1172,1175,1179,1182,1185],{"className":1156},[247],[212,1158],{"className":1159,"style":336},[251],[212,1161,11],{"className":1162},[256,257],[212,1164,310],{"className":1165},[343],[212,1167,971],{"className":1168},[256,257],[212,1170,317],{"className":1171},[350],[212,1173,1138],{"className":1174},[256],[212,1176,1141],{"className":1177,"style":1178},[256,257],"margin-right:0.0359em;",[212,1180,310],{"className":1181},[343],[212,1183,971],{"className":1184},[256,257],[212,1186,317],{"className":1187},[350],"）。",[24,1190,1191,1427,1834,1866,2446],{},[11,1192,1193,1197,1198,1299,1300,1365,1366,865,1394,1422,1423,1426],{},[1194,1195,1196],"strong",{},"定义 1.1（f-散度）"," 给定一个凸函数 ",[212,1199,1201,1235],{"className":1200,"translate":216},[215],[212,1202,1204],{"className":1203},[220],[222,1205,1206],{"xmlns":224},[226,1207,1208,1232],{},[229,1209,1210,1212,1215,1217,1219,1221,1224,1226,1229],{},[232,1211,234],{},[307,1213,1214],{},":",[307,1216,427],{"stretchy":309},[312,1218,323],{},[307,1220,748],{"separator":243},[232,1222,1223],{"mathvariant":406},"∞",[307,1225,317],{"stretchy":309},[307,1227,1228],{},"→",[232,1230,1231],{"mathvariant":419},"R",[236,1233,1234],{"encoding":238},"f:[0,\\infty)\\to\\mathbb R",[212,1236,1238,1256,1289],{"className":1237,"ariaHidden":243},[242],[212,1239,1241,1244,1247,1250,1253],{"className":1240},[247],[212,1242],{"className":1243,"style":252},[251],[212,1245,234],{"className":1246,"style":258},[256,257],[212,1248],{"className":1249,"style":355},[354],[212,1251,1214],{"className":1252},[359],[212,1254],{"className":1255,"style":355},[354],[212,1257,1259,1262,1265,1268,1271,1274,1277,1280,1283,1286],{"className":1258},[247],[212,1260],{"className":1261,"style":336},[251],[212,1263,427],{"className":1264},[343],[212,1266,323],{"className":1267},[256],[212,1269,748],{"className":1270},[770],[212,1272],{"className":1273,"style":603},[354],[212,1275,1223],{"className":1276},[256],[212,1278,317],{"className":1279},[350],[212,1281],{"className":1282,"style":355},[354],[212,1284,1228],{"className":1285},[359],[212,1287],{"className":1288,"style":355},[354],[212,1290,1292,1296],{"className":1291},[247],[212,1293],{"className":1294,"style":1295},[251],"height:0.6889em;",[212,1297,1231],{"className":1298},[256,563],"，且满足 ",[212,1301,1303,1326],{"className":1302,"translate":216},[215],[212,1304,1306],{"className":1305},[220],[222,1307,1308],{"xmlns":224},[226,1309,1310,1324],{},[229,1311,1312,1314,1316,1318,1320,1322],{},[232,1313,234],{},[307,1315,310],{"stretchy":309},[312,1317,314],{},[307,1319,317],{"stretchy":309},[307,1321,320],{},[312,1323,323],{},[236,1325,326],{"encoding":238},[212,1327,1329,1356],{"className":1328,"ariaHidden":243},[242],[212,1330,1332,1335,1338,1341,1344,1347,1350,1353],{"className":1331},[247],[212,1333],{"className":1334,"style":336},[251],[212,1336,234],{"className":1337,"style":258},[256,257],[212,1339,310],{"className":1340},[343],[212,1342,314],{"className":1343},[256],[212,1345,317],{"className":1346},[350],[212,1348],{"className":1349,"style":355},[354],[212,1351,320],{"className":1352},[359],[212,1354],{"className":1355,"style":355},[354],[212,1357,1359,1362],{"className":1358},[247],[212,1360],{"className":1361,"style":369},[251],[212,1363,323],{"className":1364},[256],"，则 ",[212,1367,1369,1382],{"className":1368,"translate":216},[215],[212,1370,1372],{"className":1371},[220],[222,1373,1374],{"xmlns":224},[226,1375,1376,1380],{},[229,1377,1378],{},[232,1379,403],{},[236,1381,403],{"encoding":238},[212,1383,1385],{"className":1384,"ariaHidden":243},[242],[212,1386,1388,1391],{"className":1387},[247],[212,1389],{"className":1390,"style":861},[251],[212,1392,403],{"className":1393,"style":531},[256,257],[212,1395,1397,1410],{"className":1396,"translate":216},[215],[212,1398,1400],{"className":1399},[220],[222,1401,1402],{"xmlns":224},[226,1403,1404,1408],{},[229,1405,1406],{},[232,1407,410],{},[236,1409,410],{"encoding":238},[212,1411,1413],{"className":1412,"ariaHidden":243},[242],[212,1414,1416,1419],{"className":1415},[247],[212,1417],{"className":1418,"style":763},[251],[212,1420,410],{"className":1421},[256,257]," 的 ",[1194,1424,1425],{},"f-散度"," 定义为",[212,1428,1430],{"className":1429,"translate":216},[377],[212,1431,1433,1540],{"className":1432,"translate":216},[215],[212,1434,1436],{"className":1435},[220],[222,1437,1438],{"xmlns":224,"display":386},[226,1439,1440,1537],{},[1441,1442,1446],"mtable",{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},"0.25em","right 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",[212,1838,1840,1853],{"className":1839,"translate":216},[215],[212,1841,1843],{"className":1842},[220],[222,1844,1845],{"xmlns":224},[226,1846,1847,1851],{},[229,1848,1849],{},[232,1850,410],{},[236,1852,410],{"encoding":238},[212,1854,1856],{"className":1855,"ariaHidden":243},[242],[212,1857,1859,1862],{"className":1858},[247],[212,1860],{"className":1861,"style":763},[251],[212,1863,410],{"className":1864},[256,257]," 的期望形式",[212,1867,1869],{"className":1868,"translate":216},[377],[212,1870,1872,2006],{"className":1871,"translate":216},[215],[212,1873,1875],{"className":1874},[220],[222,1876,1877],{"xmlns":224,"display":386},[226,1878,1879,2003],{},[1441,1880,1881,1953],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,1882,1883,1905],{},[1450,1884,1885],{},[1453,1886,1887],{"scriptlevel":323,"displaystyle":243},[229,1888,1889,1895,1897,1899,1901,1903],{},[392,1890,1891,1893],{},[232,1892,396],{},[232,1894,234],{},[307,1896,310],{"stretchy":309},[232,1898,403],{},[232,1900,407],{"mathvariant":406},[232,1902,410],{},[307,1904,317],{"stretchy":309},[1450,1906,1907],{},[1453,1908,1909],{"scriptlevel":323,"displaystyle":243},[229,1910,1911,1913,1915,1921,1923],{},[229,1912],{},[307,1914,320],{},[392,1916,1917,1919],{},[232,1918,420],{"mathvariant":419},[232,1920,410],{},[1495,1922,1502],{},[229,1924,1925,1927,1929,1931,1951],{},[307,1926,427],{"fence":243},[232,1928,234],{},[1495,1930,1502],{},[229,1932,1933,1935,1949],{},[307,1934,310],{"fence":243},[435,1936,1937,1943],{},[229,1938,1939,1941],{},[232,1940,441],{},[232,1942,403],{},[229,1944,1945,1947],{},[232,1946,441],{},[232,1948,410],{},[307,1950,317],{"fence":243},[307,1952,454],{"fence":243},[1447,1954,1955,1961],{},[1450,1956,1957],{},[1453,1958,1959],{"scriptlevel":323,"displaystyle":243},[229,1960],{},[1450,1962,1963],{},[1453,1964,1965],{"scriptlevel":323,"displaystyle":243},[229,1966,1967,1969,1971,1973,1975,1977,1997,1999,2001],{},[229,1968],{},[307,1970,320],{},[307,1972,1485],{},[232,1974,234],{},[1495,1976,1502],{},[229,1978,1979,1981,1995],{},[307,1980,310],{"fence":243},[435,1982,1983,1989],{},[229,1984,1985,1987],{},[232,1986,441],{},[232,1988,403],{},[229,1990,1991,1993],{},[232,1992,441],{},[232,1994,410],{},[307,1996,317],{"fence":243},[232,1998,441],{},[232,2000,410],{},[307,2002,748],{"separator":243},[236,2004,2005],{"encoding":238},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\mathbb E_Q\\!\\left[\nf\\!\\left(\\frac{dP}{dQ}\\right)\\right]\\\\\n&=\\int f\\!\\left(\\frac{dP}{dQ}\\right)dQ,\n\\end{aligned}",[212,2007,2009],{"className":2008,"ariaHidden":243},[242],[212,2010,2012,2016],{"className":2011},[247],[212,2013],{"className":2014,"style":2015},[251],"height:5.1001em;vertical-align:-2.3em;",[212,2017,2019],{"className":2018},[256],[212,2020,2022,2120],{"className":2021},[1441],[212,2023,2025],{"className":2024},[1558],[212,2026,2028,2111],{"className":2027},[482,483],[212,2029,2031,2108],{"className":2030},[487],[212,2032,2035,2099],{"className":2033,"style":2034},[491],"height:2.8em;",[212,2036,2038,2041],{"style":2037},"top:-4.8em;",[212,2039],{"className":2040,"style":1575},[499],[212,2042,2044,2084,2087,2090,2093,2096],{"className":2043},[256],[212,2045,2047,2050],{"className":2046},[256],[212,2048,396],{"className":2049,"style":474},[256,257],[212,2051,2053],{"className":2052},[478],[212,2054,2056,2076],{"className":2055},[482,483],[212,2057,2059,2073],{"className":2058},[487],[212,2060,2062],{"className":2061,"style":492},[491],[212,2063,2064,2067],{"style":495},[212,2065],{"className":2066,"style":500},[499],[212,2068,2070],{"className":2069},[504,505,506,507],[212,2071,234],{"className":2072,"style":258},[256,257,507],[212,2074,515],{"className":2075},[514],[212,2077,2079],{"className":2078},[487],[212,2080,2082],{"className":2081,"style":522},[491],[212,2083],{},[212,2085,310],{"className":2086},[343],[212,2088,403],{"className":2089,"style":531},[256,257],[212,2091,407],{"className":2092},[256],[212,2094,410],{"className":2095},[256,257],[212,2097,317],{"className":2098},[350],[212,2100,2102,2105],{"style":2101},"top:-2.1em;",[212,2103],{"className":2104,"style":1575},[499],[212,2106],{"className":2107},[256],[212,2109,515],{"className":2110},[514],[212,2112,2114],{"className":2113},[487],[212,2115,2118],{"className":2116,"style":2117},[491],"height:2.3em;",[212,2119],{},[212,2121,2123],{"className":2122},[1649],[212,2124,2126,2438],{"className":2125},[482,483],[212,2127,2129,2435],{"className":2128},[487],[212,2130,2132,2305],{"className":2131,"style":2034},[491],[212,2133,2134,2137],{"style":2037},[212,2135],{"className":2136,"style":1575},[499],[212,2138,2140,2143,2146,2149,2152,2192,2195,2198],{"className":2139},[256],[212,2141],{"className":2142},[256],[212,2144],{"className":2145,"style":355},[354],[212,2147,320],{"className":2148},[359],[212,2150],{"className":2151,"style":355},[354],[212,2153,2155,2158],{"className":2154},[256],[212,2156,420],{"className":2157},[256,563],[212,2159,2161],{"className":2160},[478],[212,2162,2164,2184],{"className":2163},[482,483],[212,2165,2167,2181],{"className":2166},[487],[212,2168,2170],{"className":2169,"style":576},[491],[212,2171,2172,2175],{"style":579},[212,2173],{"className":2174,"style":500},[499],[212,2176,2178],{"className":2177},[504,505,506,507],[212,2179,410],{"className":2180},[256,257,507],[212,2182,515],{"className":2183},[514],[212,2185,2187],{"className":2186},[487],[212,2188,2190],{"className":2189,"style":522},[491],[212,2191],{},[212,2193],{"className":2194,"style":1710},[354],[212,2196],{"className":2197,"style":603},[354],[212,2199,2201,2207,2210,2213,2216,2299],{"className":2200},[607],[212,2202,2204],{"className":2203,"style":612},[343,611],[212,2205,427],{"className":2206},[616,506],[212,2208,234],{"className":2209,"style":258},[256,257],[212,2211],{"className":2212,"style":1710},[354],[212,2214],{"className":2215,"style":603},[354],[212,2217,2219,2225,2293],{"className":2218},[607],[212,2220,2222],{"className":2221,"style":612},[343,611],[212,2223,310],{"className":2224},[616,506],[212,2226,2228,2231,2290],{"className":2227},[256],[212,2229],{"className":2230},[343,638],[212,2232,2234],{"className":2233},[435],[212,2235,2237,2282],{"className":2236},[482,483],[212,2238,2240,2279],{"className":2239},[487],[212,2241,2243,2257,2265],{"className":2242,"style":651},[491],[212,2244,2245,2248],{"style":654},[212,2246],{"className":2247,"style":658},[499],[212,2249,2251,2254],{"className":2250},[256],[212,2252,441],{"className":2253},[256,257],[212,2255,410],{"className":2256},[256,257],[212,2258,2259,2262],{"style":670},[212,2260],{"className":2261,"style":658},[499],[212,2263],{"className":2264,"style":678},[677],[212,2266,2267,2270],{"style":681},[212,2268],{"className":2269,"style":658},[499],[212,2271,2273,2276],{"className":2272},[256],[212,2274,441],{"className":2275},[256,257],[212,2277,403],{"className":2278,"style":531},[256,257],[212,2280,515],{"className":2281},[514],[212,2283,2285],{"className":2284},[487],[212,2286,2288],{"className":2287,"style":703},[491],[212,2289],{},[212,2291],{"className":2292},[350,638],[212,2294,2296],{"className":2295,"style":612},[350,611],[212,2297,317],{"className":2298},[616,506],[212,2300,2302],{"className":2301,"style":612},[350,611],[212,2303,454],{"className":2304},[616,506],[212,2306,2307,2310],{"style":2101},[212,2308],{"className":2309,"style":1575},[499],[212,2311,2313,2316,2319,2322,2325,2328,2331,2334,2337,2340,2423,2426,2429,2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",[212,2450,2452,2465],{"className":2451,"translate":216},[215],[212,2453,2455],{"className":2454},[220],[222,2456,2457],{"xmlns":224},[226,2458,2459,2463],{},[229,2460,2461],{},[232,2462,1141],{},[236,2464,1141],{"encoding":238},[212,2466,2468],{"className":2467,"ariaHidden":243},[242],[212,2469,2471,2475],{"className":2470},[247],[212,2472],{"className":2473,"style":2474},[251],"height:0.625em;vertical-align:-0.1944em;",[212,2476,1141],{"className":2477,"style":1178},[256,257]," 是 ",[212,2480,2482,2495],{"className":2481,"translate":216},[215],[212,2483,2485],{"className":2484},[220],[222,2486,2487],{"xmlns":224},[226,2488,2489,2493],{},[229,2490,2491],{},[232,2492,410],{},[236,2494,410],{"encoding":238},[212,2496,2498],{"className":2497,"ariaHidden":243},[242],[212,2499,2501,2504],{"className":2500},[247],[212,2502],{"className":2503,"style":763},[251],[212,2505,410],{"className":2506},[256,257]," 的密度。",[2509,2510,2512],"h3",{"id":2511},"_11-不依赖参考测度","1.1 不依赖参考测度",[11,2514,2515,2516,2547,2548,2578,2579,2607,2608,2636,2637,2805,2806,2943,2944,3081,3082,3146,3147,3352],{},"上面的定义里出现了「密度」，这会让读者误以为它依赖 Lebesgue 测度。其实 f-散度只依赖两个分布本身。取任一 ",[212,2517,2519,2534],{"className":2518,"translate":216},[215],[212,2520,2522],{"className":2521},[220],[222,2523,2524],{"xmlns":224},[226,2525,2526,2531],{},[229,2527,2528],{},[232,2529,2530],{},"σ",[236,2532,2533],{"encoding":238},"\\sigma",[212,2535,2537],{"className":2536,"ariaHidden":243},[242],[212,2538,2540,2544],{"className":2539},[247],[212,2541],{"className":2542,"style":2543},[251],"height:0.4306em;",[212,2545,2530],{"className":2546,"style":1178},[256,257],"-有限测度 ",[212,2549,2551,2566],{"className":2550,"translate":216},[215],[212,2552,2554],{"className":2553},[220],[222,2555,2556],{"xmlns":224},[226,2557,2558,2563],{},[229,2559,2560],{},[232,2561,2562],{},"μ",[236,2564,2565],{"encoding":238},"\\mu",[212,2567,2569],{"className":2568,"ariaHidden":243},[242],[212,2570,2572,2575],{"className":2571},[247],[212,2573],{"className":2574,"style":2474},[251],[212,2576,2562],{"className":2577},[256,257]," 同时控制 ",[212,2580,2582,2595],{"className":2581,"translate":216},[215],[212,2583,2585],{"className":2584},[220],[222,2586,2587],{"xmlns":224},[226,2588,2589,2593],{},[229,2590,2591],{},[232,2592,403],{},[236,2594,403],{"encoding":238},[212,2596,2598],{"className":2597,"ariaHidden":243},[242],[212,2599,2601,2604],{"className":2600},[247],[212,2602],{"className":2603,"style":861},[251],[212,2605,403],{"className":2606,"style":531},[256,257]," 与 ",[212,2609,2611,2624],{"className":2610,"translate":216},[215],[212,2612,2614],{"className":2613},[220],[222,2615,2616],{"xmlns":224},[226,2617,2618,2622],{},[229,2619,2620],{},[232,2621,410],{},[236,2623,410],{"encoding":238},[212,2625,2627],{"className":2626,"ariaHidden":243},[242],[212,2628,2630,2633],{"className":2629},[247],[212,2631],{"className":2632,"style":763},[251],[212,2634,410],{"className":2635},[256,257],"（例如 ",[212,2638,2640,2676],{"className":2639,"translate":216},[215],[212,2641,2643],{"className":2642},[220],[222,2644,2645],{"xmlns":224},[226,2646,2647,2673],{},[229,2648,2649,2651,2653,2662,2664,2666,2669,2671],{},[232,2650,2562],{},[307,2652,320],{},[1453,2654,2655],{"scriptlevel":323,"displaystyle":309},[435,2656,2657,2659],{},[312,2658,314],{},[312,2660,2661],{},"2",[307,2663,310],{"stretchy":309},[232,2665,403],{},[307,2667,2668],{},"+",[232,2670,410],{},[307,2672,317],{"stretchy":309},[236,2674,2675],{"encoding":238},"\\mu=\\tfrac12(P+Q)",[212,2677,2679,2697,2793],{"className":2678,"ariaHidden":243},[242],[212,2680,2682,2685,2688,2691,2694],{"className":2681},[247],[212,2683],{"className":2684,"style":2474},[251],[212,2686,2562],{"className":2687},[256,257],[212,2689],{"className":2690,"style":355},[354],[212,2692,320],{"className":2693},[359],[212,2695],{"className":2696,"style":355},[354],[212,2698,2700,2704,2776,2779,2782,2786,2790],{"className":2699},[247],[212,2701],{"className":2702,"style":2703},[251],"height:1.1901em;vertical-align:-0.345em;",[212,2705,2707,2710,2773],{"className":2706},[256],[212,2708],{"className":2709},[343,638],[212,2711,2713],{"className":2712},[435],[212,2714,2716,2764],{"className":2715},[482,483],[212,2717,2719,2761],{"className":2718},[487],[212,2720,2723,2738,2746],{"className":2721,"style":2722},[491],"height:0.8451em;",[212,2724,2726,2729],{"style":2725},"top:-2.655em;",[212,2727],{"className":2728,"style":658},[499],[212,2730,2732],{"className":2731},[504,505,506,507],[212,2733,2735],{"className":2734},[256,507],[212,2736,2661],{"className":2737},[256,507],[212,2739,2740,2743],{"style":670},[212,2741],{"className":2742,"style":658},[499],[212,2744],{"className":2745,"style":678},[677],[212,2747,2749,2752],{"style":2748},"top:-3.394em;",[212,2750],{"className":2751,"style":658},[499],[212,2753,2755],{"className":2754},[504,505,506,507],[212,2756,2758],{"className":2757},[256,507],[212,2759,314],{"className":2760},[256,507],[212,2762,515],{"className":2763},[514],[212,2765,2767],{"className":2766},[487],[212,2768,2771],{"className":2769,"style":2770},[491],"height:0.345em;",[212,2772],{},[212,2774],{"className":2775},[350,638],[212,2777,310],{"className":2778},[343],[212,2780,403],{"className":2781,"style":531},[256,257],[212,2783],{"className":2784,"style":2785},[354],"margin-right:0.2222em;",[212,2787,2668],{"className":2788},[2789],"mbin",[212,2791],{"className":2792,"style":2785},[354],[212,2794,2796,2799,2802],{"className":2795},[247],[212,2797],{"className":2798,"style":336},[251],[212,2800,410],{"className":2801},[256,257],[212,2803,317],{"className":2804},[350],"），令 ",[212,2807,2809,2839],{"className":2808,"translate":216},[215],[212,2810,2812],{"className":2811},[220],[222,2813,2814],{"xmlns":224},[226,2815,2816,2836],{},[229,2817,2818,2820,2822],{},[232,2819,11],{},[307,2821,320],{},[435,2823,2824,2830],{},[229,2825,2826,2828],{},[232,2827,441],{},[232,2829,403],{},[229,2831,2832,2834],{},[232,2833,441],{},[232,2835,2562],{},[236,2837,2838],{"encoding":238},"p=\\frac{dP}{d\\mu}",[212,2840,2842,2860],{"className":2841,"ariaHidden":243},[242],[212,2843,2845,2848,2851,2854,2857],{"className":2844},[247],[212,2846],{"className":2847,"style":2474},[251],[212,2849,11],{"className":2850},[256,257],[212,2852],{"className":2853,"style":355},[354],[212,2855,320],{"className":2856},[359],[212,2858],{"className":2859,"style":355},[354],[212,2861,2863,2867],{"className":2862},[247],[212,2864],{"className":2865,"style":2866},[251],"height:1.3612em;vertical-align:-0.4811em;",[212,2868,2870,2873,2940],{"className":2869},[256],[212,2871],{"className":2872},[343,638],[212,2874,2876],{"className":2875},[435],[212,2877,2879,2931],{"className":2878},[482,483],[212,2880,2882,2928],{"className":2881},[487],[212,2883,2886,2903,2911],{"className":2884,"style":2885},[491],"height:0.8801em;",[212,2887,2888,2891],{"style":2725},[212,2889],{"className":2890,"style":658},[499],[212,2892,2894],{"className":2893},[504,505,506,507],[212,2895,2897,2900],{"className":2896},[256,507],[212,2898,441],{"className":2899},[256,257,507],[212,2901,2562],{"className":2902},[256,257,507],[212,2904,2905,2908],{"style":670},[212,2906],{"className":2907,"style":658},[499],[212,2909],{"className":2910,"style":678},[677],[212,2912,2913,2916],{"style":2748},[212,2914],{"className":2915,"style":658},[499],[212,2917,2919],{"className":2918},[504,505,506,507],[212,2920,2922,2925],{"className":2921},[256,507],[212,2923,441],{"className":2924},[256,257,507],[212,2926,403],{"className":2927,"style":531},[256,257,507],[212,2929,515],{"className":2930},[514],[212,2932,2934],{"className":2933},[487],[212,2935,2938],{"className":2936,"style":2937},[491],"height:0.4811em;",[212,2939],{},[212,2941],{"className":2942},[350,638],"，",[212,2945,2947,2977],{"className":2946,"translate":216},[215],[212,2948,2950],{"className":2949},[220],[222,2951,2952],{"xmlns":224},[226,2953,2954,2974],{},[229,2955,2956,2958,2960],{},[232,2957,1141],{},[307,2959,320],{},[435,2961,2962,2968],{},[229,2963,2964,2966],{},[232,2965,441],{},[232,2967,410],{},[229,2969,2970,2972],{},[232,2971,441],{},[232,2973,2562],{},[236,2975,2976],{"encoding":238},"q=\\frac{dQ}{d\\mu}",[212,2978,2980,2998],{"className":2979,"ariaHidden":243},[242],[212,2981,2983,2986,2989,2992,2995],{"className":2982},[247],[212,2984],{"className":2985,"style":2474},[251],[212,2987,1141],{"className":2988,"style":1178},[256,257],[212,2990],{"className":2991,"style":355},[354],[212,2993,320],{"className":2994},[359],[212,2996],{"className":2997,"style":355},[354],[212,2999,3001,3005],{"className":3000},[247],[212,3002],{"className":3003,"style":3004},[251],"height:1.4133em;vertical-align:-0.4811em;",[212,3006,3008,3011,3078],{"className":3007},[256],[212,3009],{"className":3010},[343,638],[212,3012,3014],{"className":3013},[435],[212,3015,3017,3070],{"className":3016},[482,483],[212,3018,3020,3067],{"className":3019},[487],[212,3021,3024,3041,3049],{"className":3022,"style":3023},[491],"height:0.9322em;",[212,3025,3026,3029],{"style":2725},[212,3027],{"className":3028,"style":658},[499],[212,3030,3032],{"className":3031},[504,505,506,507],[212,3033,3035,3038],{"className":3034},[256,507],[212,3036,441],{"className":3037},[256,257,507],[212,3039,2562],{"className":3040},[256,257,507],[212,3042,3043,3046],{"style":670},[212,3044],{"className":3045,"style":658},[499],[212,3047],{"className":3048,"style":678},[677],[212,3050,3052,3055],{"style":3051},"top:-3.4461em;",[212,3053],{"className":3054,"style":658},[499],[212,3056,3058],{"className":3057},[504,505,506,507],[212,3059,3061,3064],{"className":3060},[256,507],[212,3062,441],{"className":3063},[256,257,507],[212,3065,410],{"className":3066},[256,257,507],[212,3068,515],{"className":3069},[514],[212,3071,3073],{"className":3072},[487],[212,3074,3076],{"className":3075,"style":2937},[491],[212,3077],{},[212,3079],{"className":3080},[350,638],"。在集合 ",[212,3083,3085,3110],{"className":3084,"translate":216},[215],[212,3086,3088],{"className":3087},[220],[222,3089,3090],{"xmlns":224},[226,3091,3092,3107],{},[229,3093,3094,3097,3099,3102,3104],{},[307,3095,3096],{"stretchy":309},"{",[232,3098,1141],{},[307,3100,3101],{},">",[312,3103,323],{},[307,3105,3106],{"stretchy":309},"}",[236,3108,3109],{"encoding":238},"\\{q>0\\}",[212,3111,3113,3134],{"className":3112,"ariaHidden":243},[242],[212,3114,3116,3119,3122,3125,3128,3131],{"className":3115},[247],[212,3117],{"className":3118,"style":336},[251],[212,3120,3096],{"className":3121},[343],[212,3123,1141],{"className":3124,"style":1178},[256,257],[212,3126],{"className":3127,"style":355},[354],[212,3129,3101],{"className":3130},[359],[212,3132],{"className":3133,"style":355},[354],[212,3135,3137,3140,3143],{"className":3136},[247],[212,3138],{"className":3139,"style":336},[251],[212,3141,323],{"className":3142},[256],[212,3144,3106],{"className":3145},[350]," 上有 ",[212,3148,3150,3184],{"className":3149,"translate":216},[215],[212,3151,3153],{"className":3152},[220],[222,3154,3155],{"xmlns":224},[226,3156,3157,3181],{},[229,3158,3159,3173,3175],{},[435,3160,3161,3167],{},[229,3162,3163,3165],{},[232,3164,441],{},[232,3166,403],{},[229,3168,3169,3171],{},[232,3170,441],{},[232,3172,410],{},[307,3174,320],{},[435,3176,3177,3179],{},[232,3178,11],{},[232,3180,1141],{},[236,3182,3183],{"encoding":238},"\\frac{dP}{dQ}=\\frac{p}{q}",[212,3185,3187,3276],{"className":3186,"ariaHidden":243},[242],[212,3188,3190,3193,3267,3270,3273],{"className":3189},[247],[212,3191],{"className":3192,"style":2866},[251],[212,3194,3196,3199,3264],{"className":3195},[256],[212,3197],{"className":3198},[343,638],[212,3200,3202],{"className":3201},[435],[212,3203,3205,3256],{"className":3204},[482,483],[212,3206,3208,3253],{"className":3207},[487],[212,3209,3211,3228,3236],{"className":3210,"style":2885},[491],[212,3212,3213,3216],{"style":2725},[212,3214],{"className":3215,"style":658},[499],[212,3217,3219],{"className":3218},[504,505,506,507],[212,3220,3222,3225],{"className":3221},[256,507],[212,3223,441],{"className":3224},[256,257,507],[212,3226,410],{"className":3227},[256,257,507],[212,3229,3230,3233],{"style":670},[212,3231],{"className":3232,"style":658},[499],[212,3234],{"className":3235,"style":678},[677],[212,3237,3238,3241],{"style":2748},[212,3239],{"className":3240,"style":658},[499],[212,3242,3244],{"className":3243},[504,505,506,507],[212,3245,3247,3250],{"className":3246},[256,507],[212,3248,441],{"className":3249},[256,257,507],[212,3251,403],{"className":3252,"style":531},[256,257,507],[212,3254,515],{"className":3255},[514],[212,3257,3259],{"className":3258},[487],[212,3260,3262],{"className":3261,"style":2937},[491],[212,3263],{},[212,3265],{"className":3266},[350,638],[212,3268],{"className":3269,"style":355},[354],[212,3271,320],{"className":3272},[359],[212,3274],{"className":3275,"style":355},[354],[212,3277,3279,3283],{"className":3278},[247],[212,3280],{"className":3281,"style":3282},[251],"height:1.2286em;vertical-align:-0.4811em;",[212,3284,3286,3289,3349],{"className":3285},[256],[212,3287],{"className":3288},[343,638],[212,3290,3292],{"className":3291},[435],[212,3293,3295,3341],{"className":3294},[482,483],[212,3296,3298,3338],{"className":3297},[487],[212,3299,3302,3316,3324],{"className":3300,"style":3301},[491],"height:0.7475em;",[212,3303,3304,3307],{"style":2725},[212,3305],{"className":3306,"style":658},[499],[212,3308,3310],{"className":3309},[504,505,506,507],[212,3311,3313],{"className":3312},[256,507],[212,3314,1141],{"className":3315,"style":1178},[256,257,507],[212,3317,3318,3321],{"style":670},[212,3319],{"className":3320,"style":658},[499],[212,3322],{"className":3323,"style":678},[677],[212,3325,3326,3329],{"style":3051},[212,3327],{"className":3328,"style":658},[499],[212,3330,3332],{"className":3331},[504,505,506,507],[212,3333,3335],{"className":3334},[256,507],[212,3336,11],{"className":3337},[256,257,507],[212,3339,515],{"className":3340},[514],[212,3342,3344],{"className":3343},[487],[212,3345,3347],{"className":3346,"style":2937},[491],[212,3348],{},[212,3350],{"className":3351},[350,638],"，于是",[212,3354,3356],{"className":3355,"translate":216},[377],[212,3357,3359,3509],{"className":3358,"translate":216},[215],[212,3360,3362],{"className":3361},[220],[222,3363,3364],{"xmlns":224,"display":386},[226,3365,3366,3506],{},[1441,3367,3368,3442],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,3369,3370,3392],{},[1450,3371,3372],{},[1453,3373,3374],{"scriptlevel":323,"displaystyle":243},[229,3375,3376,3382,3384,3386,3388,3390],{},[392,3377,3378,3380],{},[232,3379,396],{},[232,3381,234],{},[307,3383,310],{"stretchy":309},[232,3385,403],{},[232,3387,407],{"mathvariant":406},[232,3389,410],{},[307,3391,317],{"stretchy":309},[1450,3393,3394],{},[1453,3395,3396],{"scriptlevel":323,"displaystyle":243},[229,3397,3398,3400,3402,3418,3420,3422,3434,3436,3438,3440],{},[229,3399],{},[307,3401,320],{},[392,3403,3404,3406],{},[307,3405,1485],{},[229,3407,3408,3410,3412,3414,3416],{},[307,3409,3096],{"stretchy":309},[232,3411,1141],{},[307,3413,3101],{},[312,3415,323],{},[307,3417,3106],{"stretchy":309},[232,3419,234],{},[1495,3421,1502],{},[229,3423,3424,3426,3432],{},[307,3425,310],{"fence":243},[435,3427,3428,3430],{},[232,3429,11],{},[232,3431,1141],{},[307,3433,317],{"fence":243},[232,3435,1141],{},[1495,3437,1497],{},[232,3439,441],{},[232,3441,2562],{},[1447,3443,3444,3450],{},[1450,3445,3446],{},[1453,3447,3448],{"scriptlevel":323,"displaystyle":243},[229,3449],{},[1450,3451,3452],{},[1453,3453,3454],{"scriptlevel":323,"displaystyle":243},[229,3455,3456,3458,3461,3463,3479,3481,3483,3495,3498,3500,3502,3504],{},[229,3457],{},[354,3459],{"width":3460},"2em",[307,3462,2668],{},[392,3464,3465,3467],{},[307,3466,1485],{},[229,3468,3469,3471,3473,3475,3477],{},[307,3470,3096],{"stretchy":309},[232,3472,1141],{},[307,3474,320],{},[312,3476,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0\\,d\\mu\n\\end{aligned}",[212,3510,3512],{"className":3511,"ariaHidden":243},[242],[212,3513,3515,3519],{"className":3514},[247],[212,3516],{"className":3517,"style":3518},[251],"height:5.2839em;vertical-align:-2.392em;",[212,3520,3522],{"className":3521},[256],[212,3523,3525,3623],{"className":3524},[1441],[212,3526,3528],{"className":3527},[1558],[212,3529,3531,3614],{"className":3530},[482,483],[212,3532,3534,3611],{"className":3533},[487],[212,3535,3538,3602],{"className":3536,"style":3537},[491],"height:2.892em;",[212,3539,3541,3544],{"style":3540},"top:-4.892em;",[212,3542],{"className":3543,"style":1575},[499],[212,3545,3547,3587,3590,3593,3596,3599],{"className":3546},[256],[212,3548,3550,3553],{"className":3549},[256],[212,3551,396],{"className":3552,"style":474},[256,257],[212,3554,3556],{"className":3555},[478],[212,3557,3559,3579],{"className":3558},[482,483],[212,3560,3562,3576],{"className":3561},[487],[212,3563,3565],{"className":3564,"style":492},[491],[212,3566,3567,3570],{"style":495},[212,3568],{"className":3569,"style":500},[499],[212,3571,3573],{"className":3572},[504,505,506,507],[212,3574,234],{"className":3575,"style":258},[256,257,507],[212,3577,515],{"className":3578},[514],[212,3580,3582],{"className":3581},[487],[212,3583,3585],{"className":3584,"style":522},[491],[212,3586],{},[212,3588,310],{"className":3589},[343],[212,3591,403],{"className":3592,"style":531},[256,257],[212,3594,407],{"className":3595},[256],[212,3597,410],{"className":3598},[256,257],[212,3600,317],{"className":3601},[350],[212,3603,3605,3608],{"style":3604},"top:-2.145em;",[212,3606],{"className":3607,"style":1575},[499],[212,3609],{"className":3610},[256],[212,3612,515],{"className":3613},[514],[212,3615,3617],{"className":3616},[487],[212,3618,3621],{"className":3619,"style":3620},[491],"height:2.392em;",[212,3622],{},[212,3624,3626],{"className":3625},[1649],[212,3627,3629,4012],{"className":3628},[482,483],[212,3630,3632,4009],{"className":3631},[487],[212,3633,3635,3818],{"className":3634,"style":3537},[491],[212,3636,3637,3640],{"style":3540},[212,3638],{"className":3639,"style":1575},[499],[212,3641,3643,3646,3649,3652,3655,3713,3716,3719,3722,3725,3803,3806,3809,3812,3815],{"className":3642},[256],[212,3644],{"className":3645},[256],[212,3647],{"className":3648,"style":355},[354],[212,3650,320],{"className":3651},[359],[212,3653],{"className":3654,"style":355},[354],[212,3656,3658,3661],{"className":3657},[1682],[212,3659,1485],{"className":3660,"style":1685},[1682,1683,1684],[212,3662,3664],{"className":3663},[478],[212,3665,3667,3704],{"className":3666},[482,483],[212,3668,3670,3701],{"className":3669},[487],[212,3671,3674],{"className":3672,"style":3673},[491],"height:-0.3869em;",[212,3675,3677,3680],{"style":3676},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[212,3678],{"className":3679,"style":500},[499],[212,3681,3683],{"className":3682},[504,505,506,507],[212,3684,3686,3689,3692,3695,3698],{"className":3685},[256,507],[212,3687,3096],{"className":3688},[343,507],[212,3690,1141],{"className":3691,"style":1178},[256,257,507],[212,3693,3101],{"className":3694},[359,507],[212,3696,323],{"className":3697},[256,507],[212,3699,3106],{"className":3700},[350,507],[212,3702,515],{"className":3703},[514],[212,3705,3707],{"className":3706},[487],[212,3708,3711],{"className":3709,"style":3710},[491],"height:1.0869em;",[212,3712],{},[212,3714],{"className":3715,"style":603},[354],[212,3717,234],{"className":3718,"style":258},[256,257],[212,3720],{"className":3721,"style":1710},[354],[212,3723],{"className":3724,"style":603},[354],[212,3726,3728,3734,3797],{"className":3727},[607],[212,3729,3731],{"className":3730,"style":612},[343,611],[212,3732,310],{"className":3733},[616,506],[212,3735,3737,3740,3794],{"className":3736},[256],[212,3738],{"className":3739},[343,638],[212,3741,3743],{"className":3742},[435],[212,3744,3746,3786],{"className":3745},[482,483],[212,3747,3749,3783],{"className":3748},[487],[212,3750,3753,3764,3772],{"className":3751,"style":3752},[491],"height:1.1076em;",[212,3754,3755,3758],{"style":654},[212,3756],{"className":3757,"style":658},[499],[212,3759,3761],{"className":3760},[256],[212,3762,1141],{"className":3763,"style":1178},[256,257],[212,3765,3766,3769],{"style":670},[212,3767],{"className":3768,"style":658},[499],[212,3770],{"className":3771,"style":678},[677],[212,3773,3774,3777],{"style":681},[212,3775],{"className":3776,"style":658},[499],[212,3778,3780],{"className":3779},[256],[212,3781,11],{"className":3782},[256,257],[212,3784,515],{"className":3785},[514],[212,3787,3789],{"className":3788},[487],[212,3790,3792],{"className":3791,"style":703},[491],[212,3793],{},[212,3795],{"className":3796},[350,638],[212,3798,3800],{"className":3799,"style":612},[350,611],[212,3801,317],{"className":3802},[616,506],[212,3804],{"className":3805,"style":603},[354],[212,3807,1141],{"className":3808,"style":1178},[256,257],[212,3810],{"className":3811,"style":603},[354],[2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",[212,4201,4203,4221],{"className":4202,"translate":216},[215],[212,4204,4206],{"className":4205},[220],[222,4207,4208],{"xmlns":224},[226,4209,4210,4218],{},[229,4211,4212],{},[392,4213,4214,4216],{},[232,4215,396],{},[232,4217,234],{},[236,4219,4220],{"encoding":238},"D_f",[212,4222,4224],{"className":4223,"ariaHidden":243},[242],[212,4225,4227,4231],{"className":4226},[247],[212,4228],{"className":4229,"style":4230},[251],"height:0.9694em;vertical-align:-0.2861em;",[212,4232,4234,4237],{"className":4233},[256],[212,4235,396],{"className":4236,"style":474},[256,257],[212,4238,4240],{"className":4239},[478],[212,4241,4243,4263],{"className":4242},[482,483],[212,4244,4246,4260],{"className":4245},[487],[212,4247,4249],{"className":4248,"style":492},[491],[212,4250,4251,4254],{"style":495},[212,4252],{"className":4253,"style":500},[499],[212,4255,4257],{"className":4256},[504,505,506,507],[212,4258,234],{"className":4259,"style":258},[256,257,507],[212,4261,515],{"className":4262},[514],[212,4264,4266],{"className":4265},[487],[212,4267,4269],{"className":4268,"style":522},[491],[212,4270],{}," 是否有限。例如对 KL 的 ",[212,4273,4275,4307],{"className":4274,"translate":216},[215],[212,4276,4278],{"className":4277},[220],[222,4279,4280],{"xmlns":224},[226,4281,4282,4304],{},[229,4283,4284,4286,4288,4290,4292,4294,4296,4299,4302],{},[232,4285,234],{},[307,4287,310],{"stretchy":309},[232,4289,966],{},[307,4291,317],{"stretchy":309},[307,4293,320],{},[232,4295,966],{},[232,4297,4298],{},"log",[307,4300,4301],{},"⁡",[232,4303,966],{},[236,4305,4306],{"encoding":238},"f(t)=t\\log t",[212,4308,4310,4337],{"className":4309,"ariaHidden":243},[242],[212,4311,4313,4316,4319,4322,4325,4328,4331,4334],{"className":4312},[247],[212,4314],{"className":4315,"style":336},[251],[212,4317,234],{"className":4318,"style":258},[256,257],[212,4320,310],{"className":4321},[343],[212,4323,966],{"className":4324},[256,257],[212,4326,317],{"className":4327},[350],[212,4329],{"className":4330,"style":355},[354],[212,4332,320],{"className":4333},[359],[212,4335],{"className":4336,"style":355},[354],[212,4338,4340,4343,4346,4349,4357,4360],{"className":4339},[247],[212,4341],{"className":4342,"style":252},[251],[212,4344,966],{"className":4345},[256,257],[212,4347],{"className":4348,"style":603},[354],[212,4350,4352,4353],{"className":4351},[1682],"lo",[212,4354,4356],{"style":4355},"margin-right:0.0139em;","g",[212,4358],{"className":4359,"style":603},[354],[212,4361,966],{"className":4362},[256,257],"，当 ",[212,4365,4367,4380],{"className":4366,"translate":216},[215],[212,4368,4370],{"className":4369},[220],[222,4371,4372],{"xmlns":224},[226,4373,4374,4378],{},[229,4375,4376],{},[232,4377,403],{},[236,4379,403],{"encoding":238},[212,4381,4383],{"className":4382,"ariaHidden":243},[242],[212,4384,4386,4389],{"className":4385},[247],[212,4387],{"className":4388,"style":861},[251],[212,4390,403],{"className":4391,"style":531},[256,257],[212,4393,4395,4408],{"className":4394,"translate":216},[215],[212,4396,4398],{"className":4397},[220],[222,4399,4400],{"xmlns":224},[226,4401,4402,4406],{},[229,4403,4404],{},[232,4405,410],{},[236,4407,410],{"encoding":238},[212,4409,4411],{"className":4410,"ariaHidden":243},[242],[212,4412,4414,4417],{"className":4413},[247],[212,4415],{"className":4416,"style":763},[251],[212,4418,410],{"className":4419},[256,257]," 的零测集上放质量时这一项为 ",[212,4422,4424,4440],{"className":4423,"translate":216},[215],[212,4425,4427],{"className":4426},[220],[222,4428,4429],{"xmlns":224},[226,4430,4431,4437],{},[229,4432,4433,4435],{},[307,4434,2668],{},[232,4436,1223],{"mathvariant":406},[236,4438,4439],{"encoding":238},"+\\infty",[212,4441,4443],{"className":4442,"ariaHidden":243},[242],[212,4444,4446,4450,4453],{"className":4445},[247],[212,4447],{"className":4448,"style":4449},[251],"height:0.6667em;vertical-align:-0.0833em;",[212,4451,2668],{"className":4452},[256],[212,4454,1223],{"className":4455},[256],"。因此约定：",[212,4458,4460],{"className":4459,"translate":216},[377],[212,4461,4463,4577],{"className":4462,"translate":216},[215],[212,4464,4466],{"className":4465},[220],[222,4467,4468],{"xmlns":224,"display":386},[226,4469,4470,4574],{},[229,4471,4472,4474,4477,4479,4482,4485,4487,4493,4495,4497,4499,4501,4503,4505],{},[232,4473,403],{},[307,4475,4476],{},"≪̸",[232,4478,410],{},[1495,4480,4481],{}," ",[307,4483,4484],{},"⟹",[1495,4486,4481],{},[392,4488,4489,4491],{},[232,4490,396],{},[232,4492,234],{},[307,4494,310],{"stretchy":309},[232,4496,403],{},[232,4498,407],{"mathvariant":406},[232,4500,410],{},[307,4502,317],{"stretchy":309},[307,4504,320],{},[229,4506,4507,4509],{},[307,4508,3096],{"fence":243},[1441,4510,4514,4549],{"rowspacing":4511,"columnalign":4512,"columnspacing":4513},"0.36em","left left","1em",[1447,4515,4516,4528],{},[1450,4517,4518],{},[1453,4519,4520],{"scriptlevel":323,"displaystyle":309},[229,4521,4522,4524,4526],{},[307,4523,2668],{},[232,4525,1223],{"mathvariant":406},[307,4527,748],{"separator":243},[1450,4529,4530],{},[1453,4531,4532],{"scriptlevel":323,"displaystyle":309},[229,4533,4534,4537,4539,4542,4544,4547],{},[1495,4535,4536],{},"若 ",[232,4538,234],{},[1495,4540,4541],{}," 在 ",[232,4543,1223],{"mathvariant":406},[1495,4545,4546],{}," 处增长",[307,4548,748],{"separator":243},[1447,4550,4551,4562],{},[1450,4552,4553],{},[1453,4554,4555],{"scriptlevel":323,"displaystyle":309},[229,4556,4557,4560],{},[1495,4558,4559],{},"有限极限值",[307,4561,748],{"separator":243},[1450,4563,4564],{},[1453,4565,4566],{"scriptlevel":323,"displaystyle":309},[229,4567,4568,4571],{},[1495,4569,4570],{},"否则",[232,4572,4573],{"mathvariant":406},".",[236,4575,4576],{"encoding":238},"P\\not\\ll Q\\ \\Longrightarrow\\\nD_f(P\\|Q)=\n\\begin{cases}\n+\\infty, & \\text{若 } f \\text{ 在 } \\infty\n\\text{ 处增长},\\\\[2pt]\n\\text{有限极限值}, & \\text{否则}.\n\\end{cases}",[212,4578,4580,4635,4659,4729],{"className":4579,"ariaHidden":243},[242],[212,4581,4583,4586,4589,4592,4625,4629,4632],{"className":4582},[247],[212,4584],{"className":4585,"style":252},[251],[212,4587,403],{"className":4588,"style":531},[256,257],[212,4590],{"className":4591,"style":355},[354],[212,4593,4595],{"className":4594},[359],[212,4596,4599],{"className":4597},[256,4598],"vbox",[212,4600,4603],{"className":4601},[4602],"thinbox",[212,4604,4607,4610,4621],{"className":4605},[4606],"rlap",[212,4608],{"className":4609,"style":252},[251],[212,4611,4614],{"className":4612},[4613],"inner",[212,4615,4617],{"className":4616},[256],[212,4618,4620],{"className":4619},[359],"",[212,4622],{"className":4623},[4624],"fix",[212,4626],{"className":4627},[354,4628],"nobreak",[212,4630,911],{"className":4631},[359],[212,4633],{"className":4634,"style":355},[354],[212,4636,4638,4641,4644,4647,4650,4653,4656],{"className":4637},[247],[212,4639],{"className":4640,"style":763},[251],[212,4642,410],{"className":4643},[256,257],[212,4645,4481],{"className":4646},[354],[212,4648],{"className":4649,"style":355},[354],[212,4651,4484],{"className":4652},[359],[212,4654,4481],{"className":4655},[354],[212,4657],{"className":4658,"style":355},[354],[212,4660,4662,4665,4705,4708,4711,4714,4717,4720,4723,4726],{"className":4661},[247],[212,4663],{"className":4664,"style":467},[251],[212,4666,4668,4671],{"className":4667},[256],[212,4669,396],{"className":4670,"style":474},[256,257],[212,4672,4674],{"className":4673},[478],[212,4675,4677,4697],{"className":4676},[482,483],[212,4678,4680,4694],{"className":4679},[487],[212,4681,4683],{"className":4682,"style":492},[491],[212,4684,4685,4688],{"style":495},[212,4686],{"className":4687,"style":500},[499],[212,4689,4691],{"className":4690},[504,505,506,507],[212,4692,234],{"className":4693,"style":258},[256,257,507],[212,4695,515],{"className":4696},[514],[212,4698,4700],{"className":4699},[487],[212,4701,4703],{"className":4702,"style":522},[491],[212,4704],{},[212,4706,310],{"className":4707},[343],[212,4709,403],{"className":4710,"style":531},[256,257],[212,4712,407],{"className":4713},[256],[212,4715,410],{"className":4716},[256,257],[212,4718,317],{"className":4719},[350],[212,4721],{"className":4722,"style":355},[354],[212,4724,320],{"className":4725},[359],[212,4727],{"className":4728,"style":355},[354],[212,4730,4732,4736],{"className":4731},[247],[212,4733],{"className":4734,"style":4735},[251],"height:3.08em;vertical-align:-1.29em;",[212,4737,4739,4746,4911],{"className":4738},[607],[212,4740,4742],{"className":4741,"style":612},[343,611],[212,4743,3096],{"className":4744},[616,4745],"size4",[212,4747,4749],{"className":4748},[256],[212,4750,4752,4816,4821],{"className":4751},[1441],[212,4753,4755],{"className":4754},[1649],[212,4756,4758,4807],{"className":4757},[482,483],[212,4759,4761,4804],{"className":4760},[487],[212,4762,4765,4784],{"className":4763,"style":4764},[491],"height:1.79em;",[212,4766,4768,4772],{"style":4767},"top:-3.79em;",[212,4769],{"className":4770,"style":4771},[499],"height:3.008em;",[212,4773,4775,4778,4781],{"className":4774},[256],[212,4776,2668],{"className":4777},[256],[212,4779,1223],{"className":4780},[256],[212,4782,748],{"className":4783},[770],[212,4785,4787,4790],{"style":4786},"top:-2.15em;",[212,4788],{"className":4789,"style":4771},[499],[212,4791,4793,4801],{"className":4792},[256],[212,4794,4797],{"className":4795},[256,4796],"text",[212,4798,4559],{"className":4799},[256,4800],"cjk_fallback",[212,4802,748],{"className":4803},[770],[212,4805,515],{"className":4806},[514],[212,4808,4810],{"className":4809},[487],[212,4811,4814],{"className":4812,"style":4813},[491],"height:1.29em;",[212,4815],{},[212,4817],{"className":4818,"style":4820},[4819],"arraycolsep","width:1em;",[212,4822,4824],{"className":4823},[1649],[212,4825,4827,4903],{"className":4826},[482,483],[212,4828,4830,4900],{"className":4829},[487],[212,4831,4833,4883],{"className":4832,"style":4764},[491],[212,4834,4835,4838],{"style":4767},[212,4836],{"className":4837,"style":4771},[499],[212,4839,4841,4851,4854,4867,4870,4880],{"className":4840},[256],[212,4842,4844,4848],{"className":4843},[256,4796],[212,4845,4847],{"className":4846},[256,4800],"若",[212,4849,4481],{"className":4850},[256],[212,4852,234],{"className":4853,"style":258},[256,257],[212,4855,4857,4860,4864],{"className":4856},[256,4796],[212,4858,4481],{"className":4859},[256],[212,4861,4863],{"className":4862},[256,4800],"在",[212,4865,4481],{"className":4866},[256],[212,4868,1223],{"className":4869},[256],[212,4871,4873,4876],{"className":4872},[256,4796],[212,4874,4481],{"className":4875},[256],[212,4877,4879],{"className":4878},[256,4800],"处增长",[212,4881,748],{"className":4882},[770],[212,4884,4885,4888],{"style":4786},[212,4886],{"className":4887,"style":4771},[499],[212,4889,4891,4897],{"className":4890},[256],[212,4892,4894],{"className":4893},[256,4796],[212,4895,4570],{"className":4896},[256,4800],[212,4898,4573],{"className":4899},[256],[212,4901,515],{"className":4902},[514],[212,4904,4906],{"className":4905},[487],[212,4907,4909],{"className":4908,"style":4813},[491],[212,4910],{},[212,4912],{"className":4913},[350,638],[11,4915,4916,4917,4051,4945,4973,4974,5150,5151,5220,5221,5271,5272,5341,5342,5399],{},"其中「否则」指 ",[212,4918,4920,4933],{"className":4919,"translate":216},[215],[212,4921,4923],{"className":4922},[220],[222,4924,4925],{"xmlns":224},[226,4926,4927,4931],{},[229,4928,4929],{},[232,4930,234],{},[236,4932,234],{"encoding":238},[212,4934,4936],{"className":4935,"ariaHidden":243},[242],[212,4937,4939,4942],{"className":4938},[247],[212,4940],{"className":4941,"style":252},[251],[212,4943,234],{"className":4944,"style":258},[256,257],[212,4946,4948,4961],{"className":4947,"translate":216},[215],[212,4949,4951],{"className":4950},[220],[222,4952,4953],{"xmlns":224},[226,4954,4955,4959],{},[229,4956,4957],{},[232,4958,1223],{"mathvariant":406},[236,4960,4068],{"encoding":238},[212,4962,4964],{"className":4963,"ariaHidden":243},[242],[212,4965,4967,4970],{"className":4966},[247],[212,4968],{"className":4969,"style":2543},[251],[212,4971,1223],{"className":4972},[256]," 处有界（如 ",[212,4975,4977,5019],{"className":4976,"translate":216},[215],[212,4978,4980],{"className":4979},[220],[222,4981,4982],{"xmlns":224},[226,4983,4984,5016],{},[229,4985,4986,4988,4990,4992,4994,4996,5004,5007,5009,5012,5014],{},[232,4987,234],{},[307,4989,310],{"stretchy":309},[232,4991,966],{},[307,4993,317],{"stretchy":309},[307,4995,320],{},[1453,4997,4998],{"scriptlevel":323,"displaystyle":309},[435,4999,5000,5002],{},[312,5001,314],{},[312,5003,2661],{},[307,5005,5006],{"stretchy":309},"∣",[232,5008,966],{},[307,5010,5011],{},"−",[312,5013,314],{},[307,5015,5006],{"stretchy":309},[236,5017,5018],{"encoding":238},"f(t)=\\tfrac12\\lvert t-1\\rvert",[212,5020,5022,5049,5138],{"className":5021,"ariaHidden":243},[242],[212,5023,5025,5028,5031,5034,5037,5040,5043,5046],{"className":5024},[247],[212,5026],{"className":5027,"style":336},[251],[212,5029,234],{"className":5030,"style":258},[256,257],[212,5032,310],{"className":5033},[343],[212,5035,966],{"className":5036},[256,257],[212,5038,317],{"className":5039},[350],[212,5041],{"className":5042,"style":355},[354],[212,5044,320],{"className":5045},[359],[212,5047],{"className":5048,"style":355},[354],[212,5050,5052,5055,5123,5126,5129,5132,5135],{"className":5051},[247],[212,5053],{"className":5054,"style":2703},[251],[212,5056,5058,5061,5120],{"className":5057},[256],[212,5059],{"className":5060},[343,638],[212,5062,5064],{"className":5063},[435],[212,5065,5067,5112],{"className":5066},[482,483],[212,5068,5070,5109],{"className":5069},[487],[212,5071,5073,5087,5095],{"className":5072,"style":2722},[491],[212,5074,5075,5078],{"style":2725},[212,5076],{"className":5077,"style":658},[499],[212,5079,5081],{"className":5080},[504,505,506,507],[212,5082,5084],{"className":5083},[256,507],[212,5085,2661],{"className":5086},[256,507],[212,5088,5089,5092],{"style":670},[212,5090],{"className":5091,"style":658},[499],[212,5093],{"className":5094,"style":678},[677],[212,5096,5097,5100],{"style":2748},[212,5098],{"className":5099,"style":658},[499],[212,5101,5103],{"className":5102},[504,505,506,507],[212,5104,5106],{"className":5105},[256,507],[212,5107,314],{"className":5108},[256,507],[212,5110,515],{"className":5111},[514],[212,5113,5115],{"className":5114},[487],[212,5116,5118],{"className":5117,"style":2770},[491],[212,5119],{},[212,5121],{"className":5122},[350,638],[212,5124,5006],{"className":5125},[343],[212,5127,966],{"className":5128},[256,257],[212,5130],{"className":5131,"style":2785},[354],[212,5133,5011],{"className":5134},[2789],[212,5136],{"className":5137,"style":2785},[354],[212,5139,5141,5144,5147],{"className":5140},[247],[212,5142],{"className":5143,"style":336},[251],[212,5145,314],{"className":5146},[256],[212,5148,5006],{"className":5149},[350],"），此时 ",[212,5152,5154,5171],{"className":5153,"translate":216},[215],[212,5155,5157],{"className":5156},[220],[222,5158,5159],{"xmlns":224},[226,5160,5161,5169],{},[229,5162,5163],{},[392,5164,5165,5167],{},[232,5166,396],{},[232,5168,234],{},[236,5170,4220],{"encoding":238},[212,5172,5174],{"className":5173,"ariaHidden":243},[242],[212,5175,5177,5180],{"className":5176},[247],[212,5178],{"className":5179,"style":4230},[251],[212,5181,5183,5186],{"className":5182},[256],[212,5184,396],{"className":5185,"style":474},[256,257],[212,5187,5189],{"className":5188},[478],[212,5190,5192,5212],{"className":5191},[482,483],[212,5193,5195,5209],{"className":5194},[487],[212,5196,5198],{"className":5197,"style":492},[491],[212,5199,5200,5203],{"style":495},[212,5201],{"className":5202,"style":500},[499],[212,5204,5206],{"className":5205},[504,505,506,507],[212,5207,234],{"className":5208,"style":258},[256,257,507],[212,5210,515],{"className":5211},[514],[212,5213,5215],{"className":5214},[487],[212,5216,5218],{"className":5217,"style":522},[491],[212,5219],{}," 取有限极限值。下文如无特别说明，默认 ",[212,5222,5224,5241],{"className":5223,"translate":216},[215],[212,5225,5227],{"className":5226},[220],[222,5228,5229],{"xmlns":224},[226,5230,5231,5239],{},[229,5232,5233,5235,5237],{},[232,5234,403],{},[307,5236,911],{},[232,5238,410],{},[236,5240,916],{"encoding":238},[212,5242,5244,5262],{"className":5243,"ariaHidden":243},[242],[212,5245,5247,5250,5253,5256,5259],{"className":5246},[247],[212,5248],{"className":5249,"style":926},[251],[212,5251,403],{"className":5252,"style":531},[256,257],[212,5254],{"className":5255,"style":355},[354],[212,5257,911],{"className":5258},[359],[212,5260],{"className":5261,"style":355},[354],[212,5263,5265,5268],{"className":5264},[247],[212,5266],{"className":5267,"style":763},[251],[212,5269,410],{"className":5270},[256,257],"，并把 ",[212,5273,5275,5292],{"className":5274,"translate":216},[215],[212,5276,5278],{"className":5277},[220],[222,5279,5280],{"xmlns":224},[226,5281,5282,5290],{},[229,5283,5284],{},[392,5285,5286,5288],{},[232,5287,396],{},[232,5289,234],{},[236,5291,4220],{"encoding":238},[212,5293,5295],{"className":5294,"ariaHidden":243},[242],[212,5296,5298,5301],{"className":5297},[247],[212,5299],{"className":5300,"style":4230},[251],[212,5302,5304,5307],{"className":5303},[256],[212,5305,396],{"className":5306,"style":474},[256,257],[212,5308,5310],{"className":5309},[478],[212,5311,5313,5333],{"className":5312},[482,483],[212,5314,5316,5330],{"className":5315},[487],[212,5317,5319],{"className":5318,"style":492},[491],[212,5320,5321,5324],{"style":495},[212,5322],{"className":5323,"style":500},[499],[212,5325,5327],{"className":5326},[504,505,506,507],[212,5328,234],{"className":5329,"style":258},[256,257,507],[212,5331,515],{"className":5332},[514],[212,5334,5336],{"className":5335},[487],[212,5337,5339],{"className":5338,"style":522},[491],[212,5340],{}," 看成 ",[212,5343,5345,5369],{"className":5344,"translate":216},[215],[212,5346,5348],{"className":5347},[220],[222,5349,5350],{"xmlns":224},[226,5351,5352,5366],{},[229,5353,5354,5356,5358,5360,5362,5364],{},[307,5355,427],{"stretchy":309},[312,5357,323],{},[307,5359,748],{"separator":243},[307,5361,2668],{},[232,5363,1223],{"mathvariant":406},[307,5365,454],{"stretchy":309},[236,5367,5368],{"encoding":238},"[0,+\\infty]",[212,5370,5372],{"className":5371,"ariaHidden":243},[242],[212,5373,5375,5378,5381,5384,5387,5390,5393,5396],{"className":5374},[247],[212,5376],{"className":5377,"style":336},[251],[212,5379,427],{"className":5380},[343],[212,5382,323],{"className":5383},[256],[212,5385,748],{"className":5386},[770],[212,5388],{"className":5389,"style":603},[354],[212,5391,2668],{"className":5392},[256],[212,5394,1223],{"className":5395},[256],[212,5397,454],{"className":5398},[350]," 中的值。",[2509,5401,5403],{"id":5402},"_12-只依赖似然比","1.2 只依赖似然比",[11,5405,5406,5407,5502,5503,5575,5576,5653,5654,5682,5683,5725],{},"由定义立刻看出：",[212,5408,5410,5438],{"className":5409,"translate":216},[215],[212,5411,5413],{"className":5412},[220],[222,5414,5415],{"xmlns":224},[226,5416,5417,5435],{},[229,5418,5419,5425,5427,5429,5431,5433],{},[392,5420,5421,5423],{},[232,5422,396],{},[232,5424,234],{},[307,5426,310],{"stretchy":309},[232,5428,403],{},[232,5430,407],{"mathvariant":406},[232,5432,410],{},[307,5434,317],{"stretchy":309},[236,5436,5437],{"encoding":238},"D_f(P\\|Q)",[212,5439,5441],{"className":5440,"ariaHidden":243},[242],[212,5442,5444,5447,5487,5490,5493,5496,5499],{"className":5443},[247],[212,5445],{"className":5446,"style":467},[251],[212,5448,5450,5453],{"className":5449},[256],[212,5451,396],{"className":5452,"style":474},[256,257],[212,5454,5456],{"className":5455},[478],[212,5457,5459,5479],{"className":5458},[482,483],[212,5460,5462,5476],{"className":5461},[487],[212,5463,5465],{"className":5464,"style":492},[491],[212,5466,5467,5470],{"style":495},[212,5468],{"className":5469,"style":500},[499],[212,5471,5473],{"className":5472},[504,505,506,507],[212,5474,234],{"className":5475,"style":258},[256,257,507],[212,5477,515],{"className":5478},[514],[212,5480,5482],{"className":5481},[487],[212,5483,5485],{"className":5484,"style":522},[491],[212,5486],{},[212,5488,310],{"className":5489},[343],[212,5491,403],{"className":5492,"style":531},[256,257],[212,5494,407],{"className":5495},[256],[212,5497,410],{"className":5498},[256,257],[212,5500,317],{"className":5501},[350]," 只通过似然比 ",[212,5504,5506,5532],{"className":5505,"translate":216},[215],[212,5507,5509],{"className":5508},[220],[222,5510,5511],{"xmlns":224},[226,5512,5513,5529],{},[229,5514,5515,5517,5519,5521,5523,5525,5527],{},[232,5516,966],{},[307,5518,320],{},[232,5520,441],{},[232,5522,403],{},[232,5524,1138],{"mathvariant":406},[232,5526,441],{},[232,5528,410],{},[236,5530,5531],{"encoding":238},"t=dP\u002FdQ",[212,5533,5535,5554],{"className":5534,"ariaHidden":243},[242],[212,5536,5538,5542,5545,5548,5551],{"className":5537},[247],[212,5539],{"className":5540,"style":5541},[251],"height:0.6151em;",[212,5543,966],{"className":5544},[256,257],[212,5546],{"className":5547,"style":355},[354],[212,5549,320],{"className":5550},[359],[212,5552],{"className":5553,"style":355},[354],[212,5555,5557,5560,5563,5566,5569,5572],{"className":5556},[247],[212,5558],{"className":5559,"style":336},[251],[212,5561,441],{"className":5562},[256,257],[212,5564,403],{"className":5565,"style":531},[256,257],[212,5567,1138],{"className":5568},[256],[212,5570,441],{"className":5571},[256,257],[212,5573,410],{"className":5574},[256,257]," 起作用。也就是说，对任意可测映射 ",[212,5577,5579,5603],{"className":5578,"translate":216},[215],[212,5580,5582],{"className":5581},[220],[222,5583,5584],{"xmlns":224},[226,5585,5586,5600],{},[229,5587,5588,5591,5593,5595,5597],{},[232,5589,5590],{},"T",[307,5592,1214],{},[232,5594,795],{"mathvariant":794},[307,5596,1228],{},[232,5598,5599],{"mathvariant":794},"Y",[236,5601,5602],{"encoding":238},"T:\\mathcal X\\to\\mathcal Y",[212,5604,5606,5624,5642],{"className":5605,"ariaHidden":243},[242],[212,5607,5609,5612,5615,5618,5621],{"className":5608},[247],[212,5610],{"className":5611,"style":861},[251],[212,5613,5590],{"className":5614,"style":531},[256,257],[212,5616],{"className":5617,"style":355},[354],[212,5619,1214],{"className":5620},[359],[212,5622],{"className":5623,"style":355},[354],[212,5625,5627,5630,5633,5636,5639],{"className":5626},[247],[212,5628],{"className":5629,"style":861},[251],[212,5631,795],{"className":5632,"style":822},[256,821],[212,5634],{"className":5635,"style":355},[354],[212,5637,1228],{"className":5638},[359],[212,5640],{"className":5641,"style":355},[354],[212,5643,5645,5649],{"className":5644},[247],[212,5646],{"className":5647,"style":5648},[251],"height:0.7805em;vertical-align:-0.0972em;",[212,5650,5599],{"className":5651,"style":5652},[256,821],"margin-right:0.0822em;","，它是 ",[212,5655,5657,5670],{"className":5656,"translate":216},[215],[212,5658,5660],{"className":5659},[220],[222,5661,5662],{"xmlns":224},[226,5663,5664,5668],{},[229,5665,5666],{},[232,5667,966],{},[236,5669,966],{"encoding":238},[212,5671,5673],{"className":5672,"ariaHidden":243},[242],[212,5674,5676,5679],{"className":5675},[247],[212,5677],{"className":5678,"style":5541},[251],[212,5680,966],{"className":5681},[256,257]," 的函数，而不是 ",[212,5684,5686,5704],{"className":5685,"translate":216},[215],[212,5687,5689],{"className":5688},[220],[222,5690,5691],{"xmlns":224},[226,5692,5693,5701],{},[229,5694,5695,5697,5699],{},[232,5696,11],{},[307,5698,748],{"separator":243},[232,5700,1141],{},[236,5702,5703],{"encoding":238},"p,q",[212,5705,5707],{"className":5706,"ariaHidden":243},[242],[212,5708,5710,5713,5716,5719,5722],{"className":5709},[247],[212,5711],{"className":5712,"style":2474},[251],[212,5714,11],{"className":5715},[256,257],[212,5717,748],{"className":5718},[770],[212,5720],{"className":5721,"style":603},[354],[212,5723,1141],{"className":5724,"style":1178},[256,257]," 各自的函数。",[11,5727,5728,5729,5768],{},"这一点是 f-散度「缺少几何」的根源，也是它与 Wasserstein 距离分道扬镳的地方（见第 6 节）：只要保持比值 ",[212,5730,5732,5750],{"className":5731,"translate":216},[215],[212,5733,5735],{"className":5734},[220],[222,5736,5737],{"xmlns":224},[226,5738,5739,5747],{},[229,5740,5741,5743,5745],{},[232,5742,11],{},[232,5744,1138],{"mathvariant":406},[232,5746,1141],{},[236,5748,5749],{"encoding":238},"p\u002Fq",[212,5751,5753],{"className":5752,"ariaHidden":243},[242],[212,5754,5756,5759,5762,5765],{"className":5755},[247],[212,5757],{"className":5758,"style":336},[251],[212,5760,11],{"className":5761},[256,257],[212,5763,1138],{"className":5764},[256],[212,5766,1141],{"className":5767,"style":1178},[256,257]," 不变，把两个分布同时「搬到别处」，f-散度的值完全不动。",[2509,5770,5772],{"id":5771},"_13-非单射与仿射自由度","1.3 非单射与仿射自由度",[11,5774,5775,5776,5843,5844,5908],{},"注意 ",[212,5777,5779,5801],{"className":5778,"translate":216},[215],[212,5780,5782],{"className":5781},[220],[222,5783,5784],{"xmlns":224},[226,5785,5786,5798],{},[229,5787,5788,5790,5792,5794,5796],{},[307,5789,1485],{},[232,5791,441],{},[232,5793,410],{},[307,5795,320],{},[312,5797,314],{},[236,5799,5800],{"encoding":238},"\\int dQ=1",[212,5802,5804,5834],{"className":5803,"ariaHidden":243},[242],[212,5805,5807,5811,5816,5819,5822,5825,5828,5831],{"className":5806},[247],[212,5808],{"className":5809,"style":5810},[251],"height:1.1111em;vertical-align:-0.3061em;",[212,5812,1485],{"className":5813,"style":5815},[1682,1683,5814],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[212,5817],{"className":5818,"style":603},[354],[212,5820,441],{"className":5821},[256,257],[212,5823,410],{"className":5824},[256,257],[212,5826],{"className":5827,"style":355},[354],[212,5829,320],{"className":5830},[359],[212,5832],{"className":5833,"style":355},[354],[212,5835,5837,5840],{"className":5836},[247],[212,5838],{"className":5839,"style":369},[251],[212,5841,314],{"className":5842},[256],"、",[212,5845,5847,5869],{"className":5846,"translate":216},[215],[212,5848,5850],{"className":5849},[220],[222,5851,5852],{"xmlns":224},[226,5853,5854,5866],{},[229,5855,5856,5858,5860,5862,5864],{},[307,5857,1485],{},[232,5859,441],{},[232,5861,403],{},[307,5863,320],{},[312,5865,314],{},[236,5867,5868],{"encoding":238},"\\int dP=1",[212,5870,5872,5899],{"className":5871,"ariaHidden":243},[242],[212,5873,5875,5878,5881,5884,5887,5890,5893,5896],{"className":5874},[247],[212,5876],{"className":5877,"style":5810},[251],[212,5879,1485],{"className":5880,"style":5815},[1682,1683,5814],[212,5882],{"className":5883,"style":603},[354],[212,5885,441],{"className":5886},[256,257],[212,5888,403],{"className":5889,"style":531},[256,257],[212,5891],{"className":5892,"style":355},[354],[212,5894,320],{"className":5895},[359],[212,5897],{"className":5898,"style":355},[354],[212,5900,5902,5905],{"className":5901},[247],[212,5903],{"className":5904,"style":369},[251],[212,5906,314],{"className":5907},[256],"，因此",[212,5910,5912],{"className":5911,"translate":216},[377],[212,5913,5915,5966],{"className":5914,"translate":216},[215],[212,5916,5918],{"className":5917},[220],[222,5919,5920],{"xmlns":224,"display":386},[226,5921,5922,5963],{},[229,5923,5924,5926,5928,5930,5932,5934,5936,5938,5940,5942,5944,5946,5948,5950,5952,5954,5956,5958,5960],{},[307,5925,1485],{},[307,5927,310],{"stretchy":309},[232,5929,966],{},[307,5931,5011],{},[312,5933,314],{},[307,5935,317],{"stretchy":309},[1495,5937,1497],{},[232,5939,441],{},[232,5941,410],{},[307,5943,320],{},[307,5945,1485],{},[232,5947,441],{},[232,5949,403],{},[307,5951,5011],{},[307,5953,1485],{},[232,5955,441],{},[232,5957,410],{},[307,5959,320],{},[312,5961,5962],{},"0.",[236,5964,5965],{"encoding":238},"\\int (t-1)\\,dQ=\\int dP-\\int dQ=0 .",[212,5967,5969,5994,6024,6051,6078],{"className":5968,"ariaHidden":243},[242],[212,5970,5972,5976,5979,5982,5985,5988,5991],{"className":5971},[247],[212,5973],{"className":5974,"style":5975},[251],"height:2.2222em;vertical-align:-0.8622em;",[212,5977,1485],{"className":5978,"style":1685},[1682,1683,1684],[212,5980,310],{"className":5981},[343],[212,5983,966],{"className":5984},[256,257],[212,5986],{"className":5987,"style":2785},[354],[212,5989,5011],{"className":5990},[2789],[212,5992],{"className":5993,"style":2785},[354],[212,5995,5997,6000,6003,6006,6009,6012,6015,6018,6021],{"className":5996},[247],[212,5998],{"className":5999,"style":336},[251],[212,6001,314],{"className":6002},[256],[212,6004,317],{"className":6005},[350],[212,6007],{"className":6008,"style":603},[354],[212,6010,441],{"className":6011},[256,257],[212,6013,410],{"className":6014},[256,257],[212,6016],{"className":6017,"style":355},[354],[212,6019,320],{"className":6020},[359],[212,6022],{"className":6023,"style":355},[354],[212,6025,6027,6030,6033,6036,6039,6042,6045,6048],{"className":6026},[247],[212,6028],{"className":6029,"style":5975},[251],[212,6031,1485],{"className":6032,"style":1685},[1682,1683,1684],[212,6034],{"className":6035,"style":603},[354],[212,6037,441],{"className":6038},[256,257],[212,6040,403],{"className":6041,"style":531},[256,257],[212,6043],{"className":6044,"style":2785},[354],[212,6046,5011],{"className":6047},[2789],[212,6049],{"className":6050,"style":2785},[354],[212,6052,6054,6057,6060,6063,6066,6069,6072,6075],{"className":6053},[247],[212,6055],{"className":6056,"style":5975},[251],[212,6058,1485],{"className":6059,"style":1685},[1682,1683,1684],[212,6061],{"className":6062,"style":603},[354],[212,6064,441],{"className":6065},[256,257],[212,6067,410],{"className":6068},[256,257],[212,6070],{"className":6071,"style":355},[354],[212,6073,320],{"className":6074},[359],[212,6076],{"className":6077,"style":355},[354],[212,6079,6081,6084],{"className":6080},[247],[212,6082],{"className":6083,"style":369},[251],[212,6085,5962],{"className":6086},[256],[11,6088,6089,6090,2943],{},"于是对任意常数 ",[212,6091,6093,6113],{"className":6092,"translate":216},[215],[212,6094,6096],{"className":6095},[220],[222,6097,6098],{"xmlns":224},[226,6099,6100,6110],{},[229,6101,6102,6105,6108],{},[232,6103,6104],{},"c",[307,6106,6107],{},"∈",[232,6109,1231],{"mathvariant":419},[236,6111,6112],{"encoding":238},"c\\in\\mathbb 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",[212,6694,6696,6713],{"className":6695,"translate":216},[215],[212,6697,6699],{"className":6698},[220],[222,6700,6701],{"xmlns":224},[226,6702,6703,6711],{},[229,6704,6705],{},[392,6706,6707,6709],{},[232,6708,396],{},[232,6710,234],{},[236,6712,4220],{"encoding":238},[212,6714,6716],{"className":6715,"ariaHidden":243},[242],[212,6717,6719,6722],{"className":6718},[247],[212,6720],{"className":6721,"style":4230},[251],[212,6723,6725,6728],{"className":6724},[256],[212,6726,396],{"className":6727,"style":474},[256,257],[212,6729,6731],{"className":6730},[478],[212,6732,6734,6754],{"className":6733},[482,483],[212,6735,6737,6751],{"className":6736},[487],[212,6738,6740],{"className":6739,"style":492},[491],[212,6741,6742,6745],{"style":495},[212,6743],{"className":6744,"style":500},[499],[212,6746,6748],{"className":6747},[504,505,506,507],[212,6749,234],{"className":6750,"style":258},[256,257,507],[212,6752,515],{"className":6753},[514],[212,6755,6757],{"className":6756},[487],[212,6758,6760],{"className":6759,"style":522},[491],[212,6761],{}," 只依赖 ",[212,6764,6766,6779],{"className":6765,"translate":216},[215],[212,6767,6769],{"className":6768},[220],[222,6770,6771],{"xmlns":224},[226,6772,6773,6777],{},[229,6774,6775],{},[232,6776,234],{},[236,6778,234],{"encoding":238},[212,6780,6782],{"className":6781,"ariaHidden":243},[242],[212,6783,6785,6788],{"className":6784},[247],[212,6786],{"className":6787,"style":252},[251],[212,6789,234],{"className":6790,"style":258},[256,257]," 在「模去 ",[212,6793,6795,6819],{"className":6794,"translate":216},[215],[212,6796,6798],{"className":6797},[220],[222,6799,6800],{"xmlns":224},[226,6801,6802,6816],{},[229,6803,6804,6806,6808,6810,6812,6814],{},[232,6805,6104],{},[307,6807,310],{"stretchy":309},[232,6809,966],{},[307,6811,5011],{},[312,6813,314],{},[307,6815,317],{"stretchy":309},[236,6817,6818],{"encoding":238},"c(t-1)",[212,6820,6822,6846],{"className":6821,"ariaHidden":243},[242],[212,6823,6825,6828,6831,6834,6837,6840,6843],{"className":6824},[247],[212,6826],{"className":6827,"style":336},[251],[212,6829,6104],{"className":6830},[256,257],[212,6832,310],{"className":6833},[343],[212,6835,966],{"className":6836},[256,257],[212,6838],{"className":6839,"style":2785},[354],[212,6841,5011],{"className":6842},[2789],[212,6844],{"className":6845,"style":2785},[354],[212,6847,6849,6852,6855],{"className":6848},[247],[212,6850],{"className":6851,"style":336},[251],[212,6853,314],{"className":6854},[256],[212,6856,317],{"className":6857},[350],"」之后的等价类。两个常用规范化是：",[6860,6861,6862,6931],"ol",{},[6863,6864,6865,6930],"li",{},[212,6866,6868,6891],{"className":6867,"translate":216},[215],[212,6869,6871],{"className":6870},[220],[222,6872,6873],{"xmlns":224},[226,6874,6875,6889],{},[229,6876,6877,6879,6881,6883,6885,6887],{},[232,6878,234],{},[307,6880,310],{"stretchy":309},[312,6882,314],{},[307,6884,317],{"stretchy":309},[307,6886,320],{},[312,6888,323],{},[236,6890,326],{"encoding":238},[212,6892,6894,6921],{"className":6893,"ariaHidden":243},[242],[212,6895,6897,6900,6903,6906,6909,6912,6915,6918],{"className":6896},[247],[212,6898],{"className":6899,"style":336},[251],[212,6901,234],{"className":6902,"style":258},[256,257],[212,6904,310],{"className":6905},[343],[212,6907,314],{"className":6908},[256],[212,6910,317],{"className":6911},[350],[212,6913],{"className":6914,"style":355},[354],[212,6916,320],{"className":6917},[359],[212,6919],{"className":6920,"style":355},[354],[212,6922,6924,6927],{"className":6923},[247],[212,6925],{"className":6926,"style":369},[251],[212,6928,323],{"className":6929},[256],"（本文采用）；",[6863,6932,6933,6998,6999,7103,7104,2943,7315,7343],{},[212,6934,6936,6959],{"className":6935,"translate":216},[215],[212,6937,6939],{"className":6938},[220],[222,6940,6941],{"xmlns":224},[226,6942,6943,6957],{},[229,6944,6945,6947,6949,6951,6953,6955],{},[232,6946,234],{},[307,6948,310],{"stretchy":309},[312,6950,314],{},[307,6952,317],{"stretchy":309},[307,6954,320],{},[312,6956,323],{},[236,6958,326],{"encoding":238},[212,6960,6962,6989],{"className":6961,"ariaHidden":243},[242],[212,6963,6965,6968,6971,6974,6977,6980,6983,6986],{"className":6964},[247],[212,6966],{"className":6967,"style":336},[251],[212,6969,234],{"className":6970,"style":258},[256,257],[212,6972,310],{"className":6973},[343],[212,6975,314],{"className":6976},[256],[212,6978,317],{"className":6979},[350],[212,6981],{"className":6982,"style":355},[354],[212,6984,320],{"className":6985},[359],[212,6987],{"className":6988,"style":355},[354],[212,6990,6992,6995],{"className":6991},[247],[212,6993],{"className":6994,"style":369},[251],[212,6996,323],{"className":6997},[256]," 且 ",[212,7000,7002,7032],{"className":7001,"translate":216},[215],[212,7003,7005],{"className":7004},[220],[222,7006,7007],{"xmlns":224},[226,7008,7009,7029],{},[229,7010,7011,7019,7021,7023,7025,7027],{},[7012,7013,7014,7016],"msup",{},[232,7015,234],{},[307,7017,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},"′",[307,7020,310],{"stretchy":309},[312,7022,314],{},[307,7024,317],{"stretchy":309},[307,7026,320],{},[312,7028,323],{},[236,7030,7031],{"encoding":238},"f'(1)=0",[212,7033,7035,7094],{"className":7034,"ariaHidden":243},[242],[212,7036,7038,7042,7076,7079,7082,7085,7088,7091],{"className":7037},[247],[212,7039],{"className":7040,"style":7041},[251],"height:1.0019em;vertical-align:-0.25em;",[212,7043,7045,7048],{"className":7044},[256],[212,7046,234],{"className":7047,"style":258},[256,257],[212,7049,7051],{"className":7050},[478],[212,7052,7054],{"className":7053},[482],[212,7055,7057],{"className":7056},[487],[212,7058,7061],{"className":7059,"style":7060},[491],"height:0.7519em;",[212,7062,7064,7067],{"style":7063},"top:-3.063em;margin-right:0.05em;",[212,7065],{"className":7066,"style":500},[499],[212,7068,7070],{"className":7069},[504,505,506,507],[212,7071,7073],{"className":7072},[256,507],[212,7074,7018],{"className":7075},[256,507],[212,7077,310],{"className":7078},[343],[212,7080,314],{"className":7081},[256],[212,7083,317],{"className":7084},[350],[212,7086],{"className":7087,"style":355},[354],[212,7089,320],{"className":7090},[359],[212,7092],{"className":7093,"style":355},[354],[212,7095,7097,7100],{"className":7096},[247],[212,7098],{"className":7099,"style":369},[251],[212,7101,323],{"className":7102},[256],"——此时由凸性 ",[212,7105,7107,7166],{"className":7106,"translate":216},[215],[212,7108,7110],{"className":7109},[220],[222,7111,7112],{"xmlns":224},[226,7113,7114,7163],{},[229,7115,7116,7118,7120,7122,7124,7127,7129,7131,7133,7135,7137,7143,7145,7147,7149,7151,7153,7155,7157,7159,7161],{},[232,7117,234],{},[307,7119,310],{"stretchy":309},[232,7121,966],{},[307,7123,317],{"stretchy":309},[307,7125,7126],{},"≥",[232,7128,234],{},[307,7130,310],{"stretchy":309},[312,7132,314],{},[307,7134,317],{"stretchy":309},[307,7136,2668],{},[7012,7138,7139,7141],{},[232,7140,234],{},[307,7142,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,7144,310],{"stretchy":309},[312,7146,314],{},[307,7148,317],{"stretchy":309},[307,7150,310],{"stretchy":309},[232,7152,966],{},[307,7154,5011],{},[312,7156,314],{},[307,7158,317],{"stretchy":309},[307,7160,320],{},[312,7162,323],{},[236,7164,7165],{"encoding":238},"f(t)\\ge f(1)+f'(1)(t-1)=0",[212,7167,7169,7196,7223,7285,7306],{"className":7168,"ariaHidden":243},[242],[212,7170,7172,7175,7178,7181,7184,7187,7190,7193],{"className":7171},[247],[212,7173],{"className":7174,"style":336},[251],[212,7176,234],{"className":7177,"style":258},[256,257],[212,7179,310],{"className":7180},[343],[212,7182,966],{"className":7183},[256,257],[212,7185,317],{"className":7186},[350],[212,7188],{"className":7189,"style":355},[354],[212,7191,7126],{"className":7192},[359],[212,7194],{"className":7195,"style":355},[354],[212,7197,7199,7202,7205,7208,7211,7214,7217,7220],{"className":7198},[247],[212,7200],{"className":7201,"style":336},[251],[212,7203,234],{"className":7204,"style":258},[256,257],[212,7206,310],{"className":7207},[343],[212,7209,314],{"className":7210},[256],[212,7212,317],{"className":7213},[350],[212,7215],{"className":7216,"style":2785},[354],[212,7218,2668],{"className":7219},[2789],[212,7221],{"className":7222,"style":2785},[354],[212,7224,7226,7229,7261,7264,7267,7270,7273,7276,7279,7282],{"className":7225},[247],[212,7227],{"className":7228,"style":7041},[251],[212,7230,7232,7235],{"className":7231},[256],[212,7233,234],{"className":7234,"style":258},[256,257],[212,7236,7238],{"className":7237},[478],[212,7239,7241],{"className":7240},[482],[212,7242,7244],{"className":7243},[487],[212,7245,7247],{"className":7246,"style":7060},[491],[212,7248,7249,7252],{"style":7063},[212,7250],{"className":7251,"style":500},[499],[212,7253,7255],{"className":7254},[504,505,506,507],[212,7256,7258],{"className":7257},[256,507],[212,7259,7018],{"className":7260},[256,507],[212,7262,310],{"className":7263},[343],[212,7265,314],{"className":7266},[256],[212,7268,317],{"className":7269},[350],[212,7271,310],{"className":7272},[343],[212,7274,966],{"className":7275},[256,257],[212,7277],{"className":7278,"style":2785},[354],[212,7280,5011],{"className":7281},[2789],[212,7283],{"className":7284,"style":2785},[354],[212,7286,7288,7291,7294,7297,7300,7303],{"className":7287},[247],[212,7289],{"className":7290,"style":336},[251],[212,7292,314],{"className":7293},[256],[212,7295,317],{"className":7296},[350],[212,7298],{"className":7299,"style":355},[354],[212,7301,320],{"className":7302},[359],[212,7304],{"className":7305,"style":355},[354],[212,7307,7309,7312],{"className":7308},[247],[212,7310],{"className":7311,"style":369},[251],[212,7313,323],{"className":7314},[256],[212,7316,7318,7331],{"className":7317,"translate":216},[215],[212,7319,7321],{"className":7320},[220],[222,7322,7323],{"xmlns":224},[226,7324,7325,7329],{},[229,7326,7327],{},[232,7328,234],{},[236,7330,234],{"encoding":238},[212,7332,7334],{"className":7333,"ariaHidden":243},[242],[212,7335,7337,7340],{"className":7336},[247],[212,7338],{"className":7339,"style":252},[251],[212,7341,234],{"className":7342,"style":258},[256,257]," 在整个定义域上非负。",[11,7345,7346,7347,7432,7433,7486,7487,7556],{},"第 3 节里的 KL 的 ",[212,7348,7350,7379],{"className":7349,"translate":216},[215],[212,7351,7353],{"className":7352},[220],[222,7354,7355],{"xmlns":224},[226,7356,7357,7377],{},[229,7358,7359,7361,7363,7365,7367,7369,7371,7373,7375],{},[232,7360,234],{},[307,7362,310],{"stretchy":309},[232,7364,966],{},[307,7366,317],{"stretchy":309},[307,7368,320],{},[232,7370,966],{},[232,7372,4298],{},[307,7374,4301],{},[232,7376,966],{},[236,7378,4306],{"encoding":238},[212,7380,7382,7409],{"className":7381,"ariaHidden":243},[242],[212,7383,7385,7388,7391,7394,7397,7400,7403,7406],{"className":7384},[247],[212,7386],{"className":7387,"style":336},[251],[212,7389,234],{"className":7390,"style":258},[256,257],[212,7392,310],{"className":7393},[343],[212,7395,966],{"className":7396},[256,257],[212,7398,317],{"className":7399},[350],[212,7401],{"className":7402,"style":355},[354],[212,7404,320],{"className":7405},[359],[212,7407],{"className":7408,"style":355},[354],[212,7410,7412,7415,7418,7421,7426,7429],{"className":7411},[247],[212,7413],{"className":7414,"style":252},[251],[212,7416,966],{"className":7417},[256,257],[212,7419],{"className":7420,"style":603},[354],[212,7422,4352,7424],{"className":7423},[1682],[212,7425,4356],{"style":4355},[212,7427],{"className":7428,"style":603},[354],[212,7430,966],{"className":7431},[256,257]," 不满足第 2 条（它在 ",[212,7434,7436,7455],{"className":7435,"translate":216},[215],[212,7437,7439],{"className":7438},[220],[222,7440,7441],{"xmlns":224},[226,7442,7443,7452],{},[229,7444,7445,7447,7450],{},[232,7446,966],{},[307,7448,7449],{},"\u003C",[312,7451,314],{},[236,7453,7454],{"encoding":238},"t\u003C1",[212,7456,7458,7477],{"className":7457,"ariaHidden":243},[242],[212,7459,7461,7465,7468,7471,7474],{"className":7460},[247],[212,7462],{"className":7463,"style":7464},[251],"height:0.6542em;vertical-align:-0.0391em;",[212,7466,966],{"className":7467},[256,257],[212,7469],{"className":7470,"style":355},[354],[212,7472,7449],{"className":7473},[359],[212,7475],{"className":7476,"style":355},[354],[212,7478,7480,7483],{"className":7479},[247],[212,7481],{"className":7482,"style":369},[251],[212,7484,314],{"className":7485},[256]," 时取负值），但这无妨：",[212,7488,7490,7507],{"className":7489,"translate":216},[215],[212,7491,7493],{"className":7492},[220],[222,7494,7495],{"xmlns":224},[226,7496,7497,7505],{},[229,7498,7499],{},[392,7500,7501,7503],{},[232,7502,396],{},[232,7504,234],{},[236,7506,4220],{"encoding":238},[212,7508,7510],{"className":7509,"ariaHidden":243},[242],[212,7511,7513,7516],{"className":7512},[247],[212,7514],{"className":7515,"style":4230},[251],[212,7517,7519,7522],{"className":7518},[256],[212,7520,396],{"className":7521,"style":474},[256,257],[212,7523,7525],{"className":7524},[478],[212,7526,7528,7548],{"className":7527},[482,483],[212,7529,7531,7545],{"className":7530},[487],[212,7532,7534],{"className":7533,"style":492},[491],[212,7535,7536,7539],{"style":495},[212,7537],{"className":7538,"style":500},[499],[212,7540,7542],{"className":7541},[504,505,506,507],[212,7543,234],{"className":7544,"style":258},[256,257,507],[212,7546,515],{"className":7547},[514],[212,7549,7551],{"className":7550},[487],[212,7552,7554],{"className":7553,"style":522},[491],[212,7555],{}," 仍然非负（见 4.1），因为「逐点非负」从来不是 f-散度非负性的必要条件。",[2509,7558,7560],{"id":7559},"_14-等价书写形式","1.4 等价书写形式",[212,7562,7564],{"className":7563,"translate":216},[377],[212,7565,7567,7801],{"className":7566,"translate":216},[215],[212,7568,7570],{"className":7569},[220],[222,7571,7572],{"xmlns":224,"display":386},[226,7573,7574,7798],{},[1441,7575,7576,7648,7720],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,7577,7578,7600],{},[1450,7579,7580],{},[1453,7581,7582],{"scriptlevel":323,"displaystyle":243},[229,7583,7584,7590,7592,7594,7596,7598],{},[392,7585,7586,7588],{},[232,7587,396],{},[232,7589,234],{},[307,7591,310],{"stretchy":309},[232,7593,403],{},[232,7595,407],{"mathvariant":406},[232,7597,410],{},[307,7599,317],{"stretchy":309},[1450,7601,7602],{},[1453,7603,7604],{"scriptlevel":323,"displaystyle":243},[229,7605,7606,7608,7610,7616,7618],{},[229,7607],{},[307,7609,320],{},[392,7611,7612,7614],{},[232,7613,420],{"mathvariant":419},[232,7615,410],{},[1495,7617,1502],{},[229,7619,7620,7622,7624,7626,7646],{},[307,7621,427],{"fence":243},[232,7623,234],{},[1495,7625,1502],{},[229,7627,7628,7630,7644],{},[307,7629,310],{"fence":243},[435,7631,7632,7638],{},[229,7633,7634,7636],{},[232,7635,441],{},[232,7637,403],{},[229,7639,7640,7642],{},[232,7641,441],{},[232,7643,410],{},[307,7645,317],{"fence":243},[307,7647,454],{"fence":243},[1447,7649,7650,7656],{},[1450,7651,7652],{},[1453,7653,7654],{"scriptlevel":323,"displaystyle":243},[229,7655],{},[1450,7657,7658],{},[1453,7659,7660],{"scriptlevel":323,"displaystyle":243},[229,7661,7662,7664,7666,7672,7674],{},[229,7663],{},[307,7665,320],{},[392,7667,7668,7670],{},[232,7669,420],{"mathvariant":419},[232,7671,403],{},[1495,7673,1502],{},[229,7675,7676,7678,7692,7694,7696,7698,7718],{},[307,7677,427],{"fence":243},[435,7679,7680,7686],{},[229,7681,7682,7684],{},[232,7683,441],{},[232,7685,410],{},[229,7687,7688,7690],{},[232,7689,441],{},[232,7691,403],{},[1495,7693,1497],{},[232,7695,234],{},[1495,7697,1502],{},[229,7699,7700,7702,7716],{},[307,7701,310],{"fence":243},[435,7703,7704,7710],{},[229,7705,7706,7708],{},[232,7707,441],{},[232,7709,403],{},[229,7711,7712,7714],{},[232,7713,441],{},[232,7715,410],{},[307,7717,317],{"fence":243},[307,7719,454],{"fence":243},[1447,7721,7722,7728],{},[1450,7723,7724],{},[1453,7725,7726],{"scriptlevel":323,"displaystyle":243},[229,7727],{},[1450,7729,7730],{},[1453,7731,7732],{"scriptlevel":323,"displaystyle":243},[229,7733,7734,7736,7738,7744,7746,7796],{},[229,7735],{},[307,7737,320],{},[392,7739,7740,7742],{},[232,7741,420],{"mathvariant":419},[232,7743,403],{},[1495,7745,1502],{},[229,7747,7748,7750,7772,7774,7794],{},[307,7749,427],{"fence":243},[7751,7752,7753,7755,7769],"msubsup",{},[232,7754,234],{},[229,7756,7757,7760,7763,7766],{},[232,7758,7759],{},"s",[232,7761,7762],{},"k",[232,7764,7765],{},"e",[232,7767,7768],{},"w",[307,7770,7771],{"lspace":1445,"rspace":1445},"∗",[1495,7773,1502],{},[229,7775,7776,7778,7792],{},[307,7777,310],{"fence":243},[435,7779,7780,7786],{},[229,7781,7782,7784],{},[232,7783,441],{},[232,7785,410],{},[229,7787,7788,7790],{},[232,7789,441],{},[232,7791,403],{},[307,7793,317],{"fence":243},[307,7795,454],{"fence":243},[307,7797,748],{"separator":243},[236,7799,7800],{"encoding":238},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\mathbb E_Q\\!\\left[\nf\\!\\left(\\frac{dP}{dQ}\\right)\\right]\\\\[2pt]\n&=\\mathbb E_P\\!\\left[\\frac{dQ}{dP}\\,\nf\\!\\left(\\frac{dP}{dQ}\\right)\\right]\\\\\n&=\\mathbb 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是后面 4.3 节的「斜共轭」。最后一个等式说明：交换 ",[212,8796,8798,8815],{"className":8797,"translate":216},[215],[212,8799,8801],{"className":8800},[220],[222,8802,8803],{"xmlns":224},[226,8804,8805,8813],{},[229,8806,8807,8809,8811],{},[232,8808,403],{},[307,8810,748],{"separator":243},[232,8812,410],{},[236,8814,753],{"encoding":238},[212,8816,8818],{"className":8817,"ariaHidden":243},[242],[212,8819,8821,8824,8827,8830,8833],{"className":8820},[247],[212,8822],{"className":8823,"style":763},[251],[212,8825,403],{"className":8826,"style":531},[256,257],[212,8828,748],{"className":8829},[770],[212,8831],{"className":8832,"style":603},[354],[212,8834,410],{"className":8835},[256,257]," 只是把 ",[212,8838,8840,8853],{"className":8839,"translate":216},[215],[212,8841,8843],{"className":8842},[220],[222,8844,8845],{"xmlns":224},[226,8846,8847,8851],{},[229,8848,8849],{},[232,8850,234],{},[236,8852,234],{"encoding":238},[212,8854,8856],{"className":8855,"ariaHidden":243},[242],[212,8857,8859,8862],{"className":8858},[247],[212,8860],{"className":8861,"style":252},[251],[212,8863,234],{"className":8864,"style":258},[256,257]," 换成 ",[212,8867,8869,8900],{"className":8868,"translate":216},[215],[212,8870,8872],{"className":8871},[220],[222,8873,8874],{"xmlns":224},[226,8875,8876,8897],{},[229,8877,8878,8880,8883,8885,8887,8889,8891,8893,8895],{},[232,8879,966],{},[307,8881,8882],{},"↦",[232,8884,966],{},[232,8886,234],{},[307,8888,310],{"stretchy":309},[312,8890,314],{},[232,8892,1138],{"mathvariant":406},[232,8894,966],{},[307,8896,317],{"stretchy":309},[236,8898,8899],{"encoding":238},"t\\mapsto t f(1\u002Ft)",[212,8901,8903,8922],{"className":8902,"ariaHidden":243},[242],[212,8904,8906,8910,8913,8916,8919],{"className":8905},[247],[212,8907],{"className":8908,"style":8909},[251],"height:0.6261em;vertical-align:-0.011em;",[212,8911,966],{"className":8912},[256,257],[212,8914],{"className":8915,"style":355},[354],[212,8917,8882],{"className":8918},[359],[212,8920],{"className":8921,"style":355},[354],[212,8923,8925,8928,8931,8934,8937,8940,8943],{"className":8924},[247],[212,8926],{"className":8927,"style":336},[251],[212,8929,966],{"className":8930},[256,257],[212,8932,234],{"className":8933,"style":258},[256,257],[212,8935,310],{"className":8936},[343],[212,8938,8787],{"className":8939},[256],[212,8941,966],{"className":8942},[256,257],[212,8944,317],{"className":8945},[350],"，这对推导「反向 KL」之类的对称性非常方便。",[725,8948,8950,8951,8979,8980],{"id":8949},"_2-为何-fff-凸且-f10f10f10","2. 为何 ",[212,8952,8954,8967],{"className":8953,"translate":216},[215],[212,8955,8957],{"className":8956},[220],[222,8958,8959],{"xmlns":224},[226,8960,8961,8965],{},[229,8962,8963],{},[232,8964,234],{},[236,8966,234],{"encoding":238},[212,8968,8970],{"className":8969,"ariaHidden":243},[242],[212,8971,8973,8976],{"className":8972},[247],[212,8974],{"className":8975,"style":252},[251],[212,8977,234],{"className":8978,"style":258},[256,257]," 凸且 ",[212,8981,8983,9006],{"className":8982,"translate":216},[215],[212,8984,8986],{"className":8985},[220],[222,8987,8988],{"xmlns":224},[226,8989,8990,9004],{},[229,8991,8992,8994,8996,8998,9000,9002],{},[232,8993,234],{},[307,8995,310],{"stretchy":309},[312,8997,314],{},[307,8999,317],{"stretchy":309},[307,9001,320],{},[312,9003,323],{},[236,9005,326],{"encoding":238},[212,9007,9009,9036],{"className":9008,"ariaHidden":243},[242],[212,9010,9012,9015,9018,9021,9024,9027,9030,9033],{"className":9011},[247],[212,9013],{"className":9014,"style":336},[251],[212,9016,234],{"className":9017,"style":258},[256,257],[212,9019,310],{"className":9020},[343],[212,9022,314],{"className":9023},[256],[212,9025,317],{"className":9026},[350],[212,9028],{"className":9029,"style":355},[354],[212,9031,320],{"className":9032},[359],[212,9034],{"className":9035,"style":355},[354],[212,9037,9039,9042],{"className":9038},[247],[212,9040],{"className":9041,"style":369},[251],[212,9043,323],{"className":9044},[256],[2509,9046,9048],{"id":9047},"_21-非负性与-jensen","2.1 非负性与 Jensen",[11,9050,731,9051,1365,9104,9148,9149,9218,9219,9289],{},[212,9052,9054,9073],{"className":9053,"translate":216},[215],[212,9055,9057],{"className":9056},[220],[222,9058,9059],{"xmlns":224},[226,9060,9061,9070],{},[229,9062,9063,9065,9068],{},[232,9064,795],{},[307,9066,9067],{},"∼",[232,9069,410],{},[236,9071,9072],{"encoding":238},"X\\sim Q",[212,9074,9076,9095],{"className":9075,"ariaHidden":243},[242],[212,9077,9079,9082,9086,9089,9092],{"className":9078},[247],[212,9080],{"className":9081,"style":861},[251],[212,9083,795],{"className":9084,"style":9085},[256,257],"margin-right:0.0785em;",[212,9087],{"className":9088,"style":355},[354],[212,9090,9067],{"className":9091},[359],[212,9093],{"className":9094,"style":355},[354],[212,9096,9098,9101],{"className":9097},[247],[212,9099],{"className":9100,"style":763},[251],[212,9102,410],{"className":9103},[256,257],[212,9105,9107,9127],{"className":9106,"translate":216},[215],[212,9108,9110],{"className":9109},[220],[222,9111,9112],{"xmlns":224},[226,9113,9114,9124],{},[229,9115,9116,9118,9120,9122],{},[232,9117,234],{},[307,9119,310],{"stretchy":309},[232,9121,795],{},[307,9123,317],{"stretchy":309},[236,9125,9126],{"encoding":238},"f(X)",[212,9128,9130],{"className":9129,"ariaHidden":243},[242],[212,9131,9133,9136,9139,9142,9145],{"className":9132},[247],[212,9134],{"className":9135,"style":336},[251],[212,9137,234],{"className":9138,"style":258},[256,257],[212,9140,310],{"className":9141},[343],[212,9143,795],{"className":9144,"style":9085},[256,257],[212,9146,317],{"className":9147},[350]," 的期望就是 ",[212,9150,9152,9169],{"className":9151,"translate":216},[215],[212,9153,9155],{"className":9154},[220],[222,9156,9157],{"xmlns":224},[226,9158,9159,9167],{},[229,9160,9161],{},[392,9162,9163,9165],{},[232,9164,396],{},[232,9166,234],{},[236,9168,4220],{"encoding":238},[212,9170,9172],{"className":9171,"ariaHidden":243},[242],[212,9173,9175,9178],{"className":9174},[247],[212,9176],{"className":9177,"style":4230},[251],[212,9179,9181,9184],{"className":9180},[256],[212,9182,396],{"className":9183,"style":474},[256,257],[212,9185,9187],{"className":9186},[478],[212,9188,9190,9210],{"className":9189},[482,483],[212,9191,9193,9207],{"className":9192},[487],[212,9194,9196],{"className":9195,"style":492},[491],[212,9197,9198,9201],{"style":495},[212,9199],{"className":9200,"style":500},[499],[212,9202,9204],{"className":9203},[504,505,506,507],[212,9205,234],{"className":9206,"style":258},[256,257,507],[212,9208,515],{"className":9209},[514],[212,9211,9213],{"className":9212},[487],[212,9214,9216],{"className":9215,"style":522},[491],[212,9217],{},"。因为 ",[212,9220,9222,9247],{"className":9221,"translate":216},[215],[212,9223,9225],{"className":9224},[220],[222,9226,9227],{"xmlns":224},[226,9228,9229,9245],{},[229,9230,9231,9233,9235,9237,9239,9241,9243],{},[232,9232,966],{},[307,9234,320],{},[232,9236,441],{},[232,9238,403],{},[232,9240,1138],{"mathvariant":406},[232,9242,441],{},[232,9244,410],{},[236,9246,5531],{"encoding":238},[212,9248,9250,9268],{"className":9249,"ariaHidden":243},[242],[212,9251,9253,9256,9259,9262,9265],{"className":9252},[247],[212,9254],{"className":9255,"style":5541},[251],[212,9257,966],{"className":9258},[256,257],[212,9260],{"className":9261,"style":355},[354],[212,9263,320],{"className":9264},[359],[212,9266],{"className":9267,"style":355},[354],[212,9269,9271,9274,9277,9280,9283,9286],{"className":9270},[247],[212,9272],{"className":9273,"style":336},[251],[212,9275,441],{"className":9276},[256,257],[212,9278,403],{"className":9279,"style":531},[256,257],[212,9281,1138],{"className":9282},[256],[212,9284,441],{"className":9285},[256,257],[212,9287,410],{"className":9288},[256,257]," 满足",[212,9291,9293],{"className":9292,"translate":216},[377],[212,9294,9296,9358],{"className":9295,"translate":216},[215],[212,9297,9299],{"className":9298},[220],[222,9300,9301],{"xmlns":224,"display":386},[226,9302,9303,9355],{},[229,9304,9305,9311,9313,9315,9317,9319,9321,9335,9337,9339,9341,9343,9345,9347,9349,9351,9353],{},[392,9306,9307,9309],{},[232,9308,420],{"mathvariant":419},[232,9310,410],{},[307,9312,427],{"stretchy":309},[232,9314,966],{},[307,9316,454],{"stretchy":309},[307,9318,320],{},[307,9320,1485],{},[435,9322,9323,9329],{},[229,9324,9325,9327],{},[232,9326,441],{},[232,9328,403],{},[229,9330,9331,9333],{},[232,9332,441],{},[232,9334,410],{},[1495,9336,1497],{},[232,9338,441],{},[232,9340,410],{},[307,9342,320],{},[307,9344,1485],{},[232,9346,441],{},[232,9348,403],{},[307,9350,320],{},[312,9352,314],{},[307,9354,748],{"separator":243},[236,9356,9357],{"encoding":238},"\\mathbb E_Q[t]=\\int \\frac{dP}{dQ}\\,dQ=\\int dP=1,",[212,9359,9361,9425,9523,9550],{"className":9360,"ariaHidden":243},[242],[212,9362,9364,9367,9407,9410,9413,9416,9419,9422],{"className":9363},[247],[212,9365],{"className":9366,"style":467},[251],[212,9368,9370,9373],{"className":9369},[256],[212,9371,420],{"className":9372},[256,563],[212,9374,9376],{"className":9375},[478],[212,9377,9379,9399],{"className":9378},[482,483],[212,9380,9382,9396],{"className":9381},[487],[212,9383,9385],{"className":9384,"style":576},[491],[212,9386,9387,9390],{"style":579},[212,9388],{"className":9389,"style":500},[499],[212,9391,9393],{"className":9392},[504,505,506,507],[212,9394,410],{"className":9395},[256,257,507],[212,9397,515],{"className":9398},[514],[212,9400,9402],{"className":9401},[487],[212,9403,9405],{"className":9404,"style":522},[491],[212,9406],{},[212,9408,427],{"className":9409},[343],[212,9411,966],{"className":9412},[256,257],[212,9414,454],{"className":9415},[350],[212,9417],{"className":9418,"style":355},[354],[212,9420,320],{"className":9421},[359],[212,9423],{"className":9424,"style":355},[354],[212,9426,9428,9431,9434,9437,9505,9508,9511,9514,9517,9520],{"className":9427},[247],[212,9429],{"className":9430,"style":1035},[251],[212,9432,1485],{"className":9433,"style":1685},[1682,1683,1684],[212,9435],{"className":9436,"style":603},[354],[212,9438,9440,9443,9502],{"className":9439},[256],[212,9441],{"className":9442},[343,638],[212,9444,9446],{"className":9445},[435],[212,9447,9449,9494],{"className":9448},[482,483],[212,9450,9452,9491],{"className":9451},[487],[212,9453,9455,9469,9477],{"className":9454,"style":651},[491],[212,9456,9457,9460],{"style":654},[212,9458],{"className":9459,"style":658},[499],[212,9461,9463,9466],{"className":9462},[256],[212,9464,441],{"className":9465},[256,257],[212,9467,410],{"className":9468},[256,257],[212,9470,9471,9474],{"style":670},[212,9472],{"className":9473,"style":658},[499],[212,9475],{"className":9476,"style":678},[677],[212,9478,9479,9482],{"style":681},[212,9480],{"className":9481,"style":658},[499],[212,9483,9485,9488],{"className":9484},[256],[212,9486,441],{"className":9487},[256,257],[212,9489,403],{"className":9490,"style":531},[256,257],[212,9492,515],{"className":9493},[514],[212,9495,9497],{"className":9496},[487],[212,9498,9500],{"className":9499,"style":703},[491],[212,9501],{},[212,9503],{"className":9504},[350,638],[212,9506],{"className":9507,"style":603},[354],[212,9509,441],{"className":9510},[256,257],[212,9512,410],{"className":9513},[256,257],[212,9515],{"className":9516,"style":355},[354],[212,9518,320],{"className":9519},[359],[212,9521],{"className":9522,"style":355},[354],[212,9524,9526,9529,9532,9535,9538,9541,9544,9547],{"className":9525},[247],[212,9527],{"className":9528,"style":5975},[251],[212,9530,1485],{"className":9531,"style":1685},[1682,1683,1684],[212,9533],{"className":9534,"style":603},[354],[212,9536,441],{"className":9537},[256,257],[212,9539,403],{"className":9540,"style":531},[256,257],[212,9542],{"className":9543,"style":355},[354],[212,9545,320],{"className":9546},[359],[212,9548],{"className":9549,"style":355},[354],[212,9551,9553,9557,9560],{"className":9552},[247],[212,9554],{"className":9555,"style":9556},[251],"height:0.8389em;vertical-align:-0.1944em;",[212,9558,314],{"className":9559},[256],[212,9561,748],{"className":9562},[770],[11,9564,9565,9566,9594,9595,9598],{},"对凸函数 ",[212,9567,9569,9582],{"className":9568,"translate":216},[215],[212,9570,9572],{"className":9571},[220],[222,9573,9574],{"xmlns":224},[226,9575,9576,9580],{},[229,9577,9578],{},[232,9579,234],{},[236,9581,234],{"encoding":238},[212,9583,9585],{"className":9584,"ariaHidden":243},[242],[212,9586,9588,9591],{"className":9587},[247],[212,9589],{"className":9590,"style":252},[251],[212,9592,234],{"className":9593,"style":258},[256,257]," 用 ",[1194,9596,9597],{},"Jensen 不等式","：",[212,9600,9602],{"className":9601,"translate":216},[377],[212,9603,9605,9724],{"className":9604,"translate":216},[215],[212,9606,9608],{"className":9607},[220],[222,9609,9610],{"xmlns":224,"display":386},[226,9611,9612,9721],{},[1441,9613,9614,9691],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,9615,9616,9659],{},[1450,9617,9618],{},[1453,9619,9620],{"scriptlevel":323,"displaystyle":243},[229,9621,9622,9628,9630,9632,9634,9636,9638,9640,9646,9649,9651,9653,9655,9657],{},[392,9623,9624,9626],{},[232,9625,396],{},[232,9627,234],{},[307,9629,310],{"stretchy":309},[232,9631,403],{},[232,9633,407],{"mathvariant":406},[232,9635,410],{},[307,9637,317],{"stretchy":309},[307,9639,320],{},[392,9641,9642,9644],{},[232,9643,420],{"mathvariant":419},[232,9645,410],{},[307,9647,427],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},"1.2em",[232,9650,234],{},[307,9652,310],{"stretchy":309},[232,9654,966],{},[307,9656,317],{"stretchy":309},[307,9658,454],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[1450,9660,9661],{},[1453,9662,9663],{"scriptlevel":323,"displaystyle":243},[229,9664,9665,9667,9669,9671,9673,9675,9677,9683,9685,9687,9689],{},[229,9666],{},[1495,9668,4481],{},[307,9670,7126],{},[1495,9672,4481],{},[232,9674,234],{},[307,9676,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[392,9678,9679,9681],{},[232,9680,420],{"mathvariant":419},[232,9682,410],{},[307,9684,427],{"stretchy":309},[232,9686,966],{},[307,9688,454],{"stretchy":309},[307,9690,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[1447,9692,9693,9699],{},[1450,9694,9695],{},[1453,9696,9697],{"scriptlevel":323,"displaystyle":243},[229,9698],{},[1450,9700,9701],{},[1453,9702,9703],{"scriptlevel":323,"displaystyle":243},[229,9704,9705,9707,9709,9711,9713,9715,9717,9719],{},[229,9706],{},[307,9708,320],{},[232,9710,234],{},[307,9712,310],{"stretchy":309},[312,9714,314],{},[307,9716,317],{"stretchy":309},[307,9718,320],{},[312,9720,5962],{},[236,9722,9723],{"encoding":238},"\\begin{aligned}\nD_f(P\\|Q)=\\mathbb E_Q\\big[f(t)\\big]\n&\\ \\ge\\ f\\big(\\mathbb E_Q[t]\\big)\\\\[2pt]\n&=f(1)=0 .\n\\end{aligned}",[212,9725,9727],{"className":9726,"ariaHidden":243},[242],[212,9728,9730,9734],{"className":9729},[247],[212,9731],{"className":9732,"style":9733},[251],"height:2.91em;vertical-align:-1.205em;",[212,9735,9737],{"className":9736},[256],[212,9738,9740,9912],{"className":9739},[1441],[212,9741,9743],{"className":9742},[1558],[212,9744,9746,9903],{"className":9745},[482,483],[212,9747,9749,9900],{"className":9748},[487],[212,9750,9753,9891],{"className":9751,"style":9752},[491],"height:1.705em;",[212,9754,9756,9759],{"style":9755},"top:-3.855em;",[212,9757],{"className":9758,"style":658},[499],[212,9760,9762,9802,9805,9808,9811,9814,9817,9820,9823,9826,9866,9873,9876,9879,9882,9885],{"className":9761},[256],[212,9763,9765,9768],{"className":9764},[256],[212,9766,396],{"className":9767,"style":474},[256,257],[212,9769,9771],{"className":9770},[478],[212,9772,9774,9794],{"className":9773},[482,483],[212,9775,9777,9791],{"className":9776},[487],[212,9778,9780],{"className":9779,"style":492},[491],[212,9781,9782,9785],{"style":495},[212,9783],{"className":9784,"style":500},[499],[212,9786,9788],{"className":9787},[504,505,506,507],[212,9789,234],{"className":9790,"style":258},[256,257,507],[212,9792,515],{"className":9793},[514],[212,9795,9797],{"className":9796},[487],[212,9798,9800],{"className":9799,"style":522},[491],[212,9801],{},[212,9803,310],{"className":9804},[343],[212,9806,403],{"className":9807,"style":531},[256,257],[212,9809,407],{"className":9810},[256],[212,9812,410],{"className":9813},[256,257],[212,9815,317],{"className":9816},[350],[212,9818],{"className":9819,"style":355},[354],[212,9821,320],{"className":9822},[359],[212,9824],{"className":9825,"style":355},[354],[212,9827,9829,9832],{"className":9828},[256],[212,9830,420],{"className":9831},[256,563],[212,9833,9835],{"className":9834},[478],[212,9836,9838,9858],{"className":9837},[482,483],[212,9839,9841,9855],{"className":9840},[487],[212,9842,9844],{"className":9843,"style":576},[491],[212,9845,9846,9849],{"style":579},[212,9847],{"className":9848,"style":500},[499],[212,9850,9852],{"className":9851},[504,505,506,507],[212,9853,410],{"className":9854},[256,257,507],[212,9856,515],{"className":9857},[514],[212,9859,9861],{"className":9860},[487],[212,9862,9864],{"className":9863,"style":522},[491],[212,9865],{},[212,9867,9869],{"className":9868},[256],[212,9870,427],{"className":9871},[616,9872],"size1",[212,9874,234],{"className":9875,"style":258},[256,257],[212,9877,310],{"className":9878},[343],[212,9880,966],{"className":9881},[256,257],[212,9883,317],{"className":9884},[350],[212,9886,9888],{"className":9887},[256],[212,9889,454],{"className":9890},[616,9872],[212,9892,9894,9897],{"style":9893},"top:-2.155em;",[212,9895],{"className":9896,"style":658},[499],[212,9898],{"className":9899},[256],[212,9901,515],{"className":9902},[514],[212,9904,9906],{"className":9905},[487],[212,9907,9910],{"className":9908,"style":9909},[491],"height:1.205em;",[212,9911],{},[212,9913,9915],{"className":9914},[1649],[212,9916,9918,10061],{"className":9917},[482,483],[212,9919,9921,10058],{"className":9920},[487],[212,9922,9924,10014],{"className":9923,"style":9752},[491],[212,9925,9926,9929],{"style":9755},[212,9927],{"className":9928,"style":658},[499],[212,9930,9932,9935,9938,9941,9944,9947,9950,9953,9959,9999,10002,10005,10008],{"className":9931},[256],[212,9933],{"className":9934},[256],[212,9936,4481],{"className":9937},[354],[212,9939],{"className":9940,"style":355},[354],[212,9942,7126],{"className":9943},[359],[212,9945,4481],{"className":9946},[354],[212,9948],{"className":9949,"style":355},[354],[212,9951,234],{"className":9952,"style":258},[256,257],[212,9954,9956],{"className":9955},[256],[212,9957,310],{"className":9958},[616,9872],[212,9960,9962,9965],{"className":9961},[256],[212,9963,420],{"className":9964},[256,563],[212,9966,9968],{"className":9967},[478],[212,9969,9971,9991],{"className":9970},[482,483],[212,9972,9974,9988],{"className":9973},[487],[212,9975,9977],{"className":9976,"style":576},[491],[212,9978,9979,9982],{"style":579},[212,9980],{"className":9981,"style":500},[499],[212,9983,9985],{"className":9984},[504,505,506,507],[212,9986,410],{"className":9987},[256,257,507],[212,9989,515],{"className":9990},[514],[212,9992,9994],{"className":9993},[487],[212,9995,9997],{"className":9996,"style":522},[491],[212,9998],{},[212,10000,427],{"className":10001},[343],[212,10003,966],{"className":10004},[256,257],[212,10006,454],{"className":10007},[350],[212,10009,10011],{"className":10010},[256],[212,10012,317],{"className":10013},[616,9872],[212,10015,10016,10019],{"style":9893},[212,10017],{"className":10018,"style":658},[499],[212,10020,10022,10025,10028,10031,10034,10037,10040,10043,10046,10049,10052,10055],{"className":10021},[256],[212,10023],{"className":10024},[256],[212,10026],{"className":10027,"style":355},[354],[212,10029,320],{"className":10030},[359],[212,10032],{"className":10033,"style":355},[354],[212,10035,234],{"className":10036,"style":258},[256,257],[212,10038,310],{"className":10039},[343],[212,10041,314],{"className":10042},[256],[212,10044,317],{"className":10045},[350],[212,10047],{"className":10048,"style":355},[354],[212,10050,320],{"className":10051},[359],[212,10053],{"className":10054,"style":355},[354],[212,10056,5962],{"className":10057},[256],[212,10059,515],{"className":10060},[514],[212,10062,10064],{"className":10063},[487],[212,10065,10067],{"className":10066,"style":9909},[491],[212,10068],{},[11,10070,10071,10072,10100,10101,10129,10130,10223],{},"这就是非负性。",[212,10073,10075,10088],{"className":10074,"translate":216},[215],[212,10076,10078],{"className":10077},[220],[222,10079,10080],{"xmlns":224},[226,10081,10082,10086],{},[229,10083,10084],{},[232,10085,234],{},[236,10087,234],{"encoding":238},[212,10089,10091],{"className":10090,"ariaHidden":243},[242],[212,10092,10094,10097],{"className":10093},[247],[212,10095],{"className":10096,"style":252},[251],[212,10098,234],{"className":10099,"style":258},[256,257]," 的凸性是关键：若 ",[212,10102,10104,10117],{"className":10103,"translate":216},[215],[212,10105,10107],{"className":10106},[220],[222,10108,10109],{"xmlns":224},[226,10110,10111,10115],{},[229,10112,10113],{},[232,10114,234],{},[236,10116,234],{"encoding":238},[212,10118,10120],{"className":10119,"ariaHidden":243},[242],[212,10121,10123,10126],{"className":10122},[247],[212,10124],{"className":10125,"style":252},[251],[212,10127,234],{"className":10128,"style":258},[256,257]," 是凹函数，Jensen 方向反转，",[212,10131,10133,10156],{"className":10132,"translate":216},[215],[212,10134,10136],{"className":10135},[220],[222,10137,10138],{"xmlns":224},[226,10139,10140,10153],{},[229,10141,10142,10148,10151],{},[392,10143,10144,10146],{},[232,10145,396],{},[232,10147,234],{},[307,10149,10150],{},"≤",[312,10152,323],{},[236,10154,10155],{"encoding":238},"D_f\\le 0",[212,10157,10159,10214],{"className":10158,"ariaHidden":243},[242],[212,10160,10162,10165,10205,10208,10211],{"className":10161},[247],[212,10163],{"className":10164,"style":4230},[251],[212,10166,10168,10171],{"className":10167},[256],[212,10169,396],{"className":10170,"style":474},[256,257],[212,10172,10174],{"className":10173},[478],[212,10175,10177,10197],{"className":10176},[482,483],[212,10178,10180,10194],{"className":10179},[487],[212,10181,10183],{"className":10182,"style":492},[491],[212,10184,10185,10188],{"style":495},[212,10186],{"className":10187,"style":500},[499],[212,10189,10191],{"className":10190},[504,505,506,507],[212,10192,234],{"className":10193,"style":258},[256,257,507],[212,10195,515],{"className":10196},[514],[212,10198,10200],{"className":10199},[487],[212,10201,10203],{"className":10202,"style":522},[491],[212,10204],{},[212,10206],{"className":10207,"style":355},[354],[212,10209,10150],{"className":10210},[359],[212,10212],{"className":10213,"style":355},[354],[212,10215,10217,10220],{"className":10216},[247],[212,10218],{"className":10219,"style":369},[251],[212,10221,323],{"className":10222},[256],"，那就不是「散度」了。",[10225,10226,10227,10379],"ul",{},[6863,10228,10229,10260,10261,10378],{},[1194,10230,10231,10259],{},[212,10232,10234,10247],{"className":10233,"translate":216},[215],[212,10235,10237],{"className":10236},[220],[222,10238,10239],{"xmlns":224},[226,10240,10241,10245],{},[229,10242,10243],{},[232,10244,234],{},[236,10246,234],{"encoding":238},[212,10248,10250],{"className":10249,"ariaHidden":243},[242],[212,10251,10253,10256],{"className":10252},[247],[212,10254],{"className":10255,"style":252},[251],[212,10257,234],{"className":10258,"style":258},[256,257]," 凸","：保证 ",[212,10262,10264,10296],{"className":10263,"translate":216},[215],[212,10265,10267],{"className":10266},[220],[222,10268,10269],{"xmlns":224},[226,10270,10271,10293],{},[229,10272,10273,10279,10281,10283,10285,10287,10289,10291],{},[392,10274,10275,10277],{},[232,10276,396],{},[232,10278,234],{},[307,10280,310],{"stretchy":309},[232,10282,403],{},[232,10284,407],{"mathvariant":406},[232,10286,410],{},[307,10288,317],{"stretchy":309},[307,10290,7126],{},[312,10292,323],{},[236,10294,10295],{"encoding":238},"D_f(P\\|Q)\\ge 0",[212,10297,10299,10369],{"className":10298,"ariaHidden":243},[242],[212,10300,10302,10305,10345,10348,10351,10354,10357,10360,10363,10366],{"className":10301},[247],[212,10303],{"className":10304,"style":467},[251],[212,10306,10308,10311],{"className":10307},[256],[212,10309,396],{"className":10310,"style":474},[256,257],[212,10312,10314],{"className":10313},[478],[212,10315,10317,10337],{"className":10316},[482,483],[212,10318,10320,10334],{"className":10319},[487],[212,10321,10323],{"className":10322,"style":492},[491],[212,10324,10325,10328],{"style":495},[212,10326],{"className":10327,"style":500},[499],[212,10329,10331],{"className":10330},[504,505,506,507],[212,10332,234],{"className":10333,"style":258},[256,257,507],[212,10335,515],{"className":10336},[514],[212,10338,10340],{"className":10339},[487],[212,10341,10343],{"className":10342,"style":522},[491],[212,10344],{},[212,10346,310],{"className":10347},[343],[212,10349,403],{"className":10350,"style":531},[256,257],[212,10352,407],{"className":10353},[256],[212,10355,410],{"className":10356},[256,257],[212,10358,317],{"className":10359},[350],[212,10361],{"className":10362,"style":355},[354],[212,10364,7126],{"className":10365},[359],[212,10367],{"className":10368,"style":355},[354],[212,10370,10372,10375],{"className":10371},[247],[212,10373],{"className":10374,"style":369},[251],[212,10376,323],{"className":10377},[256],"。",[6863,10380,10381,10448,10449,10500,10501,10635,10636,10378],{},[1194,10382,10383],{},[212,10384,10386,10409],{"className":10385,"translate":216},[215],[212,10387,10389],{"className":10388},[220],[222,10390,10391],{"xmlns":224},[226,10392,10393,10407],{},[229,10394,10395,10397,10399,10401,10403,10405],{},[232,10396,234],{},[307,10398,310],{"stretchy":309},[312,10400,314],{},[307,10402,317],{"stretchy":309},[307,10404,320],{},[312,10406,323],{},[236,10408,326],{"encoding":238},[212,10410,10412,10439],{"className":10411,"ariaHidden":243},[242],[212,10413,10415,10418,10421,10424,10427,10430,10433,10436],{"className":10414},[247],[212,10416],{"className":10417,"style":336},[251],[212,10419,234],{"className":10420,"style":258},[256,257],[212,10422,310],{"className":10423},[343],[212,10425,314],{"className":10426},[256],[212,10428,317],{"className":10429},[350],[212,10431],{"className":10432,"style":355},[354],[212,10434,320],{"className":10435},[359],[212,10437],{"className":10438,"style":355},[354],[212,10440,10442,10445],{"className":10441},[247],[212,10443],{"className":10444,"style":369},[251],[212,10446,323],{"className":10447},[256],"：保证当 ",[212,10450,10452,10470],{"className":10451,"translate":216},[215],[212,10453,10455],{"className":10454},[220],[222,10456,10457],{"xmlns":224},[226,10458,10459,10467],{},[229,10460,10461,10463,10465],{},[232,10462,403],{},[307,10464,320],{},[232,10466,410],{},[236,10468,10469],{"encoding":238},"P=Q",[212,10471,10473,10491],{"className":10472,"ariaHidden":243},[242],[212,10474,10476,10479,10482,10485,10488],{"className":10475},[247],[212,10477],{"className":10478,"style":861},[251],[212,10480,403],{"className":10481,"style":531},[256,257],[212,10483],{"className":10484,"style":355},[354],[212,10486,320],{"className":10487},[359],[212,10489],{"className":10490,"style":355},[354],[212,10492,10494,10497],{"className":10493},[247],[212,10495],{"className":10496,"style":763},[251],[212,10498,410],{"className":10499},[256,257]," 时，",[212,10502,10504,10534],{"className":10503,"translate":216},[215],[212,10505,10507],{"className":10506},[220],[222,10508,10509],{"xmlns":224},[226,10510,10511,10531],{},[229,10512,10513,10527,10529],{},[435,10514,10515,10521],{},[229,10516,10517,10519],{},[232,10518,441],{},[232,10520,403],{},[229,10522,10523,10525],{},[232,10524,441],{},[232,10526,410],{},[307,10528,320],{},[312,10530,314],{},[236,10532,10533],{"encoding":238},"\\frac{dP}{dQ}=1",[212,10535,10537,10626],{"className":10536,"ariaHidden":243},[242],[212,10538,10540,10543,10617,10620,10623],{"className":10539},[247],[212,10541],{"className":10542,"style":2866},[251],[212,10544,10546,10549,10614],{"className":10545},[256],[212,10547],{"className":10548},[343,638],[212,10550,10552],{"className":10551},[435],[212,10553,10555,10606],{"className":10554},[482,483],[212,10556,10558,10603],{"className":10557},[487],[212,10559,10561,10578,10586],{"className":10560,"style":2885},[491],[212,10562,10563,10566],{"style":2725},[212,10564],{"className":10565,"style":658},[499],[212,10567,10569],{"className":10568},[504,505,506,507],[212,10570,10572,10575],{"className":10571},[256,507],[212,10573,441],{"className":10574},[256,257,507],[212,10576,410],{"className":10577},[256,257,507],[212,10579,10580,10583],{"style":670},[212,10581],{"className":10582,"style":658},[499],[212,10584],{"className":10585,"style":678},[677],[212,10587,10588,10591],{"style":2748},[212,10589],{"className":10590,"style":658},[499],[212,10592,10594],{"className":10593},[504,505,506,507],[212,10595,10597,10600],{"className":10596},[256,507],[212,10598,441],{"className":10599},[256,257,507],[212,10601,403],{"className":10602,"style":531},[256,257,507],[212,10604,515],{"className":10605},[514],[212,10607,10609],{"className":10608},[487],[212,10610,10612],{"className":10611,"style":2937},[491],[212,10613],{},[212,10615],{"className":10616},[350,638],[212,10618],{"className":10619,"style":355},[354],[212,10621,320],{"className":10622},[359],[212,10624],{"className":10625,"style":355},[354],[212,10627,10629,10632],{"className":10628},[247],[212,10630],{"className":10631,"style":369},[251],[212,10633,314],{"className":10634},[256],"，从而 ",[212,10637,10639,10671],{"className":10638,"translate":216},[215],[212,10640,10642],{"className":10641},[220],[222,10643,10644],{"xmlns":224},[226,10645,10646,10668],{},[229,10647,10648,10654,10656,10658,10660,10662,10664,10666],{},[392,10649,10650,10652],{},[232,10651,396],{},[232,10653,234],{},[307,10655,310],{"stretchy":309},[232,10657,403],{},[232,10659,407],{"mathvariant":406},[232,10661,403],{},[307,10663,317],{"stretchy":309},[307,10665,320],{},[312,10667,323],{},[236,10669,10670],{"encoding":238},"D_f(P\\|P)=0",[212,10672,10674,10744],{"className":10673,"ariaHidden":243},[242],[212,10675,10677,10680,10720,10723,10726,10729,10732,10735,10738,10741],{"className":10676},[247],[212,10678],{"className":10679,"style":467},[251],[212,10681,10683,10686],{"className":10682},[256],[212,10684,396],{"className":10685,"style":474},[256,257],[212,10687,10689],{"className":10688},[478],[212,10690,10692,10712],{"className":10691},[482,483],[212,10693,10695,10709],{"className":10694},[487],[212,10696,10698],{"className":10697,"style":492},[491],[212,10699,10700,10703],{"style":495},[212,10701],{"className":10702,"style":500},[499],[212,10704,10706],{"className":10705},[504,505,506,507],[212,10707,234],{"className":10708,"style":258},[256,257,507],[212,10710,515],{"className":10711},[514],[212,10713,10715],{"className":10714},[487],[212,10716,10718],{"className":10717,"style":522},[491],[212,10719],{},[212,10721,310],{"className":10722},[343],[212,10724,403],{"className":10725,"style":531},[256,257],[212,10727,407],{"className":10728},[256],[212,10730,403],{"className":10731,"style":531},[256,257],[212,10733,317],{"className":10734},[350],[212,10736],{"className":10737,"style":355},[354],[212,10739,320],{"className":10740},[359],[212,10742],{"className":10743,"style":355},[354],[212,10745,10747,10750],{"className":10746},[247],[212,10748],{"className":10749,"style":369},[251],[212,10751,323],{"className":10752},[256],[11,10754,10755],{},"因此 f-散度天然具有非负性和「相同分布散度为零」的性质。",[2509,10757,10759],{"id":10758},"_22-凸性为何必需","2.2 凸性为何必需",[11,10761,10762,10763,10832,10833,10861],{},"有人会问：凸性是不是一个过强的技术条件？答案是否定的。若要求 ",[212,10764,10766,10783],{"className":10765,"translate":216},[215],[212,10767,10769],{"className":10768},[220],[222,10770,10771],{"xmlns":224},[226,10772,10773,10781],{},[229,10774,10775],{},[392,10776,10777,10779],{},[232,10778,396],{},[232,10780,234],{},[236,10782,4220],{"encoding":238},[212,10784,10786],{"className":10785,"ariaHidden":243},[242],[212,10787,10789,10792],{"className":10788},[247],[212,10790],{"className":10791,"style":4230},[251],[212,10793,10795,10798],{"className":10794},[256],[212,10796,396],{"className":10797,"style":474},[256,257],[212,10799,10801],{"className":10800},[478],[212,10802,10804,10824],{"className":10803},[482,483],[212,10805,10807,10821],{"className":10806},[487],[212,10808,10810],{"className":10809,"style":492},[491],[212,10811,10812,10815],{"style":495},[212,10813],{"className":10814,"style":500},[499],[212,10816,10818],{"className":10817},[504,505,506,507],[212,10819,234],{"className":10820,"style":258},[256,257,507],[212,10822,515],{"className":10823},[514],[212,10825,10827],{"className":10826},[487],[212,10828,10830],{"className":10829,"style":522},[491],[212,10831],{}," 对一切「随机变换」（马尔可夫核）单调不增（即第 4.5 节的数据处理不等式），那么 ",[212,10834,10836,10849],{"className":10835,"translate":216},[215],[212,10837,10839],{"className":10838},[220],[222,10840,10841],{"xmlns":224},[226,10842,10843,10847],{},[229,10844,10845],{},[232,10846,234],{},[236,10848,234],{"encoding":238},[212,10850,10852],{"className":10851,"ariaHidden":243},[242],[212,10853,10855,10858],{"className":10854},[247],[212,10856],{"className":10857,"style":252},[251],[212,10859,234],{"className":10860,"style":258},[256,257]," 必须凸。二元分布上就能看到这一点。",[24,10863,10864],{},[11,10865,10866,10869,10870,11065,11066,11107,11108,11136,11137,11165],{},[1194,10867,10868],{},"命题 2.1（Csiszár 刻画）"," 若数据处理不等式 ",[212,10871,10873,10924],{"className":10872,"translate":216},[215],[212,10874,10876],{"className":10875},[220],[222,10877,10878],{"xmlns":224},[226,10879,10880,10921],{},[229,10881,10882,10888,10890,10892,10895,10897,10899,10901,10903,10905,10911,10913,10915,10917,10919],{},[392,10883,10884,10886],{},[232,10885,396],{},[232,10887,234],{},[307,10889,310],{"stretchy":309},[232,10891,403],{},[232,10893,10894],{},"K",[232,10896,407],{"mathvariant":406},[232,10898,410],{},[232,10900,10894],{},[307,10902,317],{"stretchy":309},[307,10904,10150],{},[392,10906,10907,10909],{},[232,10908,396],{},[232,10910,234],{},[307,10912,310],{"stretchy":309},[232,10914,403],{},[232,10916,407],{"mathvariant":406},[232,10918,410],{},[307,10920,317],{"stretchy":309},[236,10922,10923],{"encoding":238},"D_f(PK\\|QK)\\le D_f(P\\|Q)",[212,10925,10927,11004],{"className":10926,"ariaHidden":243},[242],[212,10928,10930,10933,10973,10976,10979,10983,10986,10989,10992,10995,10998,11001],{"className":10929},[247],[212,10931],{"className":10932,"style":467},[251],[212,10934,10936,10939],{"className":10935},[256],[212,10937,396],{"className":10938,"style":474},[256,257],[212,10940,10942],{"className":10941},[478],[212,10943,10945,10965],{"className":10944},[482,483],[212,10946,10948,10962],{"className":10947},[487],[212,10949,10951],{"className":10950,"style":492},[491],[212,10952,10953,10956],{"style":495},[212,10954],{"className":10955,"style":500},[499],[212,10957,10959],{"className":10958},[504,505,506,507],[212,10960,234],{"className":10961,"style":258},[256,257,507],[212,10963,515],{"className":10964},[514],[212,10966,10968],{"className":10967},[487],[212,10969,10971],{"className":10970,"style":522},[491],[212,10972],{},[212,10974,310],{"className":10975},[343],[212,10977,403],{"className":10978,"style":531},[256,257],[212,10980,10894],{"className":10981,"style":10982},[256,257],"margin-right:0.0715em;",[212,10984,407],{"className":10985},[256],[212,10987,410],{"className":10988},[256,257],[212,10990,10894],{"className":10991,"style":10982},[256,257],[212,10993,317],{"className":10994},[350],[212,10996],{"className":10997,"style":355},[354],[212,10999,10150],{"className":11000},[359],[212,11002],{"className":11003,"style":355},[354],[212,11005,11007,11010,11050,11053,11056,11059,11062],{"className":11006},[247],[212,11008],{"className":11009,"style":467},[251],[212,11011,11013,11016],{"className":11012},[256],[212,11014,396],{"className":11015,"style":474},[256,257],[212,11017,11019],{"className":11018},[478],[212,11020,11022,11042],{"className":11021},[482,483],[212,11023,11025,11039],{"className":11024},[487],[212,11026,11028],{"className":11027,"style":492},[491],[212,11029,11030,11033],{"style":495},[212,11031],{"className":11032,"style":500},[499],[212,11034,11036],{"className":11035},[504,505,506,507],[212,11037,234],{"className":11038,"style":258},[256,257,507],[212,11040,515],{"className":11041},[514],[212,11043,11045],{"className":11044},[487],[212,11046,11048],{"className":11047,"style":522},[491],[212,11049],{},[212,11051,310],{"className":11052},[343],[212,11054,403],{"className":11055,"style":531},[256,257],[212,11057,407],{"className":11058},[256],[212,11060,410],{"className":11061},[256,257],[212,11063,317],{"className":11064},[350]," 对一切概率对 ",[212,11067,11069,11086],{"className":11068,"translate":216},[215],[212,11070,11072],{"className":11071},[220],[222,11073,11074],{"xmlns":224},[226,11075,11076,11084],{},[229,11077,11078,11080,11082],{},[232,11079,403],{},[307,11081,748],{"separator":243},[232,11083,410],{},[236,11085,753],{"encoding":238},[212,11087,11089],{"className":11088,"ariaHidden":243},[242],[212,11090,11092,11095,11098,11101,11104],{"className":11091},[247],[212,11093],{"className":11094,"style":763},[251],[212,11096,403],{"className":11097,"style":531},[256,257],[212,11099,748],{"className":11100},[770],[212,11102],{"className":11103,"style":603},[354],[212,11105,410],{"className":11106},[256,257]," 与一切马尔可夫核 ",[212,11109,11111,11124],{"className":11110,"translate":216},[215],[212,11112,11114],{"className":11113},[220],[222,11115,11116],{"xmlns":224},[226,11117,11118,11122],{},[229,11119,11120],{},[232,11121,10894],{},[236,11123,10894],{"encoding":238},[212,11125,11127],{"className":11126,"ariaHidden":243},[242],[212,11128,11130,11133],{"className":11129},[247],[212,11131],{"className":11132,"style":861},[251],[212,11134,10894],{"className":11135,"style":10982},[256,257]," 成立，则 ",[212,11138,11140,11153],{"className":11139,"translate":216},[215],[212,11141,11143],{"className":11142},[220],[222,11144,11145],{"xmlns":224},[226,11146,11147,11151],{},[229,11148,11149],{},[232,11150,234],{},[236,11152,234],{"encoding":238},[212,11154,11156],{"className":11155,"ariaHidden":243},[242],[212,11157,11159,11162],{"className":11158},[247],[212,11160],{"className":11161,"style":252},[251],[212,11163,234],{"className":11164,"style":258},[256,257]," 凸。",[11,11167,11168],{},[1194,11169,11170],{},"证明（两步）。",[11,11172,11173,11260,11261,2478,11495,11524,11525,11601,11602,5843,11800,11997,11998,12135],{},[1194,11174,11175,11176,6692,11207,11259],{},"第一步：DPI ",[212,11177,11179,11194],{"className":11178,"translate":216},[215],[212,11180,11182],{"className":11181},[220],[222,11183,11184],{"xmlns":224},[226,11185,11186,11191],{},[229,11187,11188],{},[307,11189,11190],{},"⇒",[236,11192,11193],{"encoding":238},"\\Rightarrow",[212,11195,11197],{"className":11196,"ariaHidden":243},[242],[212,11198,11200,11204],{"className":11199},[247],[212,11201],{"className":11202,"style":11203},[251],"height:0.3669em;",[212,11205,11190],{"className":11206},[359],[212,11208,11210,11232],{"className":11209,"translate":216},[215],[212,11211,11213],{"className":11212},[220],[222,11214,11215],{"xmlns":224},[226,11216,11217,11229],{},[229,11218,11219,11221,11223,11225,11227],{},[307,11220,310],{"stretchy":309},[232,11222,403],{},[307,11224,748],{"separator":243},[232,11226,410],{},[307,11228,317],{"stretchy":309},[236,11230,11231],{"encoding":238},"(P,Q)",[212,11233,11235],{"className":11234,"ariaHidden":243},[242],[212,11236,11238,11241,11244,11247,11250,11253,11256],{"className":11237},[247],[212,11239],{"className":11240,"style":336},[251],[212,11242,310],{"className":11243},[343],[212,11245,403],{"className":11246,"style":531},[256,257],[212,11248,748],{"className":11249},[770],[212,11251],{"className":11252,"style":603},[354],[212,11254,410],{"className":11255},[256,257],[212,11257,317],{"className":11258},[350]," 联合凸。"," 设 ",[212,11262,11264,11306],{"className":11263,"translate":216},[215],[212,11265,11267],{"className":11266},[220],[222,11268,11269],{"xmlns":224},[226,11270,11271,11303],{},[229,11272,11273,11279,11281,11287,11289,11295,11297],{},[392,11274,11275,11277],{},[232,11276,403],{},[312,11278,314],{},[307,11280,748],{"separator":243},[392,11282,11283,11285],{},[232,11284,403],{},[312,11286,2661],{},[307,11288,748],{"separator":243},[392,11290,11291,11293],{},[232,11292,410],{},[312,11294,314],{},[307,11296,748],{"separator":243},[392,11298,11299,11301],{},[232,11300,410],{},[312,11302,2661],{},[236,11304,11305],{"encoding":238},"P_1,P_2,Q_1,Q_2",[212,11307,11309],{"className":11308,"ariaHidden":243},[242],[212,11310,11312,11315,11357,11360,11363,11403,11406,11409,11449,11452,11455],{"className":11311},[247],[212,11313],{"className":11314,"style":763},[251],[212,11316,11318,11321],{"className":11317},[256],[212,11319,403],{"className":11320,"style":531},[256,257],[212,11322,11324],{"className":11323},[478],[212,11325,11327,11349],{"className":11326},[482,483],[212,11328,11330,11346],{"className":11329},[487],[212,11331,11334],{"className":11332,"style":11333},[491],"height:0.3011em;",[212,11335,11337,11340],{"style":11336},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[212,11338],{"className":11339,"style":500},[499],[212,11341,11343],{"className":11342},[504,505,506,507],[212,11344,314],{"className":11345},[256,507],[212,11347,515],{"className":11348},[514],[212,11350,11352],{"className":11351},[487],[212,11353,11355],{"className":11354,"style":8166},[491],[212,11356],{},[212,11358,748],{"className":11359},[770],[212,11361],{"className":11362,"style":603},[354],[212,11364,11366,11369],{"className":11365},[256],[212,11367,403],{"className":11368,"style":531},[256,257],[212,11370,11372],{"className":11371},[478],[212,11373,11375,11395],{"className":11374},[482,483],[212,11376,11378,11392],{"className":11377},[487],[212,11379,11381],{"className":11380,"style":11333},[491],[212,11382,11383,11386],{"style":11336},[212,11384],{"className":11385,"style":500},[499],[212,11387,11389],{"className":11388},[504,505,506,507],[212,11390,2661],{"className":11391},[256,507],[212,11393,515],{"className":11394},[514],[212,11396,11398],{"className":11397},[487],[212,11399,11401],{"className":11400,"style":8166},[491],[212,11402],{},[212,11404,748],{"className":11405},[770],[212,11407],{"className":11408,"style":603},[354],[212,11410,11412,11415],{"className":11411},[256],[212,11413,410],{"className":11414},[256,257],[212,11416,11418],{"className":11417},[478],[212,11419,11421,11441],{"className":11420},[482,483],[212,11422,11424,11438],{"className":11423},[487],[212,11425,11427],{"className":11426,"style":11333},[491],[212,11428,11429,11432],{"style":579},[212,11430],{"className":11431,"style":500},[499],[212,11433,11435],{"className":11434},[504,505,506,507],[212,11436,314],{"className":11437},[256,507],[212,11439,515],{"className":11440},[514],[212,11442,11444],{"className":11443},[487],[212,11445,11447],{"className":11446,"style":8166},[491],[212,11448],{},[212,11450,748],{"className":11451},[770],[212,11453],{"className":11454,"style":603},[354],[212,11456,11458,11461],{"className":11457},[256],[212,11459,410],{"className":11460},[256,257],[212,11462,11464],{"className":11463},[478],[212,11465,11467,11487],{"className":11466},[482,483],[212,11468,11470,11484],{"className":11469},[487],[212,11471,11473],{"className":11472,"style":11333},[491],[212,11474,11475,11478],{"style":579},[212,11476],{"className":11477,"style":500},[499],[212,11479,11481],{"className":11480},[504,505,506,507],[212,11482,2661],{"className":11483},[256,507],[212,11485,515],{"className":11486},[514],[212,11488,11490],{"className":11489},[487],[212,11491,11493],{"className":11492,"style":8166},[491],[212,11494],{},[212,11496,11498,11512],{"className":11497,"translate":216},[215],[212,11499,11501],{"className":11500},[220],[222,11502,11503],{"xmlns":224},[226,11504,11505,11509],{},[229,11506,11507],{},[232,11508,795],{"mathvariant":794},[236,11510,11511],{"encoding":238},"\\mathcal X",[212,11513,11515],{"className":11514,"ariaHidden":243},[242],[212,11516,11518,11521],{"className":11517},[247],[212,11519],{"className":11520,"style":861},[251],[212,11522,795],{"className":11523,"style":822},[256,821]," 上任给的四对分布，",[212,11526,11528,11555],{"className":11527,"translate":216},[215],[212,11529,11531],{"className":11530},[220],[222,11532,11533],{"xmlns":224},[226,11534,11535,11552],{},[229,11536,11537,11540,11542,11544,11546,11548,11550],{},[232,11538,11539],{},"λ",[307,11541,6107],{},[307,11543,310],{"stretchy":309},[312,11545,323],{},[307,11547,748],{"separator":243},[312,11549,314],{},[307,11551,317],{"stretchy":309},[236,11553,11554],{"encoding":238},"\\lambda\\in(0,1)",[212,11556,11558,11577],{"className":11557,"ariaHidden":243},[242],[212,11559,11561,11565,11568,11571,11574],{"className":11560},[247],[212,11562],{"className":11563,"style":11564},[251],"height:0.7335em;vertical-align:-0.0391em;",[212,11566,11539],{"className":11567},[256,257],[212,11569],{"className":11570,"style":355},[354],[212,11572,6107],{"className":11573},[359],[212,11575],{"className":11576,"style":355},[354],[212,11578,11580,11583,11586,11589,11592,11595,11598],{"className":11579},[247],[212,11581],{"className":11582,"style":336},[251],[212,11584,310],{"className":11585},[343],[212,11587,323],{"className":11588},[256],[212,11590,748],{"className":11591},[770],[212,11593],{"className":11594,"style":603},[354],[212,11596,314],{"className":11597},[256],[212,11599,317],{"className":11600},[350],"，记 ",[212,11603,11605,11647],{"className":11604,"translate":216},[215],[212,11606,11608],{"className":11607},[220],[222,11609,11610],{"xmlns":224},[226,11611,11612,11644],{},[229,11613,11614,11616,11618,11620,11626,11628,11630,11632,11634,11636,11638],{},[232,11615,403],{},[307,11617,320],{},[232,11619,11539],{},[392,11621,11622,11624],{},[232,11623,403],{},[312,11625,314],{},[307,11627,2668],{},[307,11629,310],{"stretchy":309},[312,11631,314],{},[307,11633,5011],{},[232,11635,11539],{},[307,11637,317],{"stretchy":309},[392,11639,11640,11642],{},[232,11641,403],{},[312,11643,2661],{},[236,11645,11646],{"encoding":238},"P=\\lambda P_1+(1-\\lambda)P_2",[212,11648,11650,11668,11727,11748],{"className":11649,"ariaHidden":243},[242],[212,11651,11653,11656,11659,11662,11665],{"className":11652},[247],[212,11654],{"className":11655,"style":861},[251],[212,11657,403],{"className":11658,"style":531},[256,257],[212,11660],{"className":11661,"style":355},[354],[212,11663,320],{"className":11664},[359],[212,11666],{"className":11667,"style":355},[354],[212,11669,11671,11675,11678,11718,11721,11724],{"className":11670},[247],[212,11672],{"className":11673,"style":11674},[251],"height:0.8444em;vertical-align:-0.15em;",[212,11676,11539],{"className":11677},[256,257],[212,11679,11681,11684],{"className":11680},[256],[212,11682,403],{"className":11683,"style":531},[256,257],[212,11685,11687],{"className":11686},[478],[212,11688,11690,11710],{"className":11689},[482,483],[212,11691,11693,11707],{"className":11692},[487],[212,11694,11696],{"className":11695,"style":11333},[491],[212,11697,11698,11701],{"style":11336},[212,11699],{"className":11700,"style":500},[499],[212,11702,11704],{"className":11703},[504,505,506,507],[212,11705,314],{"className":11706},[256,507],[212,11708,515],{"className":11709},[514],[212,11711,11713],{"className":11712},[487],[212,11714,11716],{"className":11715,"style":8166},[491],[212,11717],{},[212,11719],{"className":11720,"style":2785},[354],[212,11722,2668],{"className":11723},[2789],[212,11725],{"className":11726,"style":2785},[354],[212,11728,11730,11733,11736,11739,11742,11745],{"className":11729},[247],[212,11731],{"className":11732,"style":336},[251],[212,11734,310],{"className":11735},[343],[212,11737,314],{"className":11738},[256],[212,11740],{"className":11741,"style":2785},[354],[212,11743,5011],{"className":11744},[2789],[212,11746],{"className":11747,"style":2785},[354],[212,11749,11751,11754,11757,11760],{"className":11750},[247],[212,11752],{"className":11753,"style":336},[251],[212,11755,11539],{"className":11756},[256,257],[212,11758,317],{"className":11759},[350],[212,11761,11763,11766],{"className":11762},[256],[212,11764,403],{"className":11765,"style":531},[256,257],[212,11767,11769],{"className":11768},[478],[212,11770,11772,11792],{"className":11771},[482,483],[212,11773,11775,11789],{"className":11774},[487],[212,11776,11778],{"className":11777,"style":11333},[491],[212,11779,11780,11783],{"style":11336},[212,11781],{"className":11782,"style":500},[499],[212,11784,11786],{"className":11785},[504,505,506,507],[212,11787,2661],{"className":11788},[256,507],[212,11790,515],{"className":11791},[514],[212,11793,11795],{"className":11794},[487],[212,11796,11798],{"className":11797,"style":8166},[491],[212,11799],{},[212,11801,11803,11845],{"className":11802,"translate":216},[215],[212,11804,11806],{"className":11805},[220],[222,11807,11808],{"xmlns":224},[226,11809,11810,11842],{},[229,11811,11812,11814,11816,11818,11824,11826,11828,11830,11832,11834,11836],{},[232,11813,410],{},[307,11815,320],{},[232,11817,11539],{},[392,11819,11820,11822],{},[232,11821,410],{},[312,11823,314],{},[307,11825,2668],{},[307,11827,310],{"stretchy":309},[312,11829,314],{},[307,11831,5011],{},[232,11833,11539],{},[307,11835,317],{"stretchy":309},[392,11837,11838,11840],{},[232,11839,410],{},[312,11841,2661],{},[236,11843,11844],{"encoding":238},"Q=\\lambda Q_1+(1-\\lambda)Q_2",[212,11846,11848,11866,11924,11945],{"className":11847,"ariaHidden":243},[242],[212,11849,11851,11854,11857,11860,11863],{"className":11850},[247],[212,11852],{"className":11853,"style":763},[251],[212,11855,410],{"className":11856},[256,257],[212,11858],{"className":11859,"style":355},[354],[212,11861,320],{"className":11862},[359],[212,11864],{"className":11865,"style":355},[354],[212,11867,11869,11872,11875,11915,11918,11921],{"className":11868},[247],[212,11870],{"className":11871,"style":252},[251],[212,11873,11539],{"className":11874},[256,257],[212,11876,11878,11881],{"className":11877},[256],[212,11879,410],{"className":11880},[256,257],[212,11882,11884],{"className":11883},[478],[212,11885,11887,11907],{"className":11886},[482,483],[212,11888,11890,11904],{"className":11889},[487],[212,11891,11893],{"className":11892,"style":11333},[491],[212,11894,11895,11898],{"style":579},[212,11896],{"className":11897,"style":500},[499],[212,11899,11901],{"className":11900},[504,505,506,507],[212,11902,314],{"className":11903},[256,507],[212,11905,515],{"className":11906},[514],[212,11908,11910],{"className":11909},[487],[212,11911,11913],{"className":11912,"style":8166},[491],[212,11914],{},[212,11916],{"className":11917,"style":2785},[354],[212,11919,2668],{"className":11920},[2789],[212,11922],{"className":11923,"style":2785},[354],[212,11925,11927,11930,11933,11936,11939,11942],{"className":11926},[247],[212,11928],{"className":11929,"style":336},[251],[212,11931,310],{"className":11932},[343],[212,11934,314],{"className":11935},[256],[212,11937],{"className":11938,"style":2785},[354],[212,11940,5011],{"className":11941},[2789],[212,11943],{"className":11944,"style":2785},[354],[212,11946,11948,11951,11954,11957],{"className":11947},[247],[212,11949],{"className":11950,"style":336},[251],[212,11952,11539],{"className":11953},[256,257],[212,11955,317],{"className":11956},[350],[212,11958,11960,11963],{"className":11959},[256],[212,11961,410],{"className":11962},[256,257],[212,11964,11966],{"className":11965},[478],[212,11967,11969,11989],{"className":11968},[482,483],[212,11970,11972,11986],{"className":11971},[487],[212,11973,11975],{"className":11974,"style":11333},[491],[212,11976,11977,11980],{"style":579},[212,11978],{"className":11979,"style":500},[499],[212,11981,11983],{"className":11982},[504,505,506,507],[212,11984,2661],{"className":11985},[256,507],[212,11987,515],{"className":11988},[514],[212,11990,11992],{"className":11991},[487],[212,11993,11995],{"className":11994,"style":8166},[491],[212,11996],{},"。构造扩大一倍的样本空间 ",[212,11999,12001,12038],{"className":12000,"translate":216},[215],[212,12002,12004],{"className":12003},[220],[222,12005,12006],{"xmlns":224},[226,12007,12008,12035],{},[229,12009,12010,12018,12020,12022,12024,12026,12028,12030,12033],{},[12011,12012,12013,12015],"mover",{"accent":243},[232,12014,795],{"mathvariant":794},[307,12016,12017],{},"~",[307,12019,320],{},[307,12021,3096],{"stretchy":309},[312,12023,314],{},[307,12025,748],{"separator":243},[312,12027,2661],{},[307,12029,3106],{"stretchy":309},[307,12031,12032],{},"×",[232,12034,795],{"mathvariant":794},[236,12036,12037],{"encoding":238},"\\tilde{\\mathcal X}=\\{1,2\\}\\times\\mathcal X",[212,12039,12041,12093,12126],{"className":12040,"ariaHidden":243},[242],[212,12042,12044,12048,12084,12087,12090],{"className":12043},[247],[212,12045],{"className":12046,"style":12047},[251],"height:0.9202em;",[212,12049,12052],{"className":12050},[256,12051],"accent",[212,12053,12055],{"className":12054},[482],[212,12056,12058],{"className":12057},[487],[212,12059,12061,12070],{"className":12060,"style":12047},[491],[212,12062,12064,12067],{"style":12063},"top:-3em;",[212,12065],{"className":12066,"style":658},[499],[212,12068,795],{"className":12069,"style":822},[256,821],[212,12071,12073,12076],{"style":12072},"top:-3.6023em;",[212,12074],{"className":12075,"style":658},[499],[212,12077,12081],{"className":12078,"style":12080},[12079],"accent-body","left:-0.1111em;",[212,12082,12017],{"className":12083},[256],[212,12085],{"className":12086,"style":355},[354],[212,12088,320],{"className":12089},[359],[212,12091],{"className":12092,"style":355},[354],[212,12094,12096,12099,12102,12105,12108,12111,12114,12117,12120,12123],{"className":12095},[247],[212,12097],{"className":12098,"style":336},[251],[212,12100,3096],{"className":12101},[343],[212,12103,314],{"className":12104},[256],[212,12106,748],{"className":12107},[770],[212,12109],{"className":12110,"style":603},[354],[212,12112,2661],{"className":12113},[256],[212,12115,3106],{"className":12116},[350],[212,12118],{"className":12119,"style":2785},[354],[212,12121,12032],{"className":12122},[2789],[212,12124],{"className":12125,"style":2785},[354],[212,12127,12129,12132],{"className":12128},[247],[212,12130],{"className":12131,"style":861},[251],[212,12133,795],{"className":12134,"style":822},[256,821]," 及其上的两个分块分布：",[212,12137,12139],{"className":12138,"translate":216},[377],[212,12140,12142,12277],{"className":12141,"translate":216},[215],[212,12143,12145],{"className":12144},[220],[222,12146,12147],{"xmlns":224,"display":386},[226,12148,12149,12274],{},[229,12150,12151,12157,12159,12161,12164,12166,12168,12170,12172,12174,12180,12182,12188,12190,12192,12194,12196,12198,12204,12206,12208,12210,12212,12214,12216,12218,12220,12226,12228,12234,12236,12238,12240,12242,12244,12250,12252,12254,12256,12258,12264,12266,12268,12270,12272],{},[12011,12152,12153,12155],{"accent":243},[232,12154,403],{},[307,12156,12017],{},[307,12158,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,12160,310],{"stretchy":309},[232,12162,12163],{},"i",[307,12165,748],{"separator":243},[232,12167,971],{},[307,12169,317],{"stretchy":309},[307,12171,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,12173,320],{},[392,12175,12176,12178],{},[232,12177,7768],{},[232,12179,12163],{},[1495,12181,1497],{},[392,12183,12184,12186],{},[232,12185,403],{},[232,12187,12163],{},[307,12189,310],{"stretchy":309},[232,12191,971],{},[307,12193,317],{"stretchy":309},[307,12195,748],{"separator":243},[354,12197],{"width":3460},[12011,12199,12200,12202],{"accent":243},[232,12201,410],{},[307,12203,12017],{},[307,12205,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,12207,310],{"stretchy":309},[232,12209,12163],{},[307,12211,748],{"separator":243},[232,12213,971],{},[307,12215,317],{"stretchy":309},[307,12217,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,12219,320],{},[392,12221,12222,12224],{},[232,12223,7768],{},[232,12225,12163],{},[1495,12227,1497],{},[392,12229,12230,12232],{},[232,12231,410],{},[232,12233,12163],{},[307,12235,310],{"stretchy":309},[232,12237,971],{},[307,12239,317],{"stretchy":309},[307,12241,748],{"separator":243},[354,12243],{"width":3460},[392,12245,12246,12248],{},[232,12247,7768],{},[312,12249,314],{},[307,12251,320],{},[232,12253,11539],{},[307,12255,748],{"separator":243},[1495,12257,4481],{},[392,12259,12260,12262],{},[232,12261,7768],{},[312,12263,2661],{},[307,12265,320],{},[312,12267,314],{},[307,12269,5011],{},[232,12271,11539],{},[232,12273,4573],{"mathvariant":406},[236,12275,12276],{"encoding":238},"\\tilde P\\big((i,x)\\big)=w_i\\,P_i(x),\\qquad\n\\tilde Q\\big((i,x)\\big)=w_i\\,Q_i(x),\\qquad\nw_1=\\lambda,\\ w_2=1-\\lambda .",[212,12278,12280,12358,12549,12705,12772,12791],{"className":12279,"ariaHidden":243},[242],[212,12281,12283,12287,12319,12325,12328,12331,12334,12337,12340,12343,12349,12352,12355],{"className":12282},[247],[212,12284],{"className":12285,"style":12286},[251],"height:1.2702em;vertical-align:-0.35em;",[212,12288,12290],{"className":12289},[256,12051],[212,12291,12293],{"className":12292},[482],[212,12294,12296],{"className":12295},[487],[212,12297,12299,12307],{"className":12298,"style":12047},[491],[212,12300,12301,12304],{"style":12063},[212,12302],{"className":12303,"style":658},[499],[212,12305,403],{"className":12306,"style":531},[256,257],[212,12308,12309,12312],{"style":12072},[212,12310],{"className":12311,"style":658},[499],[212,12313,12316],{"className":12314,"style":12315},[12079],"left:-0.1667em;",[212,12317,12017],{"className":12318},[256],[212,12320,12322],{"className":12321},[256],[212,12323,310],{"className":12324},[616,9872],[212,12326,310],{"className":12327},[343],[212,12329,12163],{"className":12330},[256,257],[212,12332,748],{"className":12333},[770],[212,12335],{"className":12336,"style":603},[354],[212,12338,971],{"className":12339},[256,257],[212,12341,317],{"className":12342},[350],[212,12344,12346],{"className":12345},[256],[212,12347,317],{"className":12348},[616,9872],[212,12350],{"className":12351,"style":355},[354],[212,12353,320],{"className":12354},[359],[212,12356],{"className":12357,"style":355},[354],[212,12359,12361,12364,12406,12409,12449,12452,12455,12458,12461,12464,12467,12510,12516,12519,12522,12525,12528,12531,12534,12540,12543,12546],{"className":12360},[247],[212,12362],{"className":12363,"style":12286},[251],[212,12365,12367,12370],{"className":12366},[256],[212,12368,7768],{"className":12369,"style":8472},[256,257],[212,12371,12373],{"className":12372},[478],[212,12374,12376,12398],{"className":12375},[482,483],[212,12377,12379,12395],{"className":12378},[487],[212,12380,12383],{"className":12381,"style":12382},[491],"height:0.3117em;",[212,12384,12386,12389],{"style":12385},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[212,12387],{"className":12388,"style":500},[499],[212,12390,12392],{"className":12391},[504,505,506,507],[212,12393,12163],{"className":12394},[256,257,507],[212,12396,515],{"className":12397},[514],[212,12399,12401],{"className":12400},[487],[212,12402,12404],{"className":12403,"style":8166},[491],[212,12405],{},[212,12407],{"className":12408,"style":603},[354],[212,12410,12412,12415],{"className":12411},[256],[212,12413,403],{"className":12414,"style":531},[256,257],[212,12416,12418],{"className":12417},[478],[212,12419,12421,12441],{"className":12420},[482,483],[212,12422,12424,12438],{"className":12423},[487],[212,12425,12427],{"className":12426,"style":12382},[491],[212,12428,12429,12432],{"style":11336},[212,12430],{"className":12431,"style":500},[499],[212,12433,12435],{"className":12434},[504,505,506,507],[212,12436,12163],{"className":12437},[256,257,507],[212,12439,515],{"className":12440},[514],[212,12442,12444],{"className":12443},[487],[212,12445,12447],{"className":12446,"style":8166},[491],[212,12448],{},[212,12450,310],{"className":12451},[343],[212,12453,971],{"className":12454},[256,257],[212,12456,317],{"className":12457},[350],[212,12459,748],{"className":12460},[770],[212,12462],{"className":12463,"style":3832},[354],[212,12465],{"className":12466,"style":603},[354],[212,12468,12470],{"className":12469},[256,12051],[212,12471,12473,12501],{"className":12472},[482,483],[212,12474,12476,12498],{"className":12475},[487],[212,12477,12479,12487],{"className":12478,"style":12047},[491],[212,12480,12481,12484],{"style":12063},[212,12482],{"className":12483,"style":658},[499],[212,12485,410],{"className":12486},[256,257],[212,12488,12489,12492],{"style":12072},[212,12490],{"className":12491,"style":658},[499],[212,12493,12495],{"className":12494,"style":12315},[12079],[212,12496,12017],{"className":12497},[256],[212,12499,515],{"className":12500},[514],[212,12502,12504],{"className":12503},[487],[212,12505,12508],{"className":12506,"style":12507},[491],"height:0.1944em;",[212,12509],{},[212,12511,12513],{"className":12512},[256],[212,12514,310],{"className":12515},[616,9872],[212,12517,310],{"className":12518},[343],[212,12520,12163],{"className":12521},[256,257],[212,12523,748],{"className":12524},[770],[212,12526],{"className":12527,"style":603},[354],[212,12529,971],{"className":12530},[256,257],[212,12532,317],{"className":12533},[350],[212,12535,12537],{"className":12536},[256],[212,12538,317],{"className":12539},[616,9872],[212,12541],{"className":12542,"style":355},[354],[212,12544,320],{"className":12545},[359],[212,12547],{"className":12548,"style":355},[354],[212,12550,12552,12555,12595,12598,12638,12641,12644,12647,12650,12653,12656,12696,12699,12702],{"className":12551},[247],[212,12553],{"className":12554,"style":336},[251],[212,12556,12558,12561],{"className":12557},[256],[212,12559,7768],{"className":12560,"style":8472},[256,257],[212,12562,12564],{"className":12563},[478],[212,12565,12567,12587],{"className":12566},[482,483],[212,12568,12570,12584],{"className":12569},[487],[212,12571,12573],{"className":12572,"style":12382},[491],[212,12574,12575,12578],{"style":12385},[212,12576],{"className":12577,"style":500},[499],[212,12579,12581],{"className":12580},[504,505,506,507],[212,12582,12163],{"className":12583},[256,257,507],[212,12585,515],{"className":12586},[514],[212,12588,12590],{"className":12589},[487],[212,12591,12593],{"className":12592,"style":8166},[491],[212,12594],{},[212,12596],{"className":12597,"style":603},[354],[212,12599,12601,12604],{"className":12600},[256],[212,12602,410],{"className":12603},[256,257],[212,12605,12607],{"className":12606},[478],[212,12608,12610,12630],{"className":12609},[482,483],[212,12611,12613,12627],{"className":12612},[487],[212,12614,12616],{"className":12615,"style":12382},[491],[212,12617,12618,12621],{"style":579},[212,12619],{"className":12620,"style":500},[499],[212,12622,12624],{"className":12623},[504,505,506,507],[212,12625,12163],{"className":12626},[256,257,507],[212,12628,515],{"className":12629},[514],[212,12631,12633],{"className":12632},[487],[212,12634,12636],{"className":12635,"style":8166},[491],[212,12637],{},[212,12639,310],{"className":12640},[343],[212,12642,971],{"className":12643},[256,257],[212,12645,317],{"className":12646},[350],[212,12648,748],{"className":12649},[770],[212,12651],{"className":12652,"style":3832},[354],[212,12654],{"className":12655,"style":603},[354],[212,12657,12659,12662],{"className":12658},[256],[212,12660,7768],{"className":12661,"style":8472},[256,257],[212,12663,12665],{"className":12664},[478],[212,12666,12668,12688],{"className":12667},[482,483],[212,12669,12671,12685],{"className":12670},[487],[212,12672,12674],{"className":12673,"style":11333},[491],[212,12675,12676,12679],{"style":12385},[212,12677],{"className":12678,"style":500},[499],[212,12680,12682],{"className":12681},[504,505,506,507],[212,12683,314],{"className":12684},[256,507],[212,12686,515],{"className":12687},[514],[212,12689,12691],{"className":12690},[487],[212,12692,12694],{"className":12693,"style":8166},[491],[212,12695],{},[212,12697],{"className":12698,"style":355},[354],[212,12700,320],{"className":12701},[359],[212,12703],{"className":12704,"style":355},[354],[212,12706,12708,12711,12714,12717,12720,12723,12763,12766,12769],{"className":12707},[247],[212,12709],{"className":12710,"style":252},[251],[212,12712,11539],{"className":12713},[256,257],[212,12715,748],{"className":12716},[770],[212,12718,4481],{"className":12719},[354],[212,12721],{"className":12722,"style":603},[354],[212,12724,12726,12729],{"className":12725},[256],[212,12727,7768],{"className":12728,"style":8472},[256,257],[212,12730,12732],{"className":12731},[478],[212,12733,12735,12755],{"className":12734},[482,483],[212,12736,12738,12752],{"className":12737},[487],[212,12739,12741],{"className":12740,"style":11333},[491],[212,12742,12743,12746],{"style":12385},[212,12744],{"className":12745,"style":500},[499],[212,12747,12749],{"className":12748},[504,505,506,507],[212,12750,2661],{"className":12751},[256,507],[212,12753,515],{"className":12754},[514],[212,12756,12758],{"className":12757},[487],[212,12759,12761],{"className":12760,"style":8166},[491],[212,12762],{},[212,12764],{"className":12765,"style":355},[354],[212,12767,320],{"className":12768},[359],[212,12770],{"className":12771,"style":355},[354],[212,12773,12775,12779,12782,12785,12788],{"className":12774},[247],[212,12776],{"className":12777,"style":12778},[251],"height:0.7278em;vertical-align:-0.0833em;",[212,12780,314],{"className":12781},[256],[212,12783],{"className":12784,"style":2785},[354],[212,12786,5011],{"className":12787},[2789],[212,12789],{"className":12790,"style":2785},[354],[212,12792,12794,12798,12801],{"className":12793},[247],[212,12795],{"className":12796,"style":12797},[251],"height:0.6944em;",[212,12799,11539],{"className":12800},[256,257],[212,12802,4573],{"className":12803},[256],[11,12805,12806,12807,6692,12810,12911,12912,12940,12941,5843,13029,13129,13130,13543,13544,13615],{},"取",[1194,12808,12809],{},"确定性核",[212,12811,12813,12845],{"className":12812,"translate":216},[215],[212,12814,12816],{"className":12815},[220],[222,12817,12818],{"xmlns":224},[226,12819,12820,12842],{},[229,12821,12822,12824,12826,12828,12830,12832,12834,12836,12838,12840],{},[232,12823,10894],{},[307,12825,1214],{},[1495,12827,1497],{},[307,12829,310],{"stretchy":309},[232,12831,12163],{},[307,12833,748],{"separator":243},[232,12835,971],{},[307,12837,317],{"stretchy":309},[307,12839,8882],{},[232,12841,971],{},[236,12843,12844],{"encoding":238},"K:\\,(i,x)\\mapsto x",[212,12846,12848,12869,12902],{"className":12847,"ariaHidden":243},[242],[212,12849,12851,12854,12857,12860,12863,12866],{"className":12850},[247],[212,12852],{"className":12853,"style":861},[251],[212,12855,10894],{"className":12856,"style":10982},[256,257],[212,12858],{"className":12859,"style":355},[354],[212,12861,1214],{"className":12862},[359],[212,12864],{"className":12865,"style":603},[354],[212,12867],{"className":12868,"style":355},[354],[212,12870,12872,12875,12878,12881,12884,12887,12890,12893,12896,12899],{"className":12871},[247],[212,12873],{"className":12874,"style":336},[251],[212,12876,310],{"className":12877},[343],[212,12879,12163],{"className":12880},[256,257],[212,12882,748],{"className":12883},[770],[212,12885],{"className":12886,"style":603},[354],[212,12888,971],{"className":12889},[256,257],[212,12891,317],{"className":12892},[350],[212,12894],{"className":12895,"style":355},[354],[212,12897,8882],{"className":12898},[359],[212,12900],{"className":12901,"style":355},[354],[212,12903,12905,12908],{"className":12904},[247],[212,12906],{"className":12907,"style":2543},[251],[212,12909,971],{"className":12910},[256,257],"（\"擦掉\"分量下标，只保留 ",[212,12913,12915,12928],{"className":12914,"translate":216},[215],[212,12916,12918],{"className":12917},[220],[222,12919,12920],{"xmlns":224},[226,12921,12922,12926],{},[229,12923,12924],{},[232,12925,971],{},[236,12927,971],{"encoding":238},[212,12929,12931],{"className":12930,"ariaHidden":243},[242],[212,12932,12934,12937],{"className":12933},[247],[212,12935],{"className":12936,"style":2543},[251],[212,12938,971],{"className":12939},[256,257],"）。由分块结构立刻算出 ",[212,12942,12944,12968],{"className":12943,"translate":216},[215],[212,12945,12947],{"className":12946},[220],[222,12948,12949],{"xmlns":224},[226,12950,12951,12965],{},[229,12952,12953,12959,12961,12963],{},[12011,12954,12955,12957],{"accent":243},[232,12956,403],{},[307,12958,12017],{},[232,12960,10894],{},[307,12962,320],{},[232,12964,403],{},[236,12966,12967],{"encoding":238},"\\tilde PK=P",[212,12969,12971,13020],{"className":12970,"ariaHidden":243},[242],[212,12972,12974,12977,13008,13011,13014,13017],{"className":12973},[247],[212,12975],{"className":12976,"style":12047},[251],[212,12978,12980],{"className":12979},[256,12051],[212,12981,12983],{"className":12982},[482],[212,12984,12986],{"className":12985},[487],[212,12987,12989,12997],{"className":12988,"style":12047},[491],[212,12990,12991,12994],{"style":12063},[212,12992],{"className":12993,"style":658},[499],[212,12995,403],{"className":12996,"style":531},[256,257],[212,12998,12999,13002],{"style":12072},[212,13000],{"className":13001,"style":658},[499],[212,13003,13005],{"className":13004,"style":12315},[12079],[212,13006,12017],{"className":13007},[256],[212,13009,10894],{"className":13010,"style":10982},[256,257],[212,13012],{"className":13013,"style":355},[354],[212,13015,320],{"className":13016},[359],[212,13018],{"className":13019,"style":355},[354],[212,13021,13023,13026],{"className":13022},[247],[212,13024],{"className":13025,"style":861},[251],[212,13027,403],{"className":13028,"style":531},[256,257],[212,13030,13032,13056],{"className":13031,"translate":216},[215],[212,13033,13035],{"className":13034},[220],[222,13036,13037],{"xmlns":224},[226,13038,13039,13053],{},[229,13040,13041,13047,13049,13051],{},[12011,13042,13043,13045],{"accent":243},[232,13044,410],{},[307,13046,12017],{},[232,13048,10894],{},[307,13050,320],{},[232,13052,410],{},[236,13054,13055],{"encoding":238},"\\tilde QK=Q",[212,13057,13059,13120],{"className":13058,"ariaHidden":243},[242],[212,13060,13062,13066,13108,13111,13114,13117],{"className":13061},[247],[212,13063],{"className":13064,"style":13065},[251],"height:1.1146em;vertical-align:-0.1944em;",[212,13067,13069],{"className":13068},[256,12051],[212,13070,13072,13100],{"className":13071},[482,483],[212,13073,13075,13097],{"className":13074},[487],[212,13076,13078,13086],{"className":13077,"style":12047},[491],[212,13079,13080,13083],{"style":12063},[212,13081],{"className":13082,"style":658},[499],[212,13084,410],{"className":13085},[256,257],[212,13087,13088,13091],{"style":12072},[212,13089],{"className":13090,"style":658},[499],[212,13092,13094],{"className":13093,"style":12315},[12079],[212,13095,12017],{"className":13096},[256],[212,13098,515],{"className":13099},[514],[212,13101,13103],{"className":13102},[487],[212,13104,13106],{"className":13105,"style":12507},[491],[212,13107],{},[212,13109,10894],{"className":13110,"style":10982},[256,257],[212,13112],{"className":13113,"style":355},[354],[212,13115,320],{"className":13116},[359],[212,13118],{"className":13119,"style":355},[354],[212,13121,13123,13126],{"className":13122},[247],[212,13124],{"className":13125,"style":763},[251],[212,13127,410],{"className":13128},[256,257],"，且似然比是分块恒定的：",[212,13131,13133,13211],{"className":13132,"translate":216},[215],[212,13134,13136],{"className":13135},[220],[222,13137,13138],{"xmlns":224},[226,13139,13140,13208],{},[229,13141,13142,13166,13168,13170,13172,13174,13176,13178,13202,13204,13206],{},[1453,13143,13144],{"scriptlevel":323,"displaystyle":243},[435,13145,13146,13156],{},[229,13147,13148,13150],{},[232,13149,441],{},[12011,13151,13152,13154],{"accent":243},[232,13153,403],{},[307,13155,12017],{},[229,13157,13158,13160],{},[232,13159,441],{},[12011,13161,13162,13164],{"accent":243},[232,13163,410],{},[307,13165,12017],{},[307,13167,310],{"stretchy":309},[232,13169,12163],{},[307,13171,748],{"separator":243},[232,13173,971],{},[307,13175,317],{"stretchy":309},[307,13177,320],{},[1453,13179,13180],{"scriptlevel":323,"displaystyle":243},[435,13181,13182,13192],{},[229,13183,13184,13186],{},[232,13185,441],{},[392,13187,13188,13190],{},[232,13189,403],{},[232,13191,12163],{},[229,13193,13194,13196],{},[232,13195,441],{},[392,13197,13198,13200],{},[232,13199,410],{},[232,13201,12163],{},[307,13203,310],{"stretchy":309},[232,13205,971],{},[307,13207,317],{"stretchy":309},[236,13209,13210],{"encoding":238},"\\dfrac{d\\tilde P}{d\\tilde Q}(i,x)=\\dfrac{dP_i}{dQ_i}(x)",[212,13212,13214,13386],{"className":13213,"ariaHidden":243},[242],[212,13215,13217,13221,13359,13362,13365,13368,13371,13374,13377,13380,13383],{"className":13216},[247],[212,13218],{"className":13219,"style":13220},[251],"height:2.6018em;vertical-align:-1.0046em;",[212,13222,13224,13227,13356],{"className":13223},[256],[212,13225],{"className":13226},[343,638],[212,13228,13230],{"className":13229},[435],[212,13231,13233,13347],{"className":13232},[482,483],[212,13234,13236,13344],{"className":13235},[487],[212,13237,13240,13294,13302],{"className":13238,"style":13239},[491],"height:1.5972em;",[212,13241,13243,13246],{"style":13242},"top:-2.1898em;",[212,13244],{"className":13245,"style":658},[499],[212,13247,13249,13252],{"className":13248},[256],[212,13250,441],{"className":13251},[256,257],[212,13253,13255],{"className":13254},[256,12051],[212,13256,13258,13286],{"className":13257},[482,483],[212,13259,13261,13283],{"className":13260},[487],[212,13262,13264,13272],{"className":13263,"style":12047},[491],[212,13265,13266,13269],{"style":12063},[212,13267],{"className":13268,"style":658},[499],[212,13270,410],{"className":13271},[256,257],[212,13273,13274,13277],{"style":12072},[212,13275],{"className":13276,"style":658},[499],[212,13278,13280],{"className":13279,"style":12315},[12079],[212,13281,12017],{"className":13282},[256],[212,13284,515],{"className":13285},[514],[212,13287,13289],{"className":13288},[487],[212,13290,13292],{"className":13291,"style":12507},[491],[212,13293],{},[212,13295,13296,13299],{"style":670},[212,13297],{"className":13298,"style":658},[499],[212,13300],{"className":13301,"style":678},[677],[212,13303,13304,13307],{"style":681},[212,13305],{"className":13306,"style":658},[499],[212,13308,13310,13313],{"className":13309},[256],[212,13311,441],{"className":13312},[256,257],[212,13314,13316],{"className":13315},[256,12051],[212,13317,13319],{"className":13318},[482],[212,13320,13322],{"className":13321},[487],[212,13323,13325,13333],{"className":13324,"style":12047},[491],[212,13326,13327,13330],{"style":12063},[212,13328],{"className":13329,"style":658},[499],[212,13331,403],{"className":13332,"style":531},[256,257],[212,13334,13335,13338],{"style":12072},[212,13336],{"className":13337,"style":658},[499],[212,13339,13341],{"className":13340,"style":12315},[12079],[212,13342,12017],{"className":13343},[256],[212,13345,515],{"className":13346},[514],[212,13348,13350],{"className":13349},[487],[212,13351,13354],{"className":13352,"style":13353},[491],"height:1.0046em;",[212,13355],{},[212,13357],{"className":13358},[350,638],[212,13360,310],{"className":13361},[343],[212,13363,12163],{"className":13364},[256,257],[212,13366,748],{"className":13367},[770],[212,13369],{"className":13370,"style":603},[354],[212,13372,971],{"className":13373},[256,257],[212,13375,317],{"className":13376},[350],[212,13378],{"className":13379,"style":355},[354],[212,13381,320],{"className":13382},[359],[212,13384],{"className":13385,"style":355},[354],[212,13387,13389,13392,13534,13537,13540],{"className":13388},[247],[212,13390],{"className":13391,"style":1035},[251],[212,13393,13395,13398,13531],{"className":13394},[256],[212,13396],{"className":13397},[343,638],[212,13399,13401],{"className":13400},[435],[212,13402,13404,13523],{"className":13403},[482,483],[212,13405,13407,13520],{"className":13406},[487],[212,13408,13410,13461,13469],{"className":13409,"style":651},[491],[212,13411,13412,13415],{"style":654},[212,13413],{"className":13414,"style":658},[499],[212,13416,13418,13421],{"className":13417},[256],[212,13419,441],{"className":13420},[256,257],[212,13422,13424,13427],{"className":13423},[256],[212,13425,410],{"className":13426},[256,257],[212,13428,13430],{"className":13429},[478],[212,13431,13433,13453],{"className":13432},[482,483],[212,13434,13436,13450],{"className":13435},[487],[212,13437,13439],{"className":13438,"style":12382},[491],[212,13440,13441,13444],{"style":579},[212,13442],{"className":13443,"style":500},[499],[212,13445,13447],{"className":13446},[504,505,506,507],[212,13448,12163],{"className":13449},[256,257,507],[212,13451,515],{"className":13452},[514],[212,13454,13456],{"className":13455},[487],[212,13457,13459],{"className":13458,"style":8166},[491],[212,13460],{},[212,13462,13463,13466],{"style":670},[212,13464],{"className":13465,"style":658},[499],[212,13467],{"className":13468,"style":678},[677],[212,13470,13471,13474],{"style":681},[212,13472],{"className":13473,"style":658},[499],[212,13475,13477,13480],{"className":13476},[256],[212,13478,441],{"className":13479},[256,257],[212,13481,13483,13486],{"className":13482},[256],[212,13484,403],{"className":13485,"style":531},[256,257],[212,13487,13489],{"className":13488},[478],[212,13490,13492,13512],{"className":13491},[482,483],[212,13493,13495,13509],{"className":13494},[487],[212,13496,13498],{"className":13497,"style":12382},[491],[212,13499,13500,13503],{"style":11336},[212,13501],{"className":13502,"style":500},[499],[212,13504,13506],{"className":13505},[504,505,506,507],[212,13507,12163],{"className":13508},[256,257,507],[212,13510,515],{"className":13511},[514],[212,13513,13515],{"className":13514},[487],[212,13516,13518],{"className":13517,"style":8166},[491],[212,13519],{},[212,13521,515],{"className":13522},[514],[212,13524,13526],{"className":13525},[487],[212,13527,13529],{"className":13528,"style":703},[491],[212,13530],{},[212,13532],{"className":13533},[350,638],[212,13535,310],{"className":13536},[343],[212,13538,971],{"className":13539},[256,257],[212,13541,317],{"className":13542},[350],"（权重 ",[212,13545,13547,13565],{"className":13546,"translate":216},[215],[212,13548,13550],{"className":13549},[220],[222,13551,13552],{"xmlns":224},[226,13553,13554,13562],{},[229,13555,13556],{},[392,13557,13558,13560],{},[232,13559,7768],{},[232,13561,12163],{},[236,13563,13564],{"encoding":238},"w_i",[212,13566,13568],{"className":13567,"ariaHidden":243},[242],[212,13569,13571,13575],{"className":13570},[247],[212,13572],{"className":13573,"style":13574},[251],"height:0.5806em;vertical-align:-0.15em;",[212,13576,13578,13581],{"className":13577},[256],[212,13579,7768],{"className":13580,"style":8472},[256,257],[212,13582,13584],{"className":13583},[478],[212,13585,13587,13607],{"className":13586},[482,483],[212,13588,13590,13604],{"className":13589},[487],[212,13591,13593],{"className":13592,"style":12382},[491],[212,13594,13595,13598],{"style":12385},[212,13596],{"className":13597,"style":500},[499],[212,13599,13601],{"className":13600},[504,505,506,507],[212,13602,12163],{"className":13603},[256,257,507],[212,13605,515],{"className":13606},[514],[212,13608,13610],{"className":13609},[487],[212,13611,13613],{"className":13612,"style":8166},[491],[212,13614],{}," 在分子分母中约去）。代入定义：",[212,13617,13619],{"className":13618,"translate":216},[377],[212,13620,13622,13765],{"className":13621,"translate":216},[215],[212,13623,13625],{"className":13624},[220],[222,13626,13627],{"xmlns":224,"display":386},[226,13628,13629,13762],{},[229,13630,13631,13637,13639,13645,13647,13653,13655,13657,13664,13670,13672,13678,13680,13686,13688,13694,13696,13698,13700,13706,13708,13714,13716,13722,13724,13726,13728,13730,13732,13734,13736,13742,13744,13750,13752,13758,13760],{},[392,13632,13633,13635],{},[232,13634,396],{},[232,13636,234],{},[307,13638,310],{"stretchy":309},[12011,13640,13641,13643],{"accent":243},[232,13642,403],{},[307,13644,12017],{},[232,13646,407],{"mathvariant":406},[12011,13648,13649,13651],{"accent":243},[232,13650,410],{},[307,13652,12017],{},[307,13654,317],{"stretchy":309},[307,13656,320],{},[6214,13658,13659,13662],{},[307,13660,13661],{},"∑",[232,13663,12163],{},[392,13665,13666,13668],{},[232,13667,7768],{},[232,13669,12163],{},[1495,13671,1497],{},[392,13673,13674,13676],{},[232,13675,396],{},[232,13677,234],{},[307,13679,310],{"stretchy":309},[392,13681,13682,13684],{},[232,13683,403],{},[232,13685,12163],{},[232,13687,407],{"mathvariant":406},[392,13689,13690,13692],{},[232,13691,410],{},[232,13693,12163],{},[307,13695,317],{"stretchy":309},[307,13697,320],{},[232,13699,11539],{},[392,13701,13702,13704],{},[232,13703,396],{},[232,13705,234],{},[307,13707,310],{"stretchy":309},[392,13709,13710,13712],{},[232,13711,403],{},[312,13713,314],{},[232,13715,407],{"mathvariant":406},[392,13717,13718,13720],{},[232,13719,410],{},[312,13721,314],{},[307,13723,317],{"stretchy":309},[307,13725,2668],{},[307,13727,310],{"stretchy":309},[312,13729,314],{},[307,13731,5011],{},[232,13733,11539],{},[307,13735,317],{"stretchy":309},[392,13737,13738,13740],{},[232,13739,396],{},[232,13741,234],{},[307,13743,310],{"stretchy":309},[392,13745,13746,13748],{},[232,13747,403],{},[312,13749,2661],{},[232,13751,407],{"mathvariant":406},[392,13753,13754,13756],{},[232,13755,410],{},[312,13757,2661],{},[307,13759,317],{"stretchy":309},[232,13761,4573],{"mathvariant":406},[236,13763,13764],{"encoding":238},"D_f(\\tilde P\\|\\tilde Q)\n=\\sum_i w_i\\,D_f(P_i\\|Q_i)\n=\\lambda D_f(P_1\\|Q_1)+(1-\\lambda)D_f(P_2\\|Q_2).",[212,13766,13768,13906,14147,14294,14315],{"className":13767,"ariaHidden":243},[242],[212,13769,13771,13775,13815,13818,13849,13852,13894,13897,13900,13903],{"className":13770},[247],[212,13772],{"className":13773,"style":13774},[251],"height:1.2063em;vertical-align:-0.2861em;",[212,13776,13778,13781],{"className":13777},[256],[212,13779,396],{"className":13780,"style":474},[256,257],[212,13782,13784],{"className":13783},[478],[212,13785,13787,13807],{"className":13786},[482,483],[212,13788,13790,13804],{"className":13789},[487],[212,13791,13793],{"className":13792,"style":492},[491],[212,13794,13795,13798],{"style":495},[212,13796],{"className":13797,"style":500},[499],[212,13799,13801],{"className":13800},[504,505,506,507],[212,13802,234],{"className":13803,"style":258},[256,257,507],[212,13805,515],{"className":13806},[514],[212,13808,13810],{"className":13809},[487],[212,13811,13813],{"className":13812,"style":522},[491],[212,13814],{},[212,13816,310],{"className":13817},[343],[212,13819,13821],{"className":13820},[256,12051],[212,13822,13824],{"className":13823},[482],[212,13825,13827],{"className":13826},[487],[212,13828,13830,13838],{"className":13829,"style":12047},[491],[212,13831,13832,13835],{"style":12063},[212,13833],{"className":13834,"style":658},[499],[212,13836,403],{"className":13837,"style":531},[256,257],[212,13839,13840,13843],{"style":12072},[212,13841],{"className":13842,"style":658},[499],[212,13844,13846],{"className":13845,"style":12315},[12079],[212,13847,12017],{"className":13848},[256],[212,13850,407],{"className":13851},[256],[212,13853,13855],{"className":13854},[256,12051],[212,13856,13858,13886],{"className":13857},[482,483],[212,13859,13861,13883],{"className":13860},[487],[212,13862,13864,13872],{"className":13863,"style":12047},[491],[212,13865,13866,13869],{"style":12063},[212,13867],{"className":13868,"style":658},[499],[212,13870,410],{"className":13871},[256,257],[212,13873,13874,13877],{"style":12072},[212,13875],{"className":13876,"style":658},[499],[212,13878,13880],{"className":13879,"style":12315},[12079],[212,13881,12017],{"className":13882},[256],[212,13884,515],{"className":13885},[514],[212,13887,13889],{"className":13888},[487],[212,13890,13892],{"className":13891,"style":12507},[491],[212,13893],{},[212,13895,317],{"className":13896},[350],[212,13898],{"className":13899,"style":355},[354],[212,13901,320],{"className":13902},[359],[212,13904],{"className":13905,"style":355},[354],[212,13907,13909,13913,13963,13966,14006,14009,14049,14052,14092,14095,14135,14138,14141,14144],{"className":13908},[247],[212,13910],{"className":13911,"style":13912},[251],"height:2.3277em;vertical-align:-1.2777em;",[212,13914,13917],{"className":13915},[1682,13916],"op-limits",[212,13918,13920,13954],{"className":13919},[482,483],[212,13921,13923,13951],{"className":13922},[487],[212,13924,13927,13940],{"className":13925,"style":13926},[491],"height:1.05em;",[212,13928,13930,13934],{"style":13929},"top:-1.8723em;margin-left:0em;",[212,13931],{"className":13932,"style":13933},[499],"height:3.05em;",[212,13935,13937],{"className":13936},[504,505,506,507],[212,13938,12163],{"className":13939},[256,257,507],[212,13941,13943,13946],{"style":13942},"top:-3.05em;",[212,13944],{"className":13945,"style":13933},[499],[212,13947,13948],{},[212,13949,13661],{"className":13950},[1682,1683,1684],[212,13952,515],{"className":13953},[514],[212,13955,13957],{"className":13956},[487],[212,13958,13961],{"className":13959,"style":13960},[491],"height:1.2777em;",[212,13962],{},[212,13964],{"className":13965,"style":603},[354],[212,13967,13969,13972],{"className":13968},[256],[212,13970,7768],{"className":13971,"style":8472},[256,257],[212,13973,13975],{"className":13974},[478],[212,13976,13978,13998],{"className":13977},[482,483],[212,13979,13981,13995],{"className":13980},[487],[212,13982,13984],{"className":13983,"style":12382},[491],[212,13985,13986,13989],{"style":12385},[212,13987],{"className":13988,"style":500},[499],[212,13990,13992],{"className":13991},[504,505,506,507],[212,13993,12163],{"className":13994},[256,257,507],[212,13996,515],{"className":13997},[514],[212,13999,14001],{"className":14000},[487],[212,14002,14004],{"className":14003,"style":8166},[491],[212,14005],{},[212,14007],{"className":14008,"style":603},[354],[212,14010,14012,14015],{"className":14011},[256],[212,14013,396],{"className":14014,"style":474},[256,257],[212,14016,14018],{"className":14017},[478],[212,14019,14021,14041],{"className":14020},[482,483],[212,14022,14024,14038],{"className":14023},[487],[212,14025,14027],{"className":14026,"style":492},[491],[212,14028,14029,14032],{"style":495},[212,14030],{"className":14031,"style":500},[499],[212,14033,14035],{"className":14034},[504,505,506,507],[212,14036,234],{"className":14037,"style":258},[256,257,507],[212,14039,515],{"className":14040},[514],[212,14042,14044],{"className":14043},[487],[212,14045,14047],{"className":14046,"style":522},[491],[212,14048],{},[212,14050,310],{"className":14051},[343],[212,14053,14055,14058],{"className":14054},[256],[212,14056,403],{"className":14057,"style":531},[256,257],[212,14059,14061],{"className":14060},[478],[212,14062,14064,14084],{"className":14063},[482,483],[212,14065,14067,14081],{"className":14066},[487],[212,14068,14070],{"className":14069,"style":12382},[491],[212,14071,14072,14075],{"style":11336},[212,14073],{"className":14074,"style":500},[499],[212,14076,14078],{"className":14077},[504,505,506,507],[212,14079,12163],{"className":14080},[256,257,507],[212,14082,515],{"className":14083},[514],[212,14085,14087],{"className":14086},[487],[212,14088,14090],{"className":14089,"style":8166},[491],[212,14091],{},[212,14093,407],{"className":14094},[256],[212,14096,14098,14101],{"className":14097},[256],[212,14099,410],{"className":14100},[256,257],[212,14102,14104],{"className":14103},[478],[212,14105,14107,14127],{"className":14106},[482,483],[212,14108,14110,14124],{"className":14109},[487],[212,14111,14113],{"className":14112,"style":12382},[491],[212,14114,14115,14118],{"style":579},[212,14116],{"className":14117,"style":500},[499],[212,14119,14121],{"className":14120},[504,505,506,507],[212,14122,12163],{"className":14123},[256,257,507],[212,14125,515],{"className":14126},[514],[212,14128,14130],{"className":14129},[487],[212,14131,14133],{"className":14132,"style":8166},[491],[212,14134],{},[212,14136,317],{"className":14137},[350],[212,14139],{"className":14140,"style":355},[354],[212,14142,320],{"className":14143},[359],[212,14145],{"className":14146,"style":355},[354],[212,14148,14150,14153,14156,14196,14199,14239,14242,14282,14285,14288,14291],{"className":14149},[247],[212,14151],{"className":14152,"style":467},[251],[212,14154,11539],{"className":14155},[256,257],[212,14157,14159,14162],{"className":14158},[256],[212,14160,396],{"className":14161,"style":474},[256,257],[212,14163,14165],{"className":14164},[478],[212,14166,14168,14188],{"className":14167},[482,483],[212,14169,14171,14185],{"className":14170},[487],[212,14172,14174],{"className":14173,"style":492},[491],[212,14175,14176,14179],{"style":495},[212,14177],{"className":14178,"style":500},[499],[212,14180,14182],{"className":14181},[504,505,506,507],[212,14183,234],{"className":14184,"style":258},[256,257,507],[212,14186,515],{"className":14187},[514],[212,14189,14191],{"className":14190},[487],[212,14192,14194],{"className":14193,"style":522},[491],[212,14195],{},[212,14197,310],{"className":14198},[343],[212,14200,14202,14205],{"className":14201},[256],[212,14203,403],{"className":14204,"style":531},[256,257],[212,14206,14208],{"className":14207},[478],[212,14209,14211,14231],{"className":14210},[482,483],[212,14212,14214,14228],{"className":14213},[487],[212,14215,14217],{"className":14216,"style":11333},[491],[212,14218,14219,14222],{"style":11336},[212,14220],{"className":14221,"style":500},[499],[212,14223,14225],{"className":14224},[504,505,506,507],[212,14226,314],{"className":14227},[256,507],[212,14229,515],{"className":14230},[514],[212,14232,14234],{"className":14233},[487],[212,14235,14237],{"className":14236,"style":8166},[491],[212,14238],{},[212,14240,407],{"className":14241},[256],[212,14243,14245,14248],{"className":14244},[256],[212,14246,410],{"className":14247},[256,257],[212,14249,14251],{"className":14250},[478],[212,14252,14254,14274],{"className":14253},[482,483],[212,14255,14257,14271],{"className":14256},[487],[212,14258,14260],{"className":14259,"style":11333},[491],[212,14261,14262,14265],{"style":579},[212,14263],{"className":14264,"style":500},[499],[212,14266,14268],{"className":14267},[504,505,506,507],[212,14269,314],{"className":14270},[256,507],[212,14272,515],{"className":14273},[514],[212,14275,14277],{"className":14276},[487],[212,14278,14280],{"className":14279,"style":8166},[491],[212,14281],{},[212,14283,317],{"className":14284},[350],[212,14286],{"className":14287,"style":2785},[354],[212,14289,2668],{"className":14290},[2789],[212,14292],{"className":14293,"style":2785},[354],[212,14295,14297,14300,14303,14306,14309,14312],{"className":14296},[247],[212,14298],{"className":14299,"style":336},[251],[212,14301,310],{"className":14302},[343],[212,14304,314],{"className":14305},[256],[212,14307],{"className":14308,"style":2785},[354],[212,14310,5011],{"className":14311},[2789],[212,14313],{"className":14314,"style":2785},[354],[212,14316,14318,14321,14324,14327,14367,14370,14410,14413,14453,14456],{"className":14317},[247],[212,14319],{"className":14320,"style":467},[251],[212,14322,11539],{"className":14323},[256,257],[212,14325,317],{"className":14326},[350],[212,14328,14330,14333],{"className":14329},[256],[212,14331,396],{"className":14332,"style":474},[256,257],[212,14334,14336],{"className":14335},[478],[212,14337,14339,14359],{"className":14338},[482,483],[212,14340,14342,14356],{"className":14341},[487],[212,14343,14345],{"className":14344,"style":492},[491],[212,14346,14347,14350],{"style":495},[212,14348],{"className":14349,"style":500},[499],[212,14351,14353],{"className":14352},[504,505,506,507],[212,14354,234],{"className":14355,"style":258},[256,257,507],[212,14357,515],{"className":14358},[514],[212,14360,14362],{"className":14361},[487],[212,14363,14365],{"className":14364,"style":522},[491],[212,14366],{},[212,14368,310],{"className":14369},[343],[212,14371,14373,14376],{"className":14372},[256],[212,14374,403],{"className":14375,"style":531},[256,257],[212,14377,14379],{"className":14378},[478],[212,14380,14382,14402],{"className":14381},[482,483],[212,14383,14385,14399],{"className":14384},[487],[212,14386,14388],{"className":14387,"style":11333},[491],[212,14389,14390,14393],{"style":11336},[212,14391],{"className":14392,"style":500},[499],[212,14394,14396],{"className":14395},[504,505,506,507],[212,14397,2661],{"className":14398},[256,507],[212,14400,515],{"className":14401},[514],[212,14403,14405],{"className":14404},[487],[212,14406,14408],{"className":14407,"style":8166},[491],[212,14409],{},[212,14411,407],{"className":14412},[256],[212,14414,14416,14419],{"className":14415},[256],[212,14417,410],{"className":14418},[256,257],[212,14420,14422],{"className":14421},[478],[212,14423,14425,14445],{"className":14424},[482,483],[212,14426,14428,14442],{"className":14427},[487],[212,14429,14431],{"className":14430,"style":11333},[491],[212,14432,14433,14436],{"style":579},[212,14434],{"className":14435,"style":500},[499],[212,14437,14439],{"className":14438},[504,505,506,507],[212,14440,2661],{"className":14441},[256,507],[212,14443,515],{"className":14444},[514],[212,14446,14448],{"className":14447},[487],[212,14449,14451],{"className":14450,"style":8166},[491],[212,14452],{},[212,14454,317],{"className":14455},[350],[212,14457,4573],{"className":14458},[256],[11,14460,14461,14462,14590],{},"对 ",[212,14463,14465,14495],{"className":14464,"translate":216},[215],[212,14466,14468],{"className":14467},[220],[222,14469,14470],{"xmlns":224},[226,14471,14472,14492],{},[229,14473,14474,14476,14482,14484,14490],{},[307,14475,310],{"stretchy":309},[12011,14477,14478,14480],{"accent":243},[232,14479,403],{},[307,14481,12017],{},[307,14483,748],{"separator":243},[12011,14485,14486,14488],{"accent":243},[232,14487,410],{},[307,14489,12017],{},[307,14491,317],{"stretchy":309},[236,14493,14494],{"encoding":238},"(\\tilde P,\\tilde Q)",[212,14496,14498],{"className":14497,"ariaHidden":243},[242],[212,14499,14501,14505,14508,14539,14542,14545,14587],{"className":14500},[247],[212,14502],{"className":14503,"style":14504},[251],"height:1.1702em;vertical-align:-0.25em;",[212,14506,310],{"className":14507},[343],[212,14509,14511],{"className":14510},[256,12051],[212,14512,14514],{"className":14513},[482],[212,14515,14517],{"className":14516},[487],[212,14518,14520,14528],{"className":14519,"style":12047},[491],[212,14521,14522,14525],{"style":12063},[212,14523],{"className":14524,"style":658},[499],[212,14526,403],{"className":14527,"style":531},[256,257],[212,14529,14530,14533],{"style":12072},[212,14531],{"className":14532,"style":658},[499],[212,14534,14536],{"className":14535,"style":12315},[12079],[212,14537,12017],{"className":14538},[256],[212,14540,748],{"className":14541},[770],[212,14543],{"className":14544,"style":603},[354],[212,14546,14548],{"className":14547},[256,12051],[212,14549,14551,14579],{"className":14550},[482,483],[212,14552,14554,14576],{"className":14553},[487],[212,14555,14557,14565],{"className":14556,"style":12047},[491],[212,14558,14559,14562],{"style":12063},[212,14560],{"className":14561,"style":658},[499],[212,14563,410],{"className":14564},[256,257],[212,14566,14567,14570],{"style":12072},[212,14568],{"className":14569,"style":658},[499],[212,14571,14573],{"className":14572,"style":12315},[12079],[212,14574,12017],{"className":14575},[256],[212,14577,515],{"className":14578},[514],[212,14580,14582],{"className":14581},[487],[212,14583,14585],{"className":14584,"style":12507},[491],[212,14586],{},[212,14588,317],{"className":14589},[350]," 使用 DPI，即得到联合凸性：",[212,14592,14594],{"className":14593,"translate":216},[377],[212,14595,14597,14777],{"className":14596,"translate":216},[215],[212,14598,14600],{"className":14599},[220],[222,14601,14602],{"xmlns":224,"display":386},[226,14603,14604,14774],{},[1441,14605,14606,14690],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,14607,14608,14614],{},[1450,14609,14610],{},[1453,14611,14612],{"scriptlevel":323,"displaystyle":243},[229,14613],{},[1450,14615,14616],{},[1453,14617,14618],{"scriptlevel":323,"displaystyle":243},[229,14619,14620,14622,14628,14630,14632,14638,14640,14642,14644,14646,14648,14650,14656,14658,14660,14662,14664,14670,14672,14674,14676,14678,14680,14682,14688],{},[229,14621],{},[392,14623,14624,14626],{},[232,14625,396],{},[232,14627,234],{},[307,14629,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,14631,11539],{},[392,14633,14634,14636],{},[232,14635,403],{},[312,14637,314],{},[307,14639,2668],{},[307,14641,310],{"stretchy":309},[312,14643,314],{},[307,14645,5011],{},[232,14647,11539],{},[307,14649,317],{"stretchy":309},[392,14651,14652,14654],{},[232,14653,403],{},[312,14655,2661],{},[1495,14657,1497],{},[307,14659,407],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[1495,14661,1497],{},[232,14663,11539],{},[392,14665,14666,14668],{},[232,14667,410],{},[312,14669,314],{},[307,14671,2668],{},[307,14673,310],{"stretchy":309},[312,14675,314],{},[307,14677,5011],{},[232,14679,11539],{},[307,14681,317],{"stretchy":309},[392,14683,14684,14686],{},[232,14685,410],{},[312,14687,2661],{},[307,14689,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[1447,14691,14692,14698],{},[1450,14693,14694],{},[1453,14695,14696],{"scriptlevel":323,"displaystyle":243},[229,14697],{},[1450,14699,14700],{},[1453,14701,14702],{"scriptlevel":323,"displaystyle":243},[229,14703,14704,14706,14708,14710,14712,14718,14720,14726,14728,14734,14736,14738,14740,14742,14744,14746,14748,14754,14756,14762,14764,14770,14772],{},[229,14705],{},[354,14707],{"width":3460},[307,14709,10150],{},[232,14711,11539],{},[392,14713,14714,14716],{},[232,14715,396],{},[232,14717,234],{},[307,14719,310],{"stretchy":309},[392,14721,14722,14724],{},[232,14723,403],{},[312,14725,314],{},[232,14727,407],{"mathvariant":406},[392,14729,14730,14732],{},[232,14731,410],{},[312,14733,314],{},[307,14735,317],{"stretchy":309},[307,14737,2668],{},[307,14739,310],{"stretchy":309},[312,14741,314],{},[307,14743,5011],{},[232,14745,11539],{},[307,14747,317],{"stretchy":309},[392,14749,14750,14752],{},[232,14751,396],{},[232,14753,234],{},[307,14755,310],{"stretchy":309},[392,14757,14758,14760],{},[232,14759,403],{},[312,14761,2661],{},[232,14763,407],{"mathvariant":406},[392,14765,14766,14768],{},[232,14767,410],{},[312,14769,2661],{},[307,14771,317],{"stretchy":309},[232,14773,4573],{"mathvariant":406},[236,14775,14776],{"encoding":238},"\\begin{aligned}\n&D_f\\big(\\lambda P_1+(1-\\lambda)P_2\n\\,\\big\\|\\,\\lambda Q_1+(1-\\lambda)Q_2\\big)\\\\\n&\\qquad\\le \\lambda D_f(P_1\\|Q_1)\n+(1-\\lambda)D_f(P_2\\|Q_2).\n\\end{aligned}",[212,14778,14780],{"className":14779,"ariaHidden":243},[242],[212,14781,14783,14787],{"className":14782},[247],[212,14784],{"className":14785,"style":14786},[251],"height:2.71em;vertical-align:-1.105em;",[212,14788,14790],{"className":14789},[256],[212,14791,14793,14837],{"className":14792},[1441],[212,14794,14796],{"className":14795},[1558],[212,14797,14799,14828],{"className":14798},[482,483],[212,14800,14802,14825],{"className":14801},[487],[212,14803,14806,14816],{"className":14804,"style":14805},[491],"height:1.605em;",[212,14807,14809,14813],{"style":14808},"top:-3.605em;",[212,14810],{"className":14811,"style":14812},[499],"height:2.85em;",[212,14814],{"className":14815},[256],[212,14817,14819,14822],{"style":14818},"top:-2.105em;",[212,14820],{"className":14821,"style":14812},[499],[212,14823],{"className":14824},[256],[212,14826,515],{"className":14827},[514],[212,14829,14831],{"className":14830},[487],[212,14832,14835],{"className":14833,"style":14834},[491],"height:1.105em;",[212,14836],{},[212,14838,14840],{"className":14839},[1649],[212,14841,14843,15512],{"className":14842},[482,483],[212,14844,14846,15509],{"className":14845},[487],[212,14847,14849,15191],{"className":14848,"style":14805},[491],[212,14850,14852,14855],{"style":14851},"top:-3.755em;",[212,14853],{"className":14854,"style":658},[499],[212,14856,14858,14861,14901,14907,14910,14950,14953,14956,14959,14962,14965,14968,14971,14974,14977,14980,15020,15023,15069,15072,15075,15115,15118,15121,15124,15127,15130,15133,15136,15139,15142,15145,15185],{"className":14857},[256],[212,14859],{"className":14860},[256],[212,14862,14864,14867],{"className":14863},[256],[212,14865,396],{"className":14866,"style":474},[256,257],[212,14868,14870],{"className":14869},[478],[212,14871,14873,14893],{"className":14872},[482,483],[212,14874,14876,14890],{"className":14875},[487],[212,14877,14879],{"className":14878,"style":492},[491],[212,14880,14881,14884],{"style":495},[212,14882],{"className":14883,"style":500},[499],[212,14885,14887],{"className":14886},[504,505,506,507],[212,14888,234],{"className":14889,"style":258},[256,257,507],[212,14891,515],{"className":14892},[514],[212,14894,14896],{"className":14895},[487],[212,14897,14899],{"className":14898,"style":522},[491],[212,14900],{},[212,14902,14904],{"className":14903},[256],[212,14905,310],{"className":14906},[616,9872],[212,14908,11539],{"className":14909},[256,257],[212,14911,14913,14916],{"className":14912},[256],[212,14914,403],{"className":14915,"style":531},[256,257],[212,14917,14919],{"className":14918},[478],[212,14920,14922,14942],{"className":14921},[482,483],[212,14923,14925,14939],{"className":14924},[487],[212,14926,14928],{"className":14927,"style":11333},[491],[212,14929,14930,14933],{"style":11336},[212,14931],{"className":14932,"style":500},[499],[212,14934,14936],{"className":14935},[504,505,506,507],[212,14937,314],{"className":14938},[256,507],[212,14940,515],{"className":14941},[514],[212,14943,14945],{"className":14944},[487],[212,14946,14948],{"className":14947,"style":8166},[491],[212,14949],{},[212,14951],{"className":14952,"style":2785},[354],[212,14954,2668],{"className":14955},[2789],[212,14957],{"className":14958,"style":2785},[354],[212,14960,310],{"className":14961},[343],[212,14963,314],{"className":14964},[256],[212,14966],{"className":14967,"style":2785},[354],[212,14969,5011],{"className":14970},[2789],[212,14972],{"className":14973,"style":2785},[354],[212,14975,11539],{"className":14976},[256,257],[212,14978,317],{"className":14979},[350],[212,14981,14983,14986],{"className":14982},[256],[212,14984,403],{"className":14985,"style":531},[256,257],[212,14987,14989],{"className":14988},[478],[212,14990,14992,15012],{"className":14991},[482,483],[212,14993,14995,15009],{"className":14994},[487],[212,14996,14998],{"className":14997,"style":11333},[491],[212,14999,15000,15003],{"style":11336},[212,15001],{"className":15002,"style":500},[499],[212,15004,15006],{"className":15005},[504,505,506,507],[212,15007,2661],{"className":15008},[256,507],[212,15010,515],{"className":15011},[514],[212,15013,15015],{"className":15014},[487],[212,15016,15018],{"className":15017,"style":8166},[491],[212,15019],{},[212,15021],{"className":15022,"style":603},[354],[212,15024,15026],{"className":15025},[256],[212,15027,15030],{"className":15028},[616,15029],"mult",[212,15031,15033,15060],{"className":15032},[482,483],[212,15034,15036,15057],{"className":15035},[487],[212,15037,15040],{"className":15038,"style":15039},[491],"height:0.85em;",[212,15041,15043,15047],{"style":15042},"top:-2.85em;",[212,15044],{"className":15045,"style":15046},[499],"height:3.2em;",[212,15048,15050],{"style":15049},"width:0.556em;height:1.2em;",[6521,15051,15054],{"xmlns":6523,"width":15052,"height":9648,"viewBox":15053},"0.556em","0 0 556 1200",[6529,15055],{"d":15056},"M145 15 v585 v0 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v0 v585 h43z\nM367 15 v585 v0 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M410 15 H367 v585 v0 v585 h43z",[212,15058,515],{"className":15059},[514],[212,15061,15063],{"className":15062},[487],[212,15064,15067],{"className":15065,"style":15066},[491],"height:0.35em;",[212,15068],{},[212,15070],{"className":15071,"style":603},[354],[212,15073,11539],{"className":15074},[256,257],[212,15076,15078,15081],{"className":15077},[256],[212,15079,410],{"className":15080},[256,257],[212,15082,15084],{"className":15083},[478],[212,15085,15087,15107],{"className":15086},[482,483],[212,15088,15090,15104],{"className":15089},[487],[212,15091,15093],{"className":15092,"style":11333},[491],[212,15094,15095,15098],{"style":579},[212,15096],{"className":15097,"style":500},[499],[212,15099,15101],{"className":15100},[504,505,506,507],[212,15102,314],{"className":15103},[256,507],[212,15105,515],{"className":15106},[514],[212,15108,15110],{"className":15109},[487],[212,15111,15113],{"className":15112,"style":8166},[491],[212,15114],{},[212,15116],{"className":15117,"style":2785},[354],[212,15119,2668],{"className":15120},[2789],[212,15122],{"className":15123,"style":2785},[354],[212,15125,310],{"className":15126},[343],[212,15128,314],{"className":15129},[256],[212,15131],{"className":15132,"style":2785},[354],[212,15134,5011],{"className":15135},[2789],[212,15137],{"className":15138,"style":2785},[354],[212,15140,11539],{"className":15141},[256,257],[212,15143,317],{"className":15144},[350],[212,15146,15148,15151],{"className":15147},[256],[212,15149,410],{"className":15150},[256,257],[212,15152,15154],{"className":15153},[478],[212,15155,15157,15177],{"className":15156},[482,483],[212,15158,15160,15174],{"className":15159},[487],[212,15161,15163],{"className":15162,"style":11333},[491],[212,15164,15165,15168],{"style":579},[212,15166],{"className":15167,"style":500},[499],[212,15169,15171],{"className":15170},[504,505,506,507],[212,15172,2661],{"className":15173},[256,507],[212,15175,515],{"className":15176},[514],[212,15178,15180],{"className":15179},[487],[212,15181,15183],{"className":15182,"style":8166},[491],[212,15184],{},[212,15186,15188],{"className":15187},[256],[212,15189,317],{"className":15190},[616,9872],[212,15192,15194,15197],{"style":15193},"top:-2.255em;",[212,15195],{"className":15196,"style":658},[499],[212,15198,15200,15203,15206,15209,15212,15215,15218,15258,15261,15301,15304,15344,15347,15350,15353,15356,15359,15362,15365,15368,15371,15374,15377,15417,15420,15460,15463,15503,15506],{"className":15199},[256],[212,15201],{"className":15202},[256],[212,15204],{"className":15205,"style":3832},[354],[212,15207],{"className":15208,"style":355},[354],[212,15210,10150],{"className":15211},[359],[212,15213],{"className":15214,"style":355},[354],[212,15216,11539],{"className":15217},[256,257],[212,15219,15221,15224],{"className":15220},[256],[212,15222,396],{"className":15223,"style":474},[256,257],[212,15225,15227],{"className":15226},[478],[212,15228,15230,15250],{"className":15229},[482,483],[212,15231,15233,15247],{"className":15232},[487],[212,15234,15236],{"className":15235,"style":492},[491],[212,15237,15238,15241],{"style":495},[212,15239],{"className":15240,"style":500},[499],[212,15242,15244],{"className":15243},[504,505,506,507],[212,15245,234],{"className":15246,"style":258},[256,257,507],[212,15248,515],{"className":15249},[514],[212,15251,15253],{"className":15252},[487],[212,15254,15256],{"className":15255,"style":522},[491],[212,15257],{},[212,15259,310],{"className":15260},[343],[212,15262,15264,15267],{"className":15263},[256],[212,15265,403],{"className":15266,"style":531},[256,257],[212,15268,15270],{"className":15269},[478],[212,15271,15273,15293],{"className":15272},[482,483],[212,15274,15276,15290],{"className":15275},[487],[212,15277,15279],{"className":15278,"style":11333},[491],[212,15280,15281,15284],{"style":11336},[212,15282],{"className":15283,"style":500},[499],[212,15285,15287],{"className":15286},[504,505,506,507],[212,15288,314],{"className":15289},[256,507],[212,15291,515],{"className":15292},[514],[212,15294,15296],{"className":15295},[487],[212,15297,15299],{"className":15298,"style":8166},[491],[212,15300],{},[212,15302,407],{"className":15303},[256],[212,15305,15307,15310],{"className":15306},[256],[212,15308,410],{"className":15309},[256,257],[212,15311,15313],{"className":15312},[478],[212,15314,15316,15336],{"className":15315},[482,483],[212,15317,15319,15333],{"className":15318},[487],[212,15320,15322],{"className":15321,"style":11333},[491],[212,15323,15324,15327],{"style":579},[212,15325],{"className":15326,"style":500},[499],[212,15328,15330],{"className":15329},[504,505,506,507],[212,15331,314],{"className":15332},[256,507],[212,15334,515],{"className":15335},[514],[212,15337,15339],{"className":15338},[487],[212,15340,15342],{"className":15341,"style":8166},[491],[212,15343],{},[212,15345,317],{"className":15346},[350],[212,15348],{"className":15349,"style":2785},[354],[212,15351,2668],{"className":15352},[2789],[212,15354],{"className":15355,"style":2785},[354],[2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",[212,15526,15528,15541],{"className":15527,"translate":216},[215],[212,15529,15531],{"className":15530},[220],[222,15532,15533],{"xmlns":224},[226,15534,15535,15539],{},[229,15536,15537],{},[307,15538,11190],{},[236,15540,11193],{"encoding":238},[212,15542,15544],{"className":15543,"ariaHidden":243},[242],[212,15545,15547,15550],{"className":15546},[247],[212,15548],{"className":15549,"style":11203},[251],[212,15551,11190],{"className":15552},[359],[212,15554,15556,15569],{"className":15555,"translate":216},[215],[212,15557,15559],{"className":15558},[220],[222,15560,15561],{"xmlns":224},[226,15562,15563,15567],{},[229,15564,15565],{},[232,15566,234],{},[236,15568,234],{"encoding":238},[212,15570,15572],{"className":15571,"ariaHidden":243},[242],[212,15573,15575,15578],{"className":15574},[247],[212,15576],{"className":15577,"style":252},[251],[212,15579,234],{"className":15580,"style":258},[256,257]," 固定 ",[212,15583,15585,15608],{"className":15584,"translate":216},[215],[212,15586,15588],{"className":15587},[220],[222,15589,15590],{"xmlns":224},[226,15591,15592,15605],{},[229,15593,15594,15596,15598,15601,15603],{},[232,15595,7759],{},[307,15597,748],{"separator":243},[232,15599,15600],{},"u",[307,15602,7126],{},[312,15604,323],{},[236,15606,15607],{"encoding":238},"s,u\\ge0",[212,15609,15611,15639],{"className":15610,"ariaHidden":243},[242],[212,15612,15614,15618,15621,15624,15627,15630,15633,15636],{"className":15613},[247],[212,15615],{"className":15616,"style":15617},[251],"height:0.8304em;vertical-align:-0.1944em;",[212,15619,7759],{"className":15620},[256,257],[212,15622,748],{"className":15623},[770],[212,15625],{"className":15626,"style":603},[354],[212,15628,15600],{"className":15629},[256,257],[212,15631],{"className":15632,"style":355},[354],[212,15634,7126],{"className":15635},[359],[212,15637],{"className":15638,"style":355},[354],[212,15640,15642,15645],{"className":15641},[247],[212,15643],{"className":15644,"style":369},[251],[212,15646,323],{"className":15647},[256],[212,15649,15651,15676],{"className":15650,"translate":216},[215],[212,15652,15654],{"className":15653},[220],[222,15655,15656],{"xmlns":224},[226,15657,15658,15674],{},[229,15659,15660,15662,15664,15666,15668,15670,15672],{},[232,15661,11539],{},[307,15663,6107],{},[307,15665,310],{"stretchy":309},[312,15667,323],{},[307,15669,748],{"separator":243},[312,15671,314],{},[307,15673,317],{"stretchy":309},[236,15675,11554],{"encoding":238},[212,15677,15679,15697],{"className":15678,"ariaHidden":243},[242],[212,15680,15682,15685,15688,15691,15694],{"className":15681},[247],[212,15683],{"className":15684,"style":11564},[251],[212,15686,11539],{"className":15687},[256,257],[212,15689],{"className":15690,"style":355},[354],[212,15692,6107],{"className":15693},[359],[212,15695],{"className":15696,"style":355},[354],[212,15698,15700,15703,15706,15709,15712,15715,15718],{"className":15699},[247],[212,15701],{"className":15702,"style":336},[251],[212,15704,310],{"className":15705},[343],[212,15707,323],{"className":15708},[256],[212,15710,748],{"className":15711},[770],[212,15713],{"className":15714,"style":603},[354],[212,15716,314],{"className":15717},[256],[212,15719,317],{"className":15720},[350],"，记目标值 ",[212,15723,15725,15759],{"className":15724,"translate":216},[215],[212,15726,15728],{"className":15727},[220],[222,15729,15730],{"xmlns":224},[226,15731,15732,15756],{},[229,15733,15734,15736,15738,15740,15742,15744,15746,15748,15750,15752,15754],{},[232,15735,7768],{},[307,15737,320],{},[232,15739,11539],{},[232,15741,7759],{},[307,15743,2668],{},[307,15745,310],{"stretchy":309},[312,15747,314],{},[307,15749,5011],{},[232,15751,11539],{},[307,15753,317],{"stretchy":309},[232,15755,15600],{},[236,15757,15758],{"encoding":238},"w=\\lambda s+(1-\\lambda)u",[212,15760,15762,15780,15802,15823],{"className":15761,"ariaHidden":243},[242],[212,15763,15765,15768,15771,15774,15777],{"className":15764},[247],[212,15766],{"className":15767,"style":2543},[251],[212,15769,7768],{"className":15770,"style":8472},[256,257],[212,15772],{"className":15773,"style":355},[354],[212,15775,320],{"className":15776},[359],[212,15778],{"className":15779,"style":355},[354],[212,15781,15783,15787,15790,15793,15796,15799],{"className":15782},[247],[212,15784],{"className":15785,"style":15786},[251],"height:0.7778em;vertical-align:-0.0833em;",[212,15788,11539],{"className":15789},[256,257],[212,15791,7759],{"className":15792},[256,257],[212,15794],{"className":15795,"style":2785},[354],[212,15797,2668],{"className":15798},[2789],[212,15800],{"className":15801,"style":2785},[354],[212,15803,15805,15808,15811,15814,15817,15820],{"className":15804},[247],[212,15806],{"className":15807,"style":336},[251],[212,15809,310],{"className":15810},[343],[212,15812,314],{"className":15813},[256],[212,15815],{"className":15816,"style":2785},[354],[212,15818,5011],{"className":15819},[2789],[212,15821],{"className":15822,"style":2785},[354],[212,15824,15826,15829,15832,15835],{"className":15825},[247],[212,15827],{"className":15828,"style":336},[251],[212,15830,11539],{"className":15831},[256,257],[212,15833,317],{"className":15834},[350],[212,15836,15600],{"className":15837},[256,257],"。在两点空间 ",[212,15840,15842,15864],{"className":15841,"translate":216},[215],[212,15843,15845],{"className":15844},[220],[222,15846,15847],{"xmlns":224},[226,15848,15849,15861],{},[229,15850,15851,15853,15855,15857,15859],{},[307,15852,3096],{"stretchy":309},[312,15854,314],{},[307,15856,748],{"separator":243},[312,15858,2661],{},[307,15860,3106],{"stretchy":309},[236,15862,15863],{"encoding":238},"\\{1,2\\}",[212,15865,15867],{"className":15866,"ariaHidden":243},[242],[212,15868,15870,15873,15876,15879,15882,15885,15888],{"className":15869},[247],[212,15871],{"className":15872,"style":336},[251],[212,15874,3096],{"className":15875},[343],[212,15877,314],{"className":15878},[256],[212,15880,748],{"className":15881},[770],[212,15883],{"className":15884,"style":603},[354],[212,15886,2661],{"className":15887},[256],[212,15889,3106],{"className":15890},[350]," 上取同一个底分布 ",[212,15893,15895,15928],{"className":15894,"translate":216},[215],[212,15896,15898],{"className":15897},[220],[222,15899,15900],{"xmlns":224},[226,15901,15902,15925],{},[229,15903,15904,15906,15908,15910,15913,15915,15917,15919,15921,15923],{},[232,15905,410],{},[307,15907,320],{},[307,15909,310],{"stretchy":309},[232,15911,15912],{},"δ",[307,15914,748],{"separator":243},[1495,15916,1497],{},[312,15918,314],{},[307,15920,5011],{},[232,15922,15912],{},[307,15924,317],{"stretchy":309},[236,15926,15927],{"encoding":238},"Q=(\\delta,\\,1-\\delta)",[212,15929,15931,15949,15983],{"className":15930,"ariaHidden":243},[242],[212,15932,15934,15937,15940,15943,15946],{"className":15933},[247],[212,15935],{"className":15936,"style":763},[251],[212,15938,410],{"className":15939},[256,257],[212,15941],{"className":15942,"style":355},[354],[212,15944,320],{"className":15945},[359],[212,15947],{"className":15948,"style":355},[354],[212,15950,15952,15955,15958,15962,15965,15968,15971,15974,15977,15980],{"className":15951},[247],[212,15953],{"className":15954,"style":336},[251],[212,15956,310],{"className":15957},[343],[212,15959,15912],{"className":15960,"style":15961},[256,257],"margin-right:0.0379em;",[212,15963,748],{"className":15964},[770],[212,15966],{"className":15967,"style":603},[354],[212,15969],{"className":15970,"style":603},[354],[212,15972,314],{"className":15973},[256],[212,15975],{"className":15976,"style":2785},[354],[212,15978,5011],{"className":15979},[2789],[212,15981],{"className":15982,"style":2785},[354],[212,15984,15986,15989,15992],{"className":15985},[247],[212,15987],{"className":15988,"style":336},[251],[212,15990,15912],{"className":15991,"style":15961},[256,257],[212,15993,317],{"className":15994},[350],"（",[212,15997,15999,16025],{"className":15998,"translate":216},[215],[212,16000,16002],{"className":16001},[220],[222,16003,16004],{"xmlns":224},[226,16005,16006,16022],{},[229,16007,16008,16010,16012,16014,16016,16018,16020],{},[232,16009,15912],{},[307,16011,6107],{},[307,16013,310],{"stretchy":309},[312,16015,323],{},[307,16017,748],{"separator":243},[312,16019,314],{},[307,16021,317],{"stretchy":309},[236,16023,16024],{"encoding":238},"\\delta\\in(0,1)",[212,16026,16028,16046],{"className":16027,"ariaHidden":243},[242],[212,16029,16031,16034,16037,16040,16043],{"className":16030},[247],[212,16032],{"className":16033,"style":11564},[251],[212,16035,15912],{"className":16036,"style":15961},[256,257],[212,16038],{"className":16039,"style":355},[354],[212,16041,6107],{"className":16042},[359],[212,16044],{"className":16045,"style":355},[354],[212,16047,16049,16052,16055,16058,16061,16064,16067],{"className":16048},[247],[212,16050],{"className":16051,"style":336},[251],[212,16053,310],{"className":16054},[343],[212,16056,323],{"className":16057},[256],[212,16059,748],{"className":16060},[770],[212,16062],{"className":16063,"style":603},[354],[212,16065,314],{"className":16066},[256],[212,16068,317],{"className":16069},[350]," 充分小），并取似然比在第一坐标上为常数的分布：",[212,16072,16074],{"className":16073,"translate":216},[377],[212,16075,16077,16152],{"className":16076,"translate":216},[215],[212,16078,16080],{"className":16079},[220],[222,16081,16082],{"xmlns":224,"display":386},[226,16083,16084,16149],{},[229,16085,16086,16092,16094,16096,16098,16100,16102,16105,16107,16109,16111,16113,16115,16117,16119,16125,16127,16129,16131,16133,16135,16137,16139,16141,16143,16145,16147],{},[392,16087,16088,16090],{},[232,16089,403],{},[312,16091,314],{},[307,16093,320],{},[307,16095,310],{"stretchy":309},[232,16097,7759],{},[232,16099,15912],{},[307,16101,748],{"separator":243},[1495,16103,16104],{},"  ",[312,16106,314],{},[307,16108,5011],{},[232,16110,7759],{},[232,16112,15912],{},[307,16114,317],{"stretchy":309},[307,16116,748],{"separator":243},[354,16118],{"width":3460},[392,16120,16121,16123],{},[232,16122,403],{},[312,16124,2661],{},[307,16126,320],{},[307,16128,310],{"stretchy":309},[232,16130,15600],{},[232,16132,15912],{},[307,16134,748],{"separator":243},[1495,16136,16104],{},[312,16138,314],{},[307,16140,5011],{},[232,16142,15600],{},[232,16144,15912],{},[307,16146,317],{"stretchy":309},[307,16148,748],{"separator":243},[236,16150,16151],{"encoding":238},"P_1=(s\\delta,\\;1-s\\delta),\\qquad\nP_2=(u\\delta,\\;1-u\\delta),",[212,16153,16155,16211,16245,16315,16351],{"className":16154,"ariaHidden":243},[242],[212,16156,16158,16162,16202,16205,16208],{"className":16157},[247],[212,16159],{"className":16160,"style":16161},[251],"height:0.8333em;vertical-align:-0.15em;",[212,16163,16165,16168],{"className":16164},[256],[212,16166,403],{"className":16167,"style":531},[256,257],[212,16169,16171],{"className":16170},[478],[212,16172,16174,16194],{"className":16173},[482,483],[212,16175,16177,16191],{"className":16176},[487],[212,16178,16180],{"className":16179,"style":11333},[491],[212,16181,16182,16185],{"style":11336},[212,16183],{"className":16184,"style":500},[499],[212,16186,16188],{"className":16187},[504,505,506,507],[212,16189,314],{"className":16190},[256,507],[212,16192,515],{"className":16193},[514],[212,16195,16197],{"className":16196},[487],[212,16198,16200],{"className":16199,"style":8166},[491],[212,16201],{},[212,16203],{"className":16204,"style":355},[354],[212,16206,320],{"className":16207},[359],[212,16209],{"className":16210,"style":355},[354],[212,16212,16214,16217,16220,16224,16227,16230,16233,16236,16239,16242],{"className":16213},[247],[212,16215],{"className":16216,"style":336},[251],[212,16218,310],{"className":16219},[343],[212,16221,16223],{"className":16222,"style":15961},[256,257],"sδ",[212,16225,748],{"className":16226},[770],[212,16228],{"className":16229,"style":355},[354],[212,16231],{"className":16232,"style":603},[354],[212,16234,314],{"className":16235},[256],[212,16237],{"className":16238,"style":2785},[354],[212,16240,5011],{"className":16241},[2789],[212,16243],{"className":16244,"style":2785},[354],[212,16246,16248,16251,16254,16257,16260,16263,16266,16306,16309,16312],{"className":16247},[247],[212,16249],{"className":16250,"style":336},[251],[212,16252,16223],{"className":16253,"style":15961},[256,257],[212,16255,317],{"className":16256},[350],[212,16258,748],{"className":16259},[770],[212,16261],{"className":16262,"style":3832},[354],[212,16264],{"className":16265,"style":603},[354],[212,16267,16269,16272],{"className":16268},[256],[212,16270,403],{"className":16271,"style":531},[256,257],[212,16273,16275],{"className":16274},[478],[212,16276,16278,16298],{"className":16277},[482,483],[212,16279,16281,16295],{"className":16280},[487],[212,16282,16284],{"className":16283,"style":11333},[491],[212,16285,16286,16289],{"style":11336},[212,16287],{"className":16288,"style":500},[499],[212,16290,16292],{"className":16291},[504,505,506,507],[212,16293,2661],{"className":16294},[256,507],[212,16296,515],{"className":16297},[514],[212,16299,16301],{"className":16300},[487],[212,16302,16304],{"className":16303,"style":8166},[491],[212,16305],{},[212,16307],{"className":16308,"style":355},[354],[212,16310,320],{"className":16311},[359],[212,16313],{"className":16314,"style":355},[354],[212,16316,16318,16321,16324,16327,16330,16333,16336,16339,16342,16345,16348],{"className":16317},[247],[212,16319],{"className":16320,"style":336},[251],[212,16322,310],{"className":16323},[343],[212,16325,15600],{"className":16326},[256,257],[212,16328,15912],{"className":16329,"style":15961},[256,257],[212,16331,748],{"className":16332},[770],[212,16334],{"className":16335,"style":355},[354],[212,16337],{"className":16338,"style":603},[354],[212,16340,314],{"className":16341},[256],[212,16343],{"className":16344,"style":2785},[354],[212,16346,5011],{"className":16347},[2789],[212,16349],{"className":16350,"style":2785},[354],[212,16352,16354,16357,16360,16363,16366],{"className":16353},[247],[212,16355],{"className":16356,"style":336},[251],[212,16358,15600],{"className":16359},[256,257],[212,16361,15912],{"className":16362,"style":15961},[256,257],[212,16364,317],{"className":16365},[350],[212,16367,748],{"className":16368},[770],[11,16370,15995,16371,16400,16401,16443,16444,2607,16472,16635,16636,16665,16666,2943],{},[212,16372,16374,16388],{"className":16373,"translate":216},[215],[212,16375,16377],{"className":16376},[220],[222,16378,16379],{"xmlns":224},[226,16380,16381,16385],{},[229,16382,16383],{},[232,16384,15912],{},[236,16386,16387],{"encoding":238},"\\delta",[212,16389,16391],{"className":16390,"ariaHidden":243},[242],[212,16392,16394,16397],{"className":16393},[247],[212,16395],{"className":16396,"style":12797},[251],[212,16398,15912],{"className":16399,"style":15961},[256,257]," 足够小时这都是合法概率分布；",[212,16402,16404,16422],{"className":16403,"translate":216},[215],[212,16405,16407],{"className":16406},[220],[222,16408,16409],{"xmlns":224},[226,16410,16411,16419],{},[229,16412,16413,16415,16417],{},[312,16414,323],{},[307,16416,748],{"separator":243},[312,16418,314],{},[236,16420,16421],{"encoding":238},"0,1",[212,16423,16425],{"className":16424,"ariaHidden":243},[242],[212,16426,16428,16431,16434,16437,16440],{"className":16427},[247],[212,16429],{"className":16430,"style":9556},[251],[212,16432,323],{"className":16433},[256],[212,16435,748],{"className":16436},[770],[212,16438],{"className":16439,"style":603},[354],[212,16441,314],{"className":16442},[256]," 两点上的似然比分别为 ",[212,16445,16447,16460],{"className":16446,"translate":216},[215],[212,16448,16450],{"className":16449},[220],[222,16451,16452],{"xmlns":224},[226,16453,16454,16458],{},[229,16455,16456],{},[232,16457,7759],{},[236,16459,7759],{"encoding":238},[212,16461,16463],{"className":16462,"ariaHidden":243},[242],[212,16464,16466,16469],{"className":16465},[247],[212,16467],{"className":16468,"style":2543},[251],[212,16470,7759],{"className":16471},[256,257],[212,16473,16475,16517],{"className":16474,"translate":216},[215],[212,16476,16478],{"className":16477},[220],[222,16479,16480],{"xmlns":224},[226,16481,16482,16514],{},[229,16483,16484,16486,16488,16490,16492,16494],{},[232,16485,4356],{},[307,16487,310],{"stretchy":309},[232,16489,7759],{},[307,16491,317],{"stretchy":309},[307,16493,320],{},[435,16495,16496,16506],{},[229,16497,16498,16500,16502,16504],{},[312,16499,314],{},[307,16501,5011],{},[232,16503,7759],{},[232,16505,15912],{},[229,16507,16508,16510,16512],{},[312,16509,314],{},[307,16511,5011],{},[232,16513,15912],{},[236,16515,16516],{"encoding":238},"g(s)=\\frac{1-s\\delta}{1-\\delta}",[212,16518,16520,16547],{"className":16519,"ariaHidden":243},[242],[212,16521,16523,16526,16529,16532,16535,16538,16541,16544],{"className":16522},[247],[212,16524],{"className":16525,"style":336},[251],[212,16527,4356],{"className":16528,"style":1178},[256,257],[212,16530,310],{"className":16531},[343],[212,16533,7759],{"className":16534},[256,257],[212,16536,317],{"className":16537},[350],[212,16539],{"className":16540,"style":355},[354],[212,16542,320],{"className":16543},[359],[212,16545],{"className":16546,"style":355},[354],[212,16548,16550,16554],{"className":16549},[247],[212,16551],{"className":16552,"style":16553},[251],"height:1.2834em;vertical-align:-0.4033em;",[212,16555,16557,16560,16632],{"className":16556},[256],[212,16558],{"className":16559},[343,638],[212,16561,16563],{"className":16562},[435],[212,16564,16566,16623],{"className":16565},[482,483],[212,16567,16569,16620],{"className":16568},[487],[212,16570,16572,16592,16600],{"className":16571,"style":2885},[491],[212,16573,16574,16577],{"style":2725},[212,16575],{"className":16576,"style":658},[499],[212,16578,16580],{"className":16579},[504,505,506,507],[212,16581,16583,16586,16589],{"className":16582},[256,507],[212,16584,314],{"className":16585},[256,507],[212,16587,5011],{"className":16588},[2789,507],[212,16590,15912],{"className":16591,"style":15961},[256,257,507],[212,16593,16594,16597],{"style":670},[212,16595],{"className":16596,"style":658},[499],[212,16598],{"className":16599,"style":678},[677],[212,16601,16602,16605],{"style":2748},[212,16603],{"className":16604,"style":658},[499],[212,16606,16608],{"className":16607},[504,505,506,507],[212,16609,16611,16614,16617],{"className":16610},[256,507],[212,16612,314],{"className":16613},[256,507],[212,16615,5011],{"className":16616},[2789,507],[212,16618,16223],{"className":16619,"style":15961},[256,257,507],[212,16621,515],{"className":16622},[514],[212,16624,16626],{"className":16625},[487],[212,16627,16630],{"className":16628,"style":16629},[491],"height:0.4033em;",[212,16631],{},[212,16633],{"className":16634},[350,638],"）。于是一般公式给出：对任何第一坐标似然比为常值 ",[212,16637,16639,16653],{"className":16638,"translate":216},[215],[212,16640,16642],{"className":16641},[220],[222,16643,16644],{"xmlns":224},[226,16645,16646,16651],{},[229,16647,16648],{},[232,16649,16650],{},"r",[236,16652,16650],{"encoding":238},[212,16654,16656],{"className":16655,"ariaHidden":243},[242],[212,16657,16659,16662],{"className":16658},[247],[212,16660],{"className":16661,"style":2543},[251],[212,16663,16650],{"className":16664,"style":474},[256,257]," 的分布 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+(1-\\delta)\\,\nf\\!\\left(\\frac{1-r\\delta}{1-\\delta}\\right).\n\\end{aligned}",[212,16849,16851],{"className":16850,"ariaHidden":243},[242],[212,16852,16854,16858],{"className":16853},[247],[212,16855],{"className":16856,"style":16857},[251],"height:3.91em;vertical-align:-1.705em;",[212,16859,16861],{"className":16860},[256],[212,16862,16864,17016],{"className":16863},[1441],[212,16865,16867],{"className":16866},[1558],[212,16868,16870,17008],{"className":16869},[482,483],[212,16871,16873,17005],{"className":16872},[487],[212,16874,16877,16996],{"className":16875,"style":16876},[491],"height:2.205em;",[212,16878,16880,16883],{"style":16879},"top:-4.805em;",[212,16881],{"className":16882,"style":1575},[499],[212,16884,16886,16926,16932,16935,16938,16941,16944,16947,16984,16987,16990],{"className":16885},[256],[212,16887,16889,16892],{"className":16888},[256],[212,16890,396],{"className":16891,"style":474},[256,257],[212,16893,16895],{"className":16894},[478],[212,16896,16898,16918],{"className":16897},[482,483],[212,16899,16901,16915],{"className":16900},[487],[212,16902,16904],{"className":16903,"style":492},[491],[212,16905,16906,16909],{"style":495},[212,16907],{"className":16908,"style":500},[499],[212,16910,16912],{"className":16911},[504,505,506,507],[212,16913,234],{"className":16914,"style":258},[256,257,507],[212,16916,515],{"className":16917},[514],[212,16919,16921],{"className":16920},[487],[212,16922,16924],{"className":16923,"style":522},[491],[212,16925],{},[212,16927,16929],{"className":16928},[256],[212,16930,310],{"className":16931},[616,9872],[212,16933,403],{"className":16934,"style":531},[256,257],[212,16936,310],{"className":16937},[343],[212,16939,16650],{"className":16940,"style":474},[256,257],[212,16942,317],{"className":16943},[350],[212,16945],{"className":16946,"style":603},[354],[212,16948,16950],{"className":16949},[256],[212,16951,16953],{"className":16952},[616,15029],[212,16954,16956,16976],{"className":16955},[482,483],[212,16957,16959,16973],{"className":16958},[487],[212,16960,16962],{"className":16961,"style":15039},[491],[212,16963,16964,16967],{"style":15042},[212,16965],{"className":16966,"style":15046},[499],[212,16968,16969],{"style":15049},[6521,16970,16971],{"xmlns":6523,"width":15052,"height":9648,"viewBox":15053},[6529,16972],{"d":15056},[212,16974,515],{"className":16975},[514],[212,16977,16979],{"className":16978},[487],[212,16980,16982],{"className":16981,"style":15066},[491],[212,16983],{},[212,16985],{"className":16986,"style":603},[354],[212,16988,410],{"className":16989},[256,257],[212,16991,16993],{"className":16992},[256],[212,16994,317],{"className":16995},[616,9872],[212,16997,16999,17002],{"style":16998},"top:-2.695em;",[212,17000],{"className":17001,"style":1575},[499],[212,17003],{"className":17004},[256],[212,17006,515],{"className":17007},[514],[212,17009,17011],{"className":17010},[487],[212,17012,17014],{"className":17013,"style":9752},[491],[212,17015],{},[212,17017,17019],{"className":17018},[1649],[212,17020,17022,17236],{"className":17021},[482,483],[212,17023,17025,17233],{"className":17024},[487],[212,17026,17028,17066],{"className":17027,"style":16876},[491],[212,17029,17030,17033],{"style":16879},[212,17031],{"className":17032,"style":1575},[499],[212,17034,17036,17039,17042,17045,17048,17051,17054,17057,17060,17063],{"className":17035},[256],[212,17037],{"className":17038},[256],[212,17040],{"className":17041,"style":355},[354],[212,17043,320],{"className":17044},[359],[212,17046],{"className":17047,"style":355},[354],[212,17049,15912],{"className":17050,"style":15961},[256,257],[212,17052],{"className":17053,"style":603},[354],[212,17055,234],{"className":17056,"style":258},[256,257],[212,17058,310],{"className":17059},[343],[212,17061,16650],{"className":17062,"style":474},[256,257],[212,17064,317],{"className":17065},[350],[212,17067,17068,17071],{"style":16998},[212,17069],{"className":17070,"style":1575},[499],[212,17072,17074,17077,17080,17083,17086,17089,17092,17095,17098,17101,17104,17107,17110,17113,17116,17119,17122,17227,17230],{"className":17073},[256],[212,17075],{"className":17076},[256],[212,17078],{"className":17079,"style":3832},[354],[212,17081],{"className":17082,"style":2785},[354],[212,17084,2668],{"className":17085},[2789],[212,17087],{"className":17088,"style":2785},[354],[212,17090,310],{"className":17091},[343],[212,17093,314],{"className":17094},[256],[212,17096],{"className":17097,"style":2785},[354],[212,17099,5011],{"className":17100},[2789],[212,17102],{"className":17103,"style":2785},[354],[212,17105,15912],{"className":17106,"style":15961},[256,257],[212,17108,317],{"className":17109},[350],[212,17111],{"className":17112,"style":603},[354],[212,17114,234],{"className":17115,"style":258},[256,257],[212,17117],{"className":17118,"style":1710},[354],[212,17120],{"className":17121,"style":603},[354],[212,17123,17125,17131,17221],{"className":17124},[607],[212,17126,17128],{"className":17127,"style":612},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",[212,17248,17250,17268],{"className":17249,"translate":216},[215],[212,17251,17253],{"className":17252},[220],[222,17254,17255],{"xmlns":224},[226,17256,17257,17265],{},[229,17258,17259,17261,17263],{},[232,17260,16650],{},[307,17262,320],{},[232,17264,7759],{},[236,17266,17267],{"encoding":238},"r=s",[212,17269,17271,17289],{"className":17270,"ariaHidden":243},[242],[212,17272,17274,17277,17280,17283,17286],{"className":17273},[247],[212,17275],{"className":17276,"style":2543},[251],[212,17278,16650],{"className":17279,"style":474},[256,257],[212,17281],{"className":17282,"style":355},[354],[212,17284,320],{"className":17285},[359],[212,17287],{"className":17288,"style":355},[354],[212,17290,17292,17295],{"className":17291},[247],[212,17293],{"className":17294,"style":2543},[251],[212,17296,7759],{"className":17297},[256,257],[212,17299,17301,17319],{"className":17300,"translate":216},[215],[212,17302,17304],{"className":17303},[220],[222,17305,17306],{"xmlns":224},[226,17307,17308,17316],{},[229,17309,17310,17312,17314],{},[232,17311,16650],{},[307,17313,320],{},[232,17315,15600],{},[236,17317,17318],{"encoding":238},"r=u",[212,17320,17322,17340],{"className":17321,"ariaHidden":243},[242],[212,17323,17325,17328,17331,17334,17337],{"className":17324},[247],[212,17326],{"className":17327,"style":2543},[251],[212,17329,16650],{"className":17330,"style":474},[256,257],[212,17332],{"className":17333,"style":355},[354],[212,17335,320],{"className":17336},[359],[212,17338],{"className":17339,"style":355},[354],[212,17341,17343,17346],{"className":17342},[247],[212,17344],{"className":17345,"style":2543},[251],[212,17347,15600],{"className":17348},[256,257],"、以及混合后的 ",[212,17351,17353,17371],{"className":17352,"translate":216},[215],[212,17354,17356],{"className":17355},[220],[222,17357,17358],{"xmlns":224},[226,17359,17360,17368],{},[229,17361,17362,17364,17366],{},[232,17363,16650],{},[307,17365,320],{},[232,17367,7768],{},[236,17369,17370],{"encoding":238},"r=w",[212,17372,17374,17392],{"className":17373,"ariaHidden":243},[242],[212,17375,17377,17380,17383,17386,17389],{"className":17376},[247],[212,17378],{"className":17379,"style":2543},[251],[212,17381,16650],{"className":17382,"style":474},[256,257],[212,17384],{"className":17385,"style":355},[354],[212,17387,320],{"className":17388},[359],[212,17390],{"className":17391,"style":355},[354],[212,17393,17395,17398],{"className":17394},[247],[212,17396],{"className":17397,"style":2543},[251],[212,17399,7768],{"className":17400,"style":8472},[256,257],"（混合后第一坐标似然比恰为 ",[212,17403,17405,17439],{"className":17404,"translate":216},[215],[212,17406,17408],{"className":17407},[220],[222,17409,17410],{"xmlns":224},[226,17411,17412,17436],{},[229,17413,17414,17416,17418,17420,17422,17424,17426,17428,17430,17432,17434],{},[232,17415,11539],{},[232,17417,7759],{},[307,17419,2668],{},[307,17421,310],{"stretchy":309},[312,17423,314],{},[307,17425,5011],{},[232,17427,11539],{},[307,17429,317],{"stretchy":309},[232,17431,15600],{},[307,17433,320],{},[232,17435,7768],{},[236,17437,17438],{"encoding":238},"\\lambda s+(1-\\lambda)u=w",[212,17440,17442,17463,17484,17508],{"className":17441,"ariaHidden":243},[242],[212,17443,17445,17448,17451,17454,17457,17460],{"className":17444},[247],[212,17446],{"className":17447,"style":15786},[251],[212,17449,11539],{"className":17450},[256,257],[212,17452,7759],{"className":17453},[256,257],[212,17455],{"className":17456,"style":2785},[354],[212,17458,2668],{"className":17459},[2789],[212,17461],{"className":17462,"style":2785},[354],[212,17464,17466,17469,17472,17475,17478,17481],{"className":17465},[247],[212,17467],{"className":17468,"style":336},[251],[212,17470,310],{"className":17471},[343],[212,17473,314],{"className":17474},[256],[212,17476],{"className":17477,"style":2785},[354],[212,17479,5011],{"className":17480},[2789],[212,17482],{"className":17483,"style":2785},[354],[212,17485,17487,17490,17493,17496,17499,17502,17505],{"className":17486},[247],[212,17488],{"className":17489,"style":336},[251],[212,17491,11539],{"className":17492},[256,257],[212,17494,317],{"className":17495},[350],[212,17497,15600],{"className":17498},[256,257],[212,17500],{"className":17501,"style":355},[354],[212,17503,320],{"className":17504},[359],[212,17506],{"className":17507,"style":355},[354],[212,17509,17511,17514],{"className":17510},[247],[212,17512],{"className":17513,"style":2543},[251],[212,17515,7768],{"className":17516,"style":8472},[256,257],"，因为两个分布在",[1194,17519,17520],{},"同一个",[212,17522,17524,17537],{"className":17523,"translate":216},[215],[212,17525,17527],{"className":17526},[220],[222,17528,17529],{"xmlns":224},[226,17530,17531,17535],{},[229,17532,17533],{},[232,17534,410],{},[236,17536,410],{"encoding":238},[212,17538,17540],{"className":17539,"ariaHidden":243},[242],[212,17541,17543,17546],{"className":17542},[247],[212,17544],{"className":17545,"style":763},[251],[212,17547,410],{"className":17548},[256,257]," 下混合，比值线性）代入第一步的联合凸性：",[212,17551,17553],{"className":17552,"translate":216},[377],[212,17554,17556,17753],{"className":17555,"translate":216},[215],[212,17557,17559],{"className":17558},[220],[222,17560,17561],{"xmlns":224,"display":386},[226,17562,17563,17750],{},[1441,17564,17565,17617,17678],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,17566,17567,17573],{},[1450,17568,17569],{},[1453,17570,17571],{"scriptlevel":323,"displaystyle":243},[229,17572],{},[1450,17574,17575],{},[1453,17576,17577],{"scriptlevel":323,"displaystyle":243},[229,17578,17579,17581,17583,17585,17587,17589,17591,17593,17595,17597,17599,17601,17603,17605,17607,17609,17611,17613,17615],{},[229,17580],{},[232,17582,15912],{},[232,17584,234],{},[307,17586,310],{"stretchy":309},[232,17588,7768],{},[307,17590,317],{"stretchy":309},[307,17592,2668],{},[307,17594,310],{"stretchy":309},[312,17596,314],{},[307,17598,5011],{},[232,17600,15912],{},[307,17602,317],{"stretchy":309},[232,17604,234],{},[307,17606,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,17608,4356],{},[307,17610,310],{"stretchy":309},[232,17612,7768],{},[307,17614,317],{"stretchy":309},[307,17616,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[1447,17618,17619,17625],{},[1450,17620,17621],{},[1453,17622,17623],{"scriptlevel":323,"displaystyle":243},[229,17624],{},[1450,17626,17627],{},[1453,17628,17629],{"scriptlevel":323,"displaystyle":243},[229,17630,17631,17633,17635,17637,17640,17642,17644,17646,17648,17650,17652,17654,17656,17658,17660,17662,17664,17666,17668,17670,17672,17674,17676],{},[229,17632],{},[307,17634,10150],{},[232,17636,11539],{},[307,17638,427],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},"1.8em",[232,17641,15912],{},[232,17643,234],{},[307,17645,310],{"stretchy":309},[232,17647,7759],{},[307,17649,317],{"stretchy":309},[307,17651,2668],{},[307,17653,310],{"stretchy":309},[312,17655,314],{},[307,17657,5011],{},[232,17659,15912],{},[307,17661,317],{"stretchy":309},[232,17663,234],{},[307,17665,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,17667,4356],{},[307,17669,310],{"stretchy":309},[232,17671,7759],{},[307,17673,317],{"stretchy":309},[307,17675,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,17677,454],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[1447,17679,17680,17686],{},[1450,17681,17682],{},[1453,17683,17684],{"scriptlevel":323,"displaystyle":243},[229,17685],{},[1450,17687,17688],{},[1453,17689,17690],{"scriptlevel":323,"displaystyle":243},[229,17691,17692,17694,17696,17698,17700,17702,17704,17706,17708,17710,17712,17714,17716,17718,17720,17722,17724,17726,17728,17730,17732,17734,17736,17738,17740,17742,17744,17746,17748],{},[229,17693],{},[354,17695],{"width":3460},[307,17697,2668],{},[307,17699,310],{"stretchy":309},[312,17701,314],{},[307,17703,5011],{},[232,17705,11539],{},[307,17707,317],{"stretchy":309},[307,17709,427],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[232,17711,15912],{},[232,17713,234],{},[307,17715,310],{"stretchy":309},[232,17717,15600],{},[307,17719,317],{"stretchy":309},[307,17721,2668],{},[307,17723,310],{"stretchy":309},[312,17725,314],{},[307,17727,5011],{},[232,17729,15912],{},[307,17731,317],{"stretchy":309},[232,17733,234],{},[307,17735,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,17737,4356],{},[307,17739,310],{"stretchy":309},[232,17741,15600],{},[307,17743,317],{"stretchy":309},[307,17745,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,17747,454],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[307,17749,748],{"separator":243},[236,17751,17752],{"encoding":238},"\\begin{aligned}\n&\\delta f(w)+(1-\\delta)f\\big(g(w)\\big)\\\\\n&\\le \\lambda\\Big[\\delta f(s)\n+(1-\\delta)f\\big(g(s)\\big)\\Big]\\\\\n&\\qquad+(1-\\lambda)\\Big[\\delta f(u)\n+(1-\\delta)f\\big(g(u)\\big)\\Big],\n\\end{aligned}",[212,17754,17756],{"className":17755,"ariaHidden":243},[242],[212,17757,17759,17763],{"className":17758},[247],[212,17760],{"className":17761,"style":17762},[251],"height:5.41em;vertical-align:-2.455em;",[212,17764,17766],{"className":17765},[256],[212,17767,17769,17822],{"className":17768},[1441],[212,17770,17772],{"className":17771},[1558],[212,17773,17775,17813],{"className":17774},[482,483],[212,17776,17778,17810],{"className":17777},[487],[212,17779,17782,17792,17801],{"className":17780,"style":17781},[491],"height:2.955em;",[212,17783,17785,17789],{"style":17784},"top:-5.255em;",[212,17786],{"className":17787,"style":17788},[499],"height:3.15em;",[212,17790],{"className":17791},[256],[212,17793,17795,17798],{"style":17794},"top:-3.445em;",[212,17796],{"className":17797,"style":17788},[499],[212,17799],{"className":17800},[256],[212,17802,17804,17807],{"style":17803},"top:-1.345em;",[212,17805],{"className":17806,"style":17788},[499],[212,17808],{"className":17809},[256],[212,17811,515],{"className":17812},[514],[212,17814,17816],{"className":17815},[487],[212,17817,17820],{"className":17818,"style":17819},[491],"height:2.455em;",[212,17821],{},[212,17823,17825],{"className":17824},[1649],[212,17826,17828,18158],{"className":17827},[482,483],[212,17829,17831,18155],{"className":17830},[487],[212,17832,17834,17917,18024],{"className":17833,"style":17781},[491],[212,17835,17836,17839],{"style":17784},[212,17837],{"className":17838,"style":17788},[499],[212,17840,17842,17845,17848,17851,17854,17857,17860,17863,17866,17869,17872,17875,17878,17881,17884,17887,17890,17893,17899,17902,17905,17908,17911],{"className":17841},[256],[212,17843],{"className":17844},[256],[212,17846,15912],{"className":17847,"style":15961},[256,257],[212,17849,234],{"className":17850,"style":258},[256,257],[212,17852,310],{"className":17853},[343],[212,17855,7768],{"className":17856,"style":8472},[256,257],[212,17858,317],{"className":17859},[350],[212,17861],{"className":17862,"style":2785},[354],[212,17864,2668],{"className":17865},[2789],[212,17867],{"className":17868,"style":2785},[354],[212,17870,310],{"className":17871},[343],[212,17873,314],{"className":17874},[256],[212,17876],{"className":17877,"style":2785},[354],[212,17879,5011],{"className":17880},[2789],[212,17882],{"className":17883,"style":2785},[354],[212,17885,15912],{"className":17886,"style":15961},[256,257],[212,17888,317],{"className":17889},[350],[212,17891,234],{"className":17892,"style":258},[256,257],[212,17894,17896],{"className":17895},[256],[212,17897,310],{"className":17898},[616,9872],[212,17900,4356],{"className":17901,"style":1178},[256,257],[212,17903,310],{"className":17904},[343],[212,17906,7768],{"className":17907,"style":8472},[256,257],[212,17909,317],{"className":17910},[350],[212,17912,17914],{"className":17913},[256],[212,17915,317],{"className":17916},[616,9872],[212,17918,17919,17922],{"style":17794},[212,17920],{"className":17921,"style":17788},[499],[212,17923,17925,17928,17931,17934,17937,17940,17946,17949,17952,17955,17958,17961,17964,17967,17970,17973,17976,17979,17982,17985,17988,17991,17994,18000,18003,18006,18009,18012,18018],{"className":17924},[256],[212,17926],{"className":17927},[256],[212,17929],{"className":17930,"style":355},[354],[212,17932,10150],{"className":17933},[359],[212,17935],{"className":17936,"style":355},[354],[212,17938,11539],{"className":17939},[256,257],[212,17941,17943],{"className":17942},[256],[212,17944,427],{"className":17945},[616,3918],[212,17947,15912],{"className":17948,"style":15961},[256,257],[212,17950,234],{"className":17951,"style":258},[256,257],[212,17953,310],{"className":17954},[343],[212,17956,7759],{"className":17957},[256,257],[212,17959,317],{"className":17960},[350],[212,17962],{"className":17963,"style":2785},[354],[212,17965,2668],{"className":17966},[2789],[212,17968],{"className":17969,"style":2785},[354],[212,17971,310],{"className":17972},[343],[212,17974,314],{"className":17975},[256],[212,17977],{"className":17978,"style":2785},[354],[212,17980,5011],{"className":17981},[2789],[212,17983],{"className":17984,"style":2785},[354],[212,17986,15912],{"className":17987,"style":15961},[256,257],[212,17989,317],{"className":17990},[350],[212,17992,234],{"className":17993,"style":258},[256,257],[212,17995,17997],{"className":17996},[256],[212,17998,310],{"className":17999},[616,9872],[212,18001,4356],{"className":18002,"style":1178},[256,257],[212,18004,310],{"className":18005},[343],[212,18007,7759],{"className":18008},[256,257],[212,18010,317],{"className":18011},[350],[212,18013,18015],{"className":18014},[256],[212,18016,317],{"className":18017},[616,9872],[212,18019,18021],{"className":18020},[256],[212,18022,454],{"className":18023},[616,3918],[212,18025,18026,18029],{"style":17803},[212,18027],{"className":18028,"style":17788},[499],[212,18030,18032,18035,18038,18041,18044,18047,18050,18053,18056,18059,18062,18065,18068,18074,18077,18080,18083,18086,18089,18092,18095,18098,18101,18104,18107,18110,18113,18116,18119,18122,18128,18131,18134,18137,18140,18146,18152],{"className":18031},[256],[212,18033],{"className":18034},[256],[212,18036],{"className":18037,"style":3832},[354],[212,18039],{"className":18040,"style":2785},[354],[212,18042,2668],{"className":18043},[2789],[212,18045],{"className":18046,"style":2785},[354],[212,18048,310],{"className":18049},[343],[212,18051,314],{"className":18052},[256],[212,18054],{"className":18055,"style":2785},[354],[212,18057,5011],{"className":18058},[2789],[212,18060],{"className":18061,"style":2785},[354],[212,18063,11539],{"className":18064},[256,257],[212,18066,317],{"className":18067},[350],[212,18069,18071],{"className":18070},[256],[212,18072,427],{"className":18073},[616,3918],[212,18075,15912],{"className":18076,"style":15961},[256,257],[212,18078,234],{"className":18079,"style":258},[256,257],[212,18081,310],{"className":18082},[343],[212,18084,15600],{"className":18085},[256,257],[212,18087,317],{"className":18088},[350],[212,18090],{"className":18091,"style":2785},[354],[212,18093,2668],{"className":18094},[2789],[212,18096],{"className":18097,"style":2785},[354],[212,18099,310],{"className":18100},[343],[212,18102,314],{"className":18103},[256],[212,18105],{"className":18106,"style":2785},[354],[212,18108,5011],{"className":18109},[2789],[212,18111],{"className":18112,"style":2785},[354],[212,18114,15912],{"className":18115,"style":15961},[256,257],[212,18117,317],{"className":18118},[350],[212,18120,234],{"className":18121,"style":258},[256,257],[212,18123,18125],{"className":18124},[256],[212,18126,310],{"className":18127},[616,9872],[212,18129,4356],{"className":18130,"style":1178},[256,257],[212,18132,310],{"className":18133},[343],[212,18135,15600],{"className":18136},[256,257],[212,18138,317],{"className":18139},[350],[212,18141,18143],{"className":18142},[256],[212,18144,317],{"className":18145},[616,9872],[212,18147,18149],{"className":18148},[256],[212,18150,454],{"className":18151},[616,3918],[212,18153,748],{"className":18154},[770],[212,18156,515],{"className":18157},[514],[212,18159,18161],{"className":18160},[487],[212,18162,18164],{"className":18163,"style":17819},[491],[212,18165],{},[11,18167,2448,18168,18341,18342,18370,18371,18531,18532,4051,18560,18588,18589,18830,18831,18908,18909,19091,19092,19162,19163,2943,19191,19248,19249,19277],{},[212,18169,18171,18215],{"className":18170,"translate":216},[215],[212,18172,18174],{"className":18173},[220],[222,18175,18176],{"xmlns":224},[226,18177,18178,18212],{},[229,18179,18180,18182,18184,18186,18188,18190],{},[232,18181,4356],{},[307,18183,310],{"stretchy":309},[232,18185,16650],{},[307,18187,317],{"stretchy":309},[307,18189,320],{},[1453,18191,18192],{"scriptlevel":323,"displaystyle":243},[435,18193,18194,18204],{},[229,18195,18196,18198,18200,18202],{},[312,18197,314],{},[307,18199,5011],{},[232,18201,16650],{},[232,18203,15912],{},[229,18205,18206,18208,18210],{},[312,18207,314],{},[307,18209,5011],{},[232,18211,15912],{},[236,18213,18214],{"encoding":238},"g(r)=\\dfrac{1-r\\delta}{1-\\delta}",[212,18216,18218,18245],{"className":18217,"ariaHidden":243},[242],[212,18219,18221,18224,18227,18230,18233,18236,18239,18242],{"className":18220},[247],[212,18222],{"className":18223,"style":336},[251],[212,18225,4356],{"className":18226,"style":1178},[256,257],[212,18228,310],{"className":18229},[343],[212,18231,16650],{"className":18232,"style":474},[256,257],[212,18234,317],{"className":18235},[350],[212,18237],{"className":18238,"style":355},[354],[212,18240,320],{"className":18241},[359],[212,18243],{"className":18244,"style":355},[354],[212,18246,18248,18252],{"className":18247},[247],[212,18249],{"className":18250,"style":18251},[251],"height:2.1408em;vertical-align:-0.7693em;",[212,18253,18255,18258,18338],{"className":18254},[256],[212,18256],{"className":18257},[343,638],[212,18259,18261],{"className":18260},[435],[212,18262,18264,18330],{"className":18263},[482,483],[212,18265,18267,18327],{"className":18266},[487],[212,18268,18270,18293,18301],{"className":18269,"style":651},[491],[212,18271,18272,18275],{"style":654},[212,18273],{"className":18274,"style":658},[499],[212,18276,18278,18281,18284,18287,18290],{"className":18277},[256],[212,18279,314],{"className":18280},[256],[212,18282],{"className":18283,"style":2785},[354],[212,18285,5011],{"className":18286},[2789],[212,18288],{"className":18289,"style":2785},[354],[212,18291,15912],{"className":18292,"style":15961},[256,257],[212,18294,18295,18298],{"style":670},[212,18296],{"className":18297,"style":658},[499],[212,18299],{"className":18300,"style":678},[677],[212,18302,18303,18306],{"style":681},[212,18304],{"className":18305,"style":658},[499],[212,18307,18309,18312,18315,18318,18321,18324],{"className":18308},[256],[212,18310,314],{"className":18311},[256],[212,18313],{"className":18314,"style":2785},[354],[212,18316,5011],{"className":18317},[2789],[212,18319],{"className":18320,"style":2785},[354],[212,18322,16650],{"className":18323,"style":474},[256,257],[212,18325,15912],{"className":18326,"style":15961},[256,257],[212,18328,515],{"className":18329},[514],[212,18331,18333],{"className":18332},[487],[212,18334,18336],{"className":18335,"style":17215},[491],[212,18337],{},[212,18339],{"className":18340},[350,638],"。注意 ",[212,18343,18345,18358],{"className":18344,"translate":216},[215],[212,18346,18348],{"className":18347},[220],[222,18349,18350],{"xmlns":224},[226,18351,18352,18356],{},[229,18353,18354],{},[232,18355,4356],{},[236,18357,4356],{"encoding":238},[212,18359,18361],{"className":18360,"ariaHidden":243},[242],[212,18362,18364,18367],{"className":18363},[247],[212,18365],{"className":18366,"style":2474},[251],[212,18368,4356],{"className":18369,"style":1178},[256,257]," 是仿射函数且 ",[212,18372,18374,18426],{"className":18373,"translate":216},[215],[212,18375,18377],{"className":18376},[220],[222,18378,18379],{"xmlns":224},[226,18380,18381,18423],{},[229,18382,18383,18385,18387,18389,18391,18393,18395,18397,18399,18401,18403,18405,18407,18409,18411,18413,18415,18417,18419,18421],{},[232,18384,4356],{},[307,18386,310],{"stretchy":309},[232,18388,7768],{},[307,18390,317],{"stretchy":309},[307,18392,320],{},[232,18394,11539],{},[232,18396,4356],{},[307,18398,310],{"stretchy":309},[232,18400,7759],{},[307,18402,317],{"stretchy":309},[307,18404,2668],{},[307,18406,310],{"stretchy":309},[312,18408,314],{},[307,18410,5011],{},[232,18412,11539],{},[307,18414,317],{"stretchy":309},[232,18416,4356],{},[307,18418,310],{"stretchy":309},[232,18420,15600],{},[307,18422,317],{"stretchy":309},[236,18424,18425],{"encoding":238},"g(w)=\\lambda g(s)+(1-\\lambda)g(u)",[212,18427,18429,18456,18486,18507],{"className":18428,"ariaHidden":243},[242],[212,18430,18432,18435,18438,18441,18444,18447,18450,18453],{"className":18431},[247],[212,18433],{"className":18434,"style":336},[251],[212,18436,4356],{"className":18437,"style":1178},[256,257],[212,18439,310],{"className":18440},[343],[212,18442,7768],{"className":18443,"style":8472},[256,257],[212,18445,317],{"className":18446},[350],[212,18448],{"className":18449,"style":355},[354],[212,18451,320],{"className":18452},[359],[212,18454],{"className":18455,"style":355},[354],[212,18457,18459,18462,18465,18468,18471,18474,18477,18480,18483],{"className":18458},[247],[212,18460],{"className":18461,"style":336},[251],[212,18463,11539],{"className":18464},[256,257],[212,18466,4356],{"className":18467,"style":1178},[256,257],[212,18469,310],{"className":18470},[343],[212,18472,7759],{"className":18473},[256,257],[212,18475,317],{"className":18476},[350],[212,18478],{"className":18479,"style":2785},[354],[212,18481,2668],{"className":18482},[2789],[212,18484],{"className":18485,"style":2785},[354],[212,18487,18489,18492,18495,18498,18501,18504],{"className":18488},[247],[212,18490],{"className":18491,"style":336},[251],[212,18493,310],{"className":18494},[343],[212,18496,314],{"className":18497},[256],[212,18499],{"className":18500,"style":2785},[354],[212,18502,5011],{"className":18503},[2789],[212,18505],{"className":18506,"style":2785},[354],[212,18508,18510,18513,18516,18519,18522,18525,18528],{"className":18509},[247],[212,18511],{"className":18512,"style":336},[251],[212,18514,11539],{"className":18515},[256,257],[212,18517,317],{"className":18518},[350],[212,18520,4356],{"className":18521,"style":1178},[256,257],[212,18523,310],{"className":18524},[343],[212,18526,15600],{"className":18527},[256,257],[212,18529,317],{"className":18530},[350],"，用 ",[212,18533,18535,18548],{"className":18534,"translate":216},[215],[212,18536,18538],{"className":18537},[220],[222,18539,18540],{"xmlns":224},[226,18541,18542,18546],{},[229,18543,18544],{},[232,18545,234],{},[236,18547,234],{"encoding":238},[212,18549,18551],{"className":18550,"ariaHidden":243},[242],[212,18552,18554,18557],{"className":18553},[247],[212,18555],{"className":18556,"style":252},[251],[212,18558,234],{"className":18559,"style":258},[256,257],[212,18561,18563,18576],{"className":18562,"translate":216},[215],[212,18564,18566],{"className":18565},[220],[222,18567,18568],{"xmlns":224},[226,18569,18570,18574],{},[229,18571,18572],{},[312,18573,314],{},[236,18575,314],{"encoding":238},[212,18577,18579],{"className":18578,"ariaHidden":243},[242],[212,18580,18582,18585],{"className":18581},[247],[212,18583],{"className":18584,"style":369},[251],[212,18586,314],{"className":18587},[256]," 处的支撑线（凸函数在可微点处 ",[212,18590,18592,18658],{"className":18591,"translate":216},[215],[212,18593,18595],{"className":18594},[220],[222,18596,18597],{"xmlns":224},[226,18598,18599,18655],{},[229,18600,18601,18603,18605,18607,18609,18611,18613,18615,18617,18619,18621,18627,18629,18631,18633,18635,18637,18639,18641,18643,18649,18651,18653],{},[232,18602,234],{},[307,18604,310],{"stretchy":309},[232,18606,966],{},[307,18608,317],{"stretchy":309},[307,18610,7126],{},[232,18612,234],{},[307,18614,310],{"stretchy":309},[312,18616,314],{},[307,18618,317],{"stretchy":309},[307,18620,2668],{},[7012,18622,18623,18625],{},[232,18624,234],{},[307,18626,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,18628,310],{"stretchy":309},[312,18630,314],{},[307,18632,317],{"stretchy":309},[307,18634,310],{"stretchy":309},[232,18636,966],{},[307,18638,5011],{},[312,18640,314],{},[307,18642,317],{"stretchy":309},[7012,18644,18645,18647],{},[232,18646,234],{},[307,18648,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,18650,310],{"stretchy":309},[312,18652,314],{},[307,18654,317],{"stretchy":309},[236,18656,18657],{"encoding":238},"f(t)\\ge f(1)+f'(1)(t-1)f'(1)",[212,18659,18661,18688,18715,18777],{"className":18660,"ariaHidden":243},[242],[212,18662,18664,18667,18670,18673,18676,18679,18682,18685],{"className":18663},[247],[212,18665],{"className":18666,"style":336},[251],[212,18668,234],{"className":18669,"style":258},[256,257],[212,18671,310],{"className":18672},[343],[212,18674,966],{"className":18675},[256,257],[212,18677,317],{"className":18678},[350],[212,18680],{"className":18681,"style":355},[354],[212,18683,7126],{"className":18684},[359],[212,18686],{"className":18687,"style":355},[354],[212,18689,18691,18694,18697,18700,18703,18706,18709,18712],{"className":18690},[247],[212,18692],{"className":18693,"style":336},[251],[212,18695,234],{"className":18696,"style":258},[256,257],[212,18698,310],{"className":18699},[343],[212,18701,314],{"className":18702},[256],[212,18704,317],{"className":18705},[350],[212,18707],{"className":18708,"style":2785},[354],[212,18710,2668],{"className":18711},[2789],[212,18713],{"className":18714,"style":2785},[354],[212,18716,18718,18721,18753,18756,18759,18762,18765,18768,18771,18774],{"className":18717},[247],[212,18719],{"className":18720,"style":7041},[251],[212,18722,18724,18727],{"className":18723},[256],[212,18725,234],{"className":18726,"style":258},[256,257],[212,18728,18730],{"className":18729},[478],[212,18731,18733],{"className":18732},[482],[212,18734,18736],{"className":18735},[487],[212,18737,18739],{"className":18738,"style":7060},[491],[212,18740,18741,18744],{"style":7063},[212,18742],{"className":18743,"style":500},[499],[212,18745,18747],{"className":18746},[504,505,506,507],[212,18748,18750],{"className":18749},[256,507],[212,18751,7018],{"className":18752},[256,507],[212,18754,310],{"className":18755},[343],[212,18757,314],{"className":18758},[256],[212,18760,317],{"className":18761},[350],[212,18763,310],{"className":18764},[343],[212,18766,966],{"className":18767},[256,257],[212,18769],{"className":18770,"style":2785},[354],[212,18772,5011],{"className":18773},[2789],[212,18775],{"className":18776,"style":2785},[354],[212,18778,18780,18783,18786,18789,18821,18824,18827],{"className":18779},[247],[212,18781],{"className":18782,"style":7041},[251],[212,18784,314],{"className":18785},[256],[212,18787,317],{"className":18788},[350],[212,18790,18792,18795],{"className":18791},[256],[212,18793,234],{"className":18794,"style":258},[256,257],[212,18796,18798],{"className":18797},[478],[212,18799,18801],{"className":18800},[482],[212,18802,18804],{"className":18803},[487],[212,18805,18807],{"className":18806,"style":7060},[491],[212,18808,18809,18812],{"style":7063},[212,18810],{"className":18811,"style":500},[499],[212,18813,18815],{"className":18814},[504,505,506,507],[212,18816,18818],{"className":18817},[256,507],[212,18819,7018],{"className":18820},[256,507],[212,18822,310],{"className":18823},[343],[212,18825,314],{"className":18826},[256],[212,18828,317],{"className":18829},[350],"，此处只需次梯度 ",[212,18832,18834,18858],{"className":18833,"translate":216},[215],[212,18835,18837],{"className":18836},[220],[222,18838,18839],{"xmlns":224},[226,18840,18841,18855],{},[229,18842,18843,18849,18851,18853],{},[7012,18844,18845,18847],{},[232,18846,234],{},[307,18848,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,18850,310],{"stretchy":309},[312,18852,314],{},[307,18854,317],{"stretchy":309},[236,18856,18857],{"encoding":238},"f'(1)",[212,18859,18861],{"className":18860,"ariaHidden":243},[242],[212,18862,18864,18867,18899,18902,18905],{"className":18863},[247],[212,18865],{"className":18866,"style":7041},[251],[212,18868,18870,18873],{"className":18869},[256],[212,18871,234],{"className":18872,"style":258},[256,257],[212,18874,18876],{"className":18875},[478],[212,18877,18879],{"className":18878},[482],[212,18880,18882],{"className":18881},[487],[212,18883,18885],{"className":18884,"style":7060},[491],[212,18886,18887,18890],{"style":7063},[212,18888],{"className":18889,"style":500},[499],[212,18891,18893],{"className":18892},[504,505,506,507],[212,18894,18896],{"className":18895},[256,507],[212,18897,7018],{"className":18898},[256,507],[212,18900,310],{"className":18901},[343],[212,18903,314],{"className":18904},[256],[212,18906,317],{"className":18907},[350],"，即 ",[212,18910,18912,18960],{"className":18911,"translate":216},[215],[212,18913,18915],{"className":18914},[220],[222,18916,18917],{"xmlns":224},[226,18918,18919,18957],{},[229,18920,18921,18923,18925,18927,18929,18931,18933,18935,18937,18939,18941,18947,18949,18951,18953,18955],{},[232,18922,234],{},[307,18924,310],{"stretchy":309},[232,18926,966],{},[307,18928,317],{"stretchy":309},[307,18930,7126],{},[232,18932,234],{},[307,18934,310],{"stretchy":309},[312,18936,314],{},[307,18938,317],{"stretchy":309},[307,18940,2668],{},[392,18942,18943,18945],{},[232,18944,4356],{},[312,18946,314],{},[307,18948,310],{"stretchy":309},[232,18950,966],{},[307,18952,5011],{},[312,18954,314],{},[307,18956,317],{"stretchy":309},[236,18958,18959],{"encoding":238},"f(t)\\ge f(1)+g_1(t-1)",[212,18961,18963,18990,19017,19079],{"className":18962,"ariaHidden":243},[242],[212,18964,18966,18969,18972,18975,18978,18981,18984,18987],{"className":18965},[247],[212,18967],{"className":18968,"style":336},[251],[212,18970,234],{"className":18971,"style":258},[256,257],[212,18973,310],{"className":18974},[343],[212,18976,966],{"className":18977},[256,257],[212,18979,317],{"className":18980},[350],[212,18982],{"className":18983,"style":355},[354],[212,18985,7126],{"className":18986},[359],[212,18988],{"className":18989,"style":355},[354],[212,18991,18993,18996,18999,19002,19005,19008,19011,19014],{"className":18992},[247],[212,18994],{"className":18995,"style":336},[251],[212,18997,234],{"className":18998,"style":258},[256,257],[212,19000,310],{"className":19001},[343],[212,19003,314],{"className":19004},[256],[212,19006,317],{"className":19007},[350],[212,19009],{"className":19010,"style":2785},[354],[212,19012,2668],{"className":19013},[2789],[212,19015],{"className":19016,"style":2785},[354],[212,19018,19020,19023,19064,19067,19070,19073,19076],{"className":19019},[247],[212,19021],{"className":19022,"style":336},[251],[212,19024,19026,19029],{"className":19025},[256],[212,19027,4356],{"className":19028,"style":1178},[256,257],[212,19030,19032],{"className":19031},[478],[212,19033,19035,19056],{"className":19034},[482,483],[212,19036,19038,19053],{"className":19037},[487],[212,19039,19041],{"className":19040,"style":11333},[491],[212,19042,19044,19047],{"style":19043},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[212,19045],{"className":19046,"style":500},[499],[212,19048,19050],{"className":19049},[504,505,506,507],[212,19051,314],{"className":19052},[256,507],[212,19054,515],{"className":19055},[514],[212,19057,19059],{"className":19058},[487],[212,19060,19062],{"className":19061,"style":8166},[491],[212,19063],{},[212,19065,310],{"className":19066},[343],[212,19068,966],{"className":19069},[256,257],[212,19071],{"className":19072,"style":2785},[354],[212,19074,5011],{"className":19075},[2789],[212,19077],{"className":19078,"style":2785},[354],[212,19080,19082,19085,19088],{"className":19081},[247],[212,19083],{"className":19084,"style":336},[251],[212,19086,314],{"className":19087},[256],[212,19089,317],{"className":19090},[350]," 对任一次梯度 ",[212,19093,19095,19113],{"className":19094,"translate":216},[215],[212,19096,19098],{"className":19097},[220],[222,19099,19100],{"xmlns":224},[226,19101,19102,19110],{},[229,19103,19104],{},[392,19105,19106,19108],{},[232,19107,4356],{},[312,19109,314],{},[236,19111,19112],{"encoding":238},"g_1",[212,19114,19116],{"className":19115,"ariaHidden":243},[242],[212,19117,19119,19122],{"className":19118},[247],[212,19120],{"className":19121,"style":2474},[251],[212,19123,19125,19128],{"className":19124},[256],[212,19126,4356],{"className":19127,"style":1178},[256,257],[212,19129,19131],{"className":19130},[478],[212,19132,19134,19154],{"className":19133},[482,483],[212,19135,19137,19151],{"className":19136},[487],[212,19138,19140],{"className":19139,"style":11333},[491],[212,19141,19142,19145],{"style":19043},[212,19143],{"className":19144,"style":500},[499],[212,19146,19148],{"className":19147},[504,505,506,507],[212,19149,314],{"className":19150},[256,507],[212,19152,515],{"className":19153},[514],[212,19155,19157],{"className":19156},[487],[212,19158,19160],{"className":19159,"style":8166},[491],[212,19161],{},"）处理非主项：对凸的 ",[212,19164,19166,19179],{"className":19165,"translate":216},[215],[212,19167,19169],{"className":19168},[220],[222,19170,19171],{"xmlns":224},[226,19172,19173,19177],{},[229,19174,19175],{},[232,19176,234],{},[236,19178,234],{"encoding":238},[212,19180,19182],{"className":19181,"ariaHidden":243},[242],[212,19183,19185,19188],{"className":19184},[247],[212,19186],{"className":19187,"style":252},[251],[212,19189,234],{"className":19190,"style":258},[256,257],[212,19192,19194,19220],{"className":19193,"translate":216},[215],[212,19195,19197],{"className":19196},[220],[222,19198,19199],{"xmlns":224},[226,19200,19201,19217],{},[229,19202,19203,19205,19207,19209,19211,19213,19215],{},[232,19204,234],{},[307,19206,310],{"stretchy":309},[232,19208,4356],{},[307,19210,310],{"stretchy":309},[232,19212,16650],{},[307,19214,317],{"stretchy":309},[307,19216,317],{"stretchy":309},[236,19218,19219],{"encoding":238},"f(g(r))",[212,19221,19223],{"className":19222,"ariaHidden":243},[242],[212,19224,19226,19229,19232,19235,19238,19241,19244],{"className":19225},[247],[212,19227],{"className":19228,"style":336},[251],[212,19230,234],{"className":19231,"style":258},[256,257],[212,19233,310],{"className":19234},[343],[212,19236,4356],{"className":19237,"style":1178},[256,257],[212,19239,310],{"className":19240},[343],[212,19242,16650],{"className":19243,"style":474},[256,257],[212,19245,19247],{"className":19246},[350],"))"," 中关于 ",[212,19250,19252,19265],{"className":19251,"translate":216},[215],[212,19253,19255],{"className":19254},[220],[222,19256,19257],{"xmlns":224},[226,19258,19259,19263],{},[229,19260,19261],{},[232,19262,16650],{},[236,19264,16650],{"encoding":238},[212,19266,19268],{"className":19267,"ariaHidden":243},[242],[212,19269,19271,19274],{"className":19270},[247],[212,19272],{"className":19273,"style":2543},[251],[212,19275,16650],{"className":19276,"style":474},[256,257]," 的\"非主项\"部分为",[212,19279,19281],{"className":19280,"translate":216},[377],[212,19282,19284,19489],{"className":19283,"translate":216},[215],[212,19285,19287],{"className":19286},[220],[222,19288,19289],{"xmlns":224,"display":386},[226,19290,19291,19486],{},[1441,19292,19293,19357,19432],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,19294,19295,19315],{},[1450,19296,19297],{},[1453,19298,19299],{"scriptlevel":323,"displaystyle":243},[229,19300,19301,19303,19305,19307,19309,19311,19313],{},[232,19302,234],{},[307,19304,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,19306,4356],{},[307,19308,310],{"stretchy":309},[232,19310,16650],{},[307,19312,317],{"stretchy":309},[307,19314,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[1450,19316,19317],{},[1453,19318,19319],{"scriptlevel":323,"displaystyle":243},[229,19320,19321,19323,19325,19327,19329,19331,19333,19335,19355],{},[229,19322],{},[307,19324,320],{},[232,19326,234],{},[307,19328,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[312,19330,314],{},[307,19332,2668],{},[232,19334,15912],{},[1453,19336,19337],{"scriptlevel":323,"displaystyle":309},[435,19338,19339,19347],{},[229,19340,19341,19343,19345],{},[312,19342,314],{},[307,19344,5011],{},[232,19346,16650],{},[229,19348,19349,19351,19353],{},[312,19350,314],{},[307,19352,5011],{},[232,19354,15912],{},[307,19356,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[1447,19358,19359,19365],{},[1450,19360,19361],{},[1453,19362,19363],{"scriptlevel":323,"displaystyle":243},[229,19364],{},[1450,19366,19367],{},[1453,19368,19369],{"scriptlevel":323,"displaystyle":243},[229,19370,19371,19373,19375,19377,19379,19381,19383,19385,19391,19393,19395,19397,19417,19419,19422,19424,19430],{},[229,19372],{},[307,19374,320],{},[232,19376,234],{},[307,19378,310],{"stretchy":309},[312,19380,314],{},[307,19382,317],{"stretchy":309},[307,19384,2668],{},[392,19386,19387,19389],{},[232,19388,4356],{},[312,19390,314],{},[307,19392,3497],{},[232,19394,15912],{},[1495,19396,1497],{},[1453,19398,19399],{"scriptlevel":323,"displaystyle":309},[435,19400,19401,19409],{},[229,19402,19403,19405,19407],{},[312,19404,314],{},[307,19406,5011],{},[232,19408,16650],{},[229,19410,19411,19413,19415],{},[312,19412,314],{},[307,19414,5011],{},[232,19416,15912],{},[307,19418,2668],{},[232,19420,19421],{},"O",[307,19423,310],{"stretchy":309},[7012,19425,19426,19428],{},[232,19427,15912],{},[312,19429,2661],{},[307,19431,317],{"stretchy":309},[1447,19433,19434,19440],{},[1450,19435,19436],{},[1453,19437,19438],{"scriptlevel":323,"displaystyle":243},[229,19439],{},[1450,19441,19442],{},[1453,19443,19444],{"scriptlevel":323,"displaystyle":243},[229,19445,19446,19448,19450,19456,19458,19460,19462,19464,19466,19468,19470,19472,19474,19476,19482,19484],{},[229,19447],{},[307,19449,320],{},[392,19451,19452,19454],{},[232,19453,4356],{},[312,19455,314],{},[1495,19457,1497],{},[232,19459,15912],{},[307,19461,310],{"stretchy":309},[312,19463,314],{},[307,19465,5011],{},[232,19467,16650],{},[307,19469,317],{"stretchy":309},[307,19471,2668],{},[232,19473,19421],{},[307,19475,310],{"stretchy":309},[7012,19477,19478,19480],{},[232,19479,15912],{},[312,19481,2661],{},[307,19483,317],{"stretchy":309},[307,19485,748],{"separator":243},[236,19487,19488],{"encoding":238},"\\begin{aligned}\nf\\big(g(r)\\big)\n&=f\\big(1+\\delta\\tfrac{1-r}{1-\\delta}\\big)\\\\\n&= f(1)+g_1\\cdot\\delta\\,\\tfrac{1-r}{1-\\delta}\n+O(\\delta^2)\\\\\n&= 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项在 ",[212,20245,20247,20260],{"className":20246,"translate":216},[215],[212,20248,20250],{"className":20249},[220],[222,20251,20252],{"xmlns":224},[226,20253,20254,20258],{},[229,20255,20256],{},[232,20257,16650],{},[236,20259,16650],{"encoding":238},[212,20261,20263],{"className":20262,"ariaHidden":243},[242],[212,20264,20266,20269],{"className":20265},[247],[212,20267],{"className":20268,"style":2543},[251],[212,20270,16650],{"className":20271,"style":474},[256,257]," 变化时一致有界，因为 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连续）。代回不等式：两边的主项（",[212,20406,20408,20430],{"className":20407,"translate":216},[215],[212,20409,20411],{"className":20410},[220],[222,20412,20413],{"xmlns":224},[226,20414,20415,20427],{},[229,20416,20417,20419,20421,20423,20425],{},[232,20418,15912],{},[232,20420,234],{},[307,20422,310],{"stretchy":309},[307,20424,3497],{},[307,20426,317],{"stretchy":309},[236,20428,20429],{"encoding":238},"\\delta f(\\cdot)",[212,20431,20433],{"className":20432,"ariaHidden":243},[242],[212,20434,20436,20439,20442,20445,20448,20451],{"className":20435},[247],[212,20437],{"className":20438,"style":336},[251],[212,20440,15912],{"className":20441,"style":15961},[256,257],[212,20443,234],{"className":20444,"style":258},[256,257],[212,20446,310],{"className":20447},[343],[212,20449,3497],{"className":20450},[256],[212,20452,317],{"className":20453},[350]," 部分）正是 ",[212,20456,20458,20506],{"className":20457,"translate":216},[215],[212,20459,20461],{"className":20460},[220],[222,20462,20463],{"xmlns":224},[226,20464,20465,20503],{},[229,20466,20467,20469,20471,20473,20475,20477,20479,20481,20483,20485,20487,20489,20491,20493,20495,20497,20499,20501],{},[232,20468,15912],{},[307,20470,427],{"stretchy":309},[232,20472,11539],{},[232,20474,234],{},[307,20476,310],{"stretchy":309},[232,20478,7759],{},[307,20480,317],{"stretchy":309},[307,20482,2668],{},[307,20484,310],{"stretchy":309},[312,20486,314],{},[307,20488,5011],{},[232,20490,11539],{},[307,20492,317],{"stretchy":309},[232,20494,234],{},[307,20496,310],{"stretchy":309},[232,20498,15600],{},[307,20500,317],{"stretchy":309},[307,20502,454],{"stretchy":309},[236,20504,20505],{"encoding":238},"\\delta[\\lambda f(s)+(1-\\lambda)f(u)]",[212,20507,20509,20545,20566],{"className":20508,"ariaHidden":243},[242],[212,20510,20512,20515,20518,20521,20524,20527,20530,20533,20536,20539,20542],{"className":20511},[247],[212,20513],{"className":20514,"style":336},[251],[212,20516,15912],{"className":20517,"style":15961},[256,257],[212,20519,427],{"className":20520},[343],[212,20522,11539],{"className":20523},[256,257],[212,20525,234],{"className":20526,"style":258},[256,257],[212,20528,310],{"className":20529},[343],[212,20531,7759],{"className":20532},[256,257],[212,20534,317],{"className":20535},[350],[212,20537],{"className":20538,"style":2785},[354],[212,20540,2668],{"className":20541},[2789],[212,20543],{"className":20544,"style":2785},[354],[212,20546,20548,20551,20554,20557,20560,20563],{"className":20547},[247],[212,20549],{"className":20550,"style":336},[251],[212,20552,310],{"className":20553},[343],[212,20555,314],{"className":20556},[256],[212,20558],{"className":20559,"style":2785},[354],[212,20561,5011],{"className":20562},[2789],[212,20564],{"className":20565,"style":2785},[354],[212,20567,20569,20572,20575,20578,20581,20584,20587],{"className":20568},[247],[212,20570],{"className":20571,"style":336},[251],[212,20573,11539],{"className":20574},[256,257],[212,20576,317],{"className":20577},[350],[212,20579,234],{"className":20580,"style":258},[256,257],[212,20582,310],{"className":20583},[343],[212,20585,15600],{"className":20586},[256,257],[212,20588,20590],{"className":20589},[350],")]",[212,20592,20594,20616],{"className":20593,"translate":216},[215],[212,20595,20597],{"className":20596},[220],[222,20598,20599],{"xmlns":224},[226,20600,20601,20613],{},[229,20602,20603,20605,20607,20609,20611],{},[232,20604,15912],{},[232,20606,234],{},[307,20608,310],{"stretchy":309},[232,20610,7768],{},[307,20612,317],{"stretchy":309},[236,20614,20615],{"encoding":238},"\\delta f(w)",[212,20617,20619],{"className":20618,"ariaHidden":243},[242],[212,20620,20622,20625,20628,20631,20634,20637],{"className":20621},[247],[212,20623],{"className":20624,"style":336},[251],[212,20626,15912],{"className":20627,"style":15961},[256,257],[212,20629,234],{"className":20630,"style":258},[256,257],[212,20632,310],{"className":20633},[343],[212,20635,7768],{"className":20636,"style":8472},[256,257],[212,20638,317],{"className":20639},[350],"；非主项部分",[212,20642,20644],{"className":20643,"translate":216},[377],[212,20645,20647,20733],{"className":20646,"translate":216},[215],[212,20648,20650],{"className":20649},[220],[222,20651,20652],{"xmlns":224,"display":386},[226,20653,20654,20730],{},[229,20655,20656,20658,20660,20662,20664,20666,20668,20674,20676,20678,20680,20682,20684,20686,20688,20690,20692,20694,20696,20698,20700,20702,20704,20706,20708,20710,20712,20714,20716,20718,20720,20722,20724,20726,20728],{},[307,20657,310],{"stretchy":309},[312,20659,314],{},[307,20661,5011],{},[232,20663,15912],{},[307,20665,317],{"stretchy":309},[1495,20667,1497],{},[392,20669,20670,20672],{},[232,20671,4356],{},[312,20673,314],{},[232,20675,15912],{},[307,20677,427],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,20679,11539],{},[307,20681,310],{"stretchy":309},[312,20683,314],{},[307,20685,5011],{},[232,20687,7759],{},[307,20689,317],{"stretchy":309},[307,20691,2668],{},[307,20693,310],{"stretchy":309},[312,20695,314],{},[307,20697,5011],{},[232,20699,11539],{},[307,20701,317],{"stretchy":309},[307,20703,310],{"stretchy":309},[312,20705,314],{},[307,20707,5011],{},[232,20709,15600],{},[307,20711,317],{"stretchy":309},[307,20713,5011],{},[307,20715,310],{"stretchy":309},[312,20717,314],{},[307,20719,5011],{},[232,20721,7768],{},[307,20723,317],{"stretchy":309},[307,20725,454],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,20727,320],{},[312,20729,323],{},[236,20731,20732],{"encoding":238},"(1-\\delta)\\,g_1\\delta\\big[\\lambda(1-s)\n+(1-\\lambda)(1-u)-(1-w)\\big]=0",[212,20734,20736,20757,20840,20861,20882,20909,20930,20951,20978],{"className":20735,"ariaHidden":243},[242],[212,20737,20739,20742,20745,20748,20751,20754],{"className":20738},[247],[212,20740],{"className":20741,"style":336},[251],[212,20743,310],{"className":20744},[343],[212,20746,314],{"className":20747},[256],[212,20749],{"className":20750,"style":2785},[354],[212,20752,5011],{"className":20753},[2789],[212,20755],{"className":20756,"style":2785},[354],[212,20758,20760,20764,20767,20770,20773,20813,20816,20822,20825,20828,20831,20834,20837],{"className":20759},[247],[212,20761],{"className":20762,"style":20763},[251],"height:1.2em;vertical-align:-0.35em;",[212,20765,15912],{"className":20766,"style":15961},[256,257],[212,20768,317],{"className":20769},[350],[212,20771],{"className":20772,"style":603},[354],[212,20774,20776,20779],{"className":20775},[256],[212,20777,4356],{"className":20778,"style":1178},[256,257],[212,20780,20782],{"className":20781},[478],[212,20783,20785,20805],{"className":20784},[482,483],[212,20786,20788,20802],{"className":20787},[487],[212,20789,20791],{"className":20790,"style":11333},[491],[212,20792,20793,20796],{"style":19043},[212,20794],{"className":20795,"style":500},[499],[212,20797,20799],{"className":20798},[504,505,506,507],[212,20800,314],{"className":20801},[256,507],[212,20803,515],{"className":20804},[514],[212,20806,20808],{"className":20807},[487],[212,20809,20811],{"className":20810,"style":8166},[491],[212,20812],{},[212,20814,15912],{"className":20815,"style":15961},[256,257],[212,20817,20819],{"className":20818},[256],[212,20820,427],{"className":20821},[616,9872],[212,20823,11539],{"className":20824},[256,257],[212,20826,310],{"className":20827},[343],[212,20829,314],{"className":20830},[256],[212,20832],{"className":20833,"style":2785},[354],[212,20835,5011],{"className":20836},[2789],[212,20838],{"className":20839,"style":2785},[354],[212,20841,20843,20846,20849,20852,20855,20858],{"className":20842},[247],[212,20844],{"className":20845,"style":336},[251],[212,20847,7759],{"className":20848},[256,257],[212,20850,317],{"className":20851},[350],[212,20853],{"className":20854,"style":2785},[354],[212,20856,2668],{"className":20857},[2789],[212,20859],{"className":20860,"style":2785},[354],[212,20862,20864,20867,20870,20873,20876,20879],{"className":20863},[247],[212,20865],{"className":20866,"style":336},[251],[212,20868,310],{"className":20869},[343],[212,20871,314],{"className":20872},[256],[212,20874],{"className":20875,"style":2785},[354],[212,20877,5011],{"className":20878},[2789],[212,20880],{"className":20881,"style":2785},[354],[212,20883,20885,20888,20891,20894,20897,20900,20903,20906],{"className":20884},[247],[212,20886],{"className":20887,"style":336},[251],[212,20889,11539],{"className":20890},[256,257],[212,20892,317],{"className":20893},[350],[212,20895,310],{"className":20896},[343],[212,20898,314],{"className":20899},[256],[212,20901],{"className":20902,"style":2785},[354],[212,20904,5011],{"className":20905},[2789],[212,20907],{"className":20908,"style":2785},[354],[212,20910,20912,20915,20918,20921,20924,20927],{"className":20911},[247],[212,20913],{"className":20914,"style":336},[251],[212,20916,15600],{"className":20917},[256,257],[212,20919,317],{"className":20920},[350],[212,20922],{"className":20923,"style":2785},[354],[212,20925,5011],{"className":20926},[2789],[212,20928],{"className":20929,"style":2785},[354],[212,20931,20933,20936,20939,20942,20945,20948],{"className":20932},[247],[212,20934],{"className":20935,"style":336},[251],[212,20937,310],{"className":20938},[343],[212,20940,314],{"className":20941},[256],[212,20943],{"className":20944,"style":2785},[354],[212,20946,5011],{"className":20947},[2789],[212,20949],{"className":20950,"style":2785},[354],[212,20952,20954,20957,20960,20963,20969,20972,20975],{"className":20953},[247],[212,20955],{"className":20956,"style":20763},[251],[212,20958,7768],{"className":20959,"style":8472},[256,257],[212,20961,317],{"className":20962},[350],[212,20964,20966],{"className":20965},[256],[212,20967,454],{"className":20968},[616,9872],[212,20970],{"className":20971,"style":355},[354],[212,20973,320],{"className":20974},[359],[212,20976],{"className":20977,"style":355},[354],[212,20979,20981,20984],{"className":20980},[247],[212,20982],{"className":20983,"style":369},[251],[212,20985,323],{"className":20986},[256],[11,20988,20989,20990,21104,21105,21156,21157,21239],{},"（方括号内恰为 0，因为 ",[212,20991,20993,21026],{"className":20992,"translate":216},[215],[212,20994,20996],{"className":20995},[220],[222,20997,20998],{"xmlns":224},[226,20999,21000,21024],{},[229,21001,21002,21004,21006,21008,21010,21012,21014,21016,21018,21020,21022],{},[232,21003,7768],{},[307,21005,320],{},[232,21007,11539],{},[232,21009,7759],{},[307,21011,2668],{},[307,21013,310],{"stretchy":309},[312,21015,314],{},[307,21017,5011],{},[232,21019,11539],{},[307,21021,317],{"stretchy":309},[232,21023,15600],{},[236,21025,15758],{"encoding":238},[212,21027,21029,21047,21068,21089],{"className":21028,"ariaHidden":243},[242],[212,21030,21032,21035,21038,21041,21044],{"className":21031},[247],[212,21033],{"className":21034,"style":2543},[251],[212,21036,7768],{"className":21037,"style":8472},[256,257],[212,21039],{"className":21040,"style":355},[354],[212,21042,320],{"className":21043},[359],[212,21045],{"className":21046,"style":355},[354],[212,21048,21050,21053,21056,21059,21062,21065],{"className":21049},[247],[212,21051],{"className":21052,"style":15786},[251],[212,21054,11539],{"className":21055},[256,257],[212,21057,7759],{"className":21058},[256,257],[212,21060],{"className":21061,"style":2785},[354],[212,21063,2668],{"className":21064},[2789],[212,21066],{"className":21067,"style":2785},[354],[212,21069,21071,21074,21077,21080,21083,21086],{"className":21070},[247],[212,21072],{"className":21073,"style":336},[251],[212,21075,310],{"className":21076},[343],[212,21078,314],{"className":21079},[256],[212,21081],{"className":21082,"style":2785},[354],[212,21084,5011],{"className":21085},[2789],[212,21087],{"className":21088,"style":2785},[354],[212,21090,21092,21095,21098,21101],{"className":21091},[247],[212,21093],{"className":21094,"style":336},[251],[212,21096,11539],{"className":21097},[256,257],[212,21099,317],{"className":21100},[350],[212,21102,15600],{"className":21103},[256,257],"）。于是不等式两边同除以 ",[212,21106,21108,21126],{"className":21107,"translate":216},[215],[212,21109,21111],{"className":21110},[220],[222,21112,21113],{"xmlns":224},[226,21114,21115,21123],{},[229,21116,21117,21119,21121],{},[232,21118,15912],{},[307,21120,3101],{},[312,21122,323],{},[236,21124,21125],{"encoding":238},"\\delta>0",[212,21127,21129,21147],{"className":21128,"ariaHidden":243},[242],[212,21130,21132,21135,21138,21141,21144],{"className":21131},[247],[212,21133],{"className":21134,"style":11564},[251],[212,21136,15912],{"className":21137,"style":15961},[256,257],[212,21139],{"className":21140,"style":355},[354],[212,21142,3101],{"className":21143},[359],[212,21145],{"className":21146,"style":355},[354],[212,21148,21150,21153],{"className":21149},[247],[212,21151],{"className":21152,"style":369},[251],[212,21154,323],{"className":21155},[256],"，令 ",[212,21158,21160,21182],{"className":21159,"translate":216},[215],[212,21161,21163],{"className":21162},[220],[222,21164,21165],{"xmlns":224},[226,21166,21167,21179],{},[229,21168,21169,21171,21173],{},[232,21170,15912],{},[307,21172,1228],{},[7012,21174,21175,21177],{},[312,21176,323],{},[307,21178,2668],{},[236,21180,21181],{"encoding":238},"\\delta\\to0^+",[212,21183,21185,21203],{"className":21184,"ariaHidden":243},[242],[212,21186,21188,21191,21194,21197,21200],{"className":21187},[247],[212,21189],{"className":21190,"style":12797},[251],[212,21192,15912],{"className":21193,"style":15961},[256,257],[212,21195],{"className":21196,"style":355},[354],[212,21198,1228],{"className":21199},[359],[212,21201],{"className":21202,"style":355},[354],[212,21204,21206,21210],{"className":21205},[247],[212,21207],{"className":21208,"style":21209},[251],"height:0.7713em;",[212,21211,21213,21216],{"className":21212},[256],[212,21214,323],{"className":21215},[256],[212,21217,21219],{"className":21218},[478],[212,21220,21222],{"className":21221},[482],[212,21223,21225],{"className":21224},[487],[212,21226,21228],{"className":21227,"style":21209},[491],[212,21229,21230,21233],{"style":7063},[212,21231],{"className":21232,"style":500},[499],[212,21234,21236],{"className":21235},[504,505,506,507],[212,21237,2668],{"className":21238},[2789,507],"，得",[212,21241,21243],{"className":21242,"translate":216},[377],[212,21244,21246,21316],{"className":21245,"translate":216},[215],[212,21247,21249],{"className":21248},[220],[222,21250,21251],{"xmlns":224,"display":386},[226,21252,21253,21313],{},[229,21254,21255,21257,21259,21261,21263,21265,21267,21269,21271,21273,21275,21277,21279,21281,21283,21285,21287,21289,21291,21293,21295,21297,21299,21301,21303,21305,21307,21309,21311],{},[232,21256,234],{},[307,21258,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,21260,11539],{},[232,21262,7759],{},[307,21264,2668],{},[307,21266,310],{"stretchy":309},[312,21268,314],{},[307,21270,5011],{},[232,21272,11539],{},[307,21274,317],{"stretchy":309},[232,21276,15600],{},[307,21278,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,21280,10150],{},[232,21282,11539],{},[232,21284,234],{},[307,21286,310],{"stretchy":309},[232,21288,7759],{},[307,21290,317],{"stretchy":309},[307,21292,2668],{},[307,21294,310],{"stretchy":309},[312,21296,314],{},[307,21298,5011],{},[232,21300,11539],{},[307,21302,317],{"stretchy":309},[232,21304,234],{},[307,21306,310],{"stretchy":309},[232,21308,15600],{},[307,21310,317],{"stretchy":309},[307,21312,748],{"separator":243},[236,21314,21315],{"encoding":238},"f\\big(\\lambda s+(1-\\lambda)u\\big)\n\\le\\lambda f(s)+(1-\\lambda)f(u),",[212,21317,21319,21349,21370,21400,21430,21451],{"className":21318,"ariaHidden":243},[242],[212,21320,21322,21325,21328,21334,21337,21340,21343,21346],{"className":21321},[247],[212,21323],{"className":21324,"style":20763},[251],[212,21326,234],{"className":21327,"style":258},[256,257],[212,21329,21331],{"className":21330},[256],[212,21332,310],{"className":21333},[616,9872],[212,21335,11539],{"className":21336},[256,257],[212,21338,7759],{"className":21339},[256,257],[212,21341],{"className":21342,"style":2785},[354],[212,21344,2668],{"className":21345},[2789],[212,21347],{"className":21348,"style":2785},[354],[212,21350,21352,21355,21358,21361,21364,21367],{"className":21351},[247],[212,21353],{"className":21354,"style":336},[251],[212,21356,310],{"className":21357},[343],[212,21359,314],{"className":21360},[256],[212,21362],{"className":21363,"style":2785},[354],[212,21365,5011],{"className":21366},[2789],[212,21368],{"className":21369,"style":2785},[354],[212,21371,21373,21376,21379,21382,21385,21391,21394,21397],{"className":21372},[247],[212,21374],{"className":21375,"style":20763},[251],[212,21377,11539],{"className":21378},[256,257],[212,21380,317],{"className":21381},[350],[212,21383,15600],{"className":21384},[256,257],[212,21386,21388],{"className":21387},[256],[212,21389,317],{"className":21390},[616,9872],[212,21392],{"className":21393,"style":355},[354],[212,21395,10150],{"className":21396},[359],[212,21398],{"className":21399,"style":355},[354],[212,21401,21403,21406,21409,21412,21415,21418,21421,21424,21427],{"className":21402},[247],[212,21404],{"className":21405,"style":336},[251],[212,21407,11539],{"className":21408},[256,257],[212,21410,234],{"className":21411,"style":258},[256,257],[212,21413,310],{"className":21414},[343],[212,21416,7759],{"className":21417},[256,257],[212,21419,317],{"className":21420},[350],[212,21422],{"className":21423,"style":2785},[354],[212,21425,2668],{"className":21426},[2789],[212,21428],{"className":21429,"style":2785},[354],[212,21431,21433,21436,21439,21442,21445,21448],{"className":21432},[247],[212,21434],{"className":21435,"style":336},[251],[212,21437,310],{"className":21438},[343],[212,21440,314],{"className":21441},[256],[212,21443],{"className":21444,"style":2785},[354],[212,21446,5011],{"className":21447},[2789],[212,21449],{"className":21450,"style":2785},[354],[212,21452,21454,21457,21460,21463,21466,21469,21472,21475],{"className":21453},[247],[212,21455],{"className":21456,"style":336},[251],[212,21458,11539],{"className":21459},[256,257],[212,21461,317],{"className":21462},[350],[212,21464,234],{"className":21465,"style":258},[256,257],[212,21467,310],{"className":21468},[343],[212,21470,15600],{"className":21471},[256,257],[212,21473,317],{"className":21474},[350],[212,21476,748],{"className":21477},[770],[11,21479,21480,21481,11165],{},"即 ",[212,21482,21484,21497],{"className":21483,"translate":216},[215],[212,21485,21487],{"className":21486},[220],[222,21488,21489],{"xmlns":224},[226,21490,21491,21495],{},[229,21492,21493],{},[232,21494,234],{},[236,21496,234],{"encoding":238},[212,21498,21500],{"className":21499,"ariaHidden":243},[242],[212,21501,21503,21506],{"className":21502},[247],[212,21504],{"className":21505,"style":252},[251],[212,21507,234],{"className":21508,"style":258},[256,257],[11,21510,21511,21512,21515,21516,21544,21545,21575,21576,21604],{},"所以\"凸\"与\"数据处理\"是同一件事的两面。这也是 f-散度族成为\"一切满足数据处理不等式的最一般散度\"的原因：它不是一堆例子的偶然汇总，而是一个有刻画定理支撑的完整族。换句话说，Csiszár–Ali–Silvey 定理给出一个完整的",[1194,21513,21514],{},"刻画","：凸函数 ",[212,21517,21519,21532],{"className":21518,"translate":216},[215],[212,21520,21522],{"className":21521},[220],[222,21523,21524],{"xmlns":224},[226,21525,21526,21530],{},[229,21527,21528],{},[232,21529,234],{},[236,21531,234],{"encoding":238},[212,21533,21535],{"className":21534,"ariaHidden":243},[242],[212,21536,21538,21541],{"className":21537},[247],[212,21539],{"className":21540,"style":252},[251],[212,21542,234],{"className":21543,"style":258},[256,257],"（模去仿射项）",[212,21546,21548,21563],{"className":21547,"translate":216},[215],[212,21549,21551],{"className":21550},[220],[222,21552,21553],{"xmlns":224},[226,21554,21555,21560],{},[229,21556,21557],{},[307,21558,21559],{},"↔",[236,21561,21562],{"encoding":238},"\\leftrightarrow",[212,21564,21566],{"className":21565,"ariaHidden":243},[242],[212,21567,21569,21572],{"className":21568},[247],[212,21570],{"className":21571,"style":11203},[251],[212,21573,21559],{"className":21574},[359]," 联合凸泛函 ",[212,21577,21579,21592],{"className":21578,"translate":216},[215],[212,21580,21582],{"className":21581},[220],[222,21583,21584],{"xmlns":224},[226,21585,21586,21590],{},[229,21587,21588],{},[307,21589,21559],{},[236,21591,21562],{"encoding":238},[212,21593,21595],{"className":21594,"ariaHidden":243},[242],[212,21596,21598,21601],{"className":21597},[247],[212,21599],{"className":21600,"style":11203},[251],[212,21602,21559],{"className":21603},[359]," 满足数据处理不等式的分布差异度量，三者一一对应。",[725,21606,21608],{"id":21607},"_3-常见散度","3. 常见散度",[11,21610,21611,21612,21640],{},"不同的 ",[212,21613,21615,21628],{"className":21614,"translate":216},[215],[212,21616,21618],{"className":21617},[220],[222,21619,21620],{"xmlns":224},[226,21621,21622,21626],{},[229,21623,21624],{},[232,21625,234],{},[236,21627,234],{"encoding":238},[212,21629,21631],{"className":21630,"ariaHidden":243},[242],[212,21632,21634,21637],{"className":21633},[247],[212,21635],{"className":21636,"style":252},[251],[212,21638,234],{"className":21639,"style":258},[256,257]," 对应不同的散度。KL、JS、全变差、卡方、Hellinger、Wasserstein、MMD 等散度，表面上都是「衡量两个分布差多少」，但它们的根本区别可以归结为几个维度：",[11,21642,21643],{},"它们对「差异」的定义方式不同，对「支撑集不重叠」的处理不同，对「几何\u002F度量结构」的利用不同，因而导出的拓扑、梯度行为和优化性质也不同。",[11,21645,21646],{},"可以把不同散度的区别归纳为五个核心问题：",[6860,21648,21649,21652,21655,21658,21661],{},[6863,21650,21651],{},"差异定义在什么量上？是密度比值、密度差、累积分布差，还是搬运质量？",[6863,21653,21654],{},"是否对称？",[6863,21656,21657],{},"是否有界？",[6863,21659,21660],{},"是否利用样本空间的几何结构？",[6863,21662,21663],{},"诱导的拓扑强弱如何？",[11,21665,21666],{},"这五点决定了散度在理论性质和实际优化中的行为差异。下面逐个把常用散度「代入模板」并验算。",[2509,21668,21670],{"id":21669},"_31-kl-散度","3.1 KL 散度",[11,21672,21673],{},"取：",[212,21675,21677],{"className":21676,"translate":216},[377],[212,21678,21680,21709],{"className":21679,"translate":216},[215],[212,21681,21683],{"className":21682},[220],[222,21684,21685],{"xmlns":224,"display":386},[226,21686,21687,21707],{},[229,21688,21689,21691,21693,21695,21697,21699,21701,21703,21705],{},[232,21690,234],{},[307,21692,310],{"stretchy":309},[232,21694,966],{},[307,21696,317],{"stretchy":309},[307,21698,320],{},[232,21700,966],{},[232,21702,4298],{},[307,21704,4301],{},[232,21706,966],{},[236,21708,4306],{"encoding":238},[212,21710,21712,21739],{"className":21711,"ariaHidden":243},[242],[212,21713,21715,21718,21721,21724,21727,21730,21733,21736],{"className":21714},[247],[212,21716],{"className":21717,"style":336},[251],[212,21719,234],{"className":21720,"style":258},[256,257],[212,21722,310],{"className":21723},[343],[212,21725,966],{"className":21726},[256,257],[212,21728,317],{"className":21729},[350],[212,21731],{"className":21732,"style":355},[354],[212,21734,320],{"className":21735},[359],[212,21737],{"className":21738,"style":355},[354],[212,21740,21742,21745,21748,21751,21756,21759],{"className":21741},[247],[212,21743],{"className":21744,"style":252},[251],[212,21746,966],{"className":21747},[256,257],[212,21749],{"className":21750,"style":603},[354],[212,21752,4352,21754],{"className":21753},[1682],[212,21755,4356],{"style":4355},[212,21757],{"className":21758,"style":603},[354],[212,21760,966],{"className":21761},[256,257],[11,21763,21764,21765,21798,21799,2943,21864,21997],{},"（下面 ",[212,21766,21768,21784],{"className":21767,"translate":216},[215],[212,21769,21771],{"className":21770},[220],[222,21772,21773],{"xmlns":224},[226,21774,21775,21781],{},[229,21776,21777,21779],{},[232,21778,4298],{},[307,21780,4301],{},[236,21782,21783],{"encoding":238},"\\log",[212,21785,21787],{"className":21786,"ariaHidden":243},[242],[212,21788,21790,21793],{"className":21789},[247],[212,21791],{"className":21792,"style":252},[251],[212,21794,4352,21796],{"className":21795},[1682],[212,21797,4356],{"style":4355}," 均为自然对数。）则 ",[212,21800,21802,21825],{"className":21801,"translate":216},[215],[212,21803,21805],{"className":21804},[220],[222,21806,21807],{"xmlns":224},[226,21808,21809,21823],{},[229,21810,21811,21813,21815,21817,21819,21821],{},[232,21812,234],{},[307,21814,310],{"stretchy":309},[312,21816,314],{},[307,21818,317],{"stretchy":309},[307,21820,320],{},[312,21822,323],{},[236,21824,326],{"encoding":238},[212,21826,21828,21855],{"className":21827,"ariaHidden":243},[242],[212,21829,21831,21834,21837,21840,21843,21846,21849,21852],{"className":21830},[247],[212,21832],{"className":21833,"style":336},[251],[212,21835,234],{"className":21836,"style":258},[256,257],[212,21838,310],{"className":21839},[343],[212,21841,314],{"className":21842},[256],[212,21844,317],{"className":21845},[350],[212,21847],{"className":21848,"style":355},[354],[212,21850,320],{"className":21851},[359],[212,21853],{"className":21854,"style":355},[354],[212,21856,21858,21861],{"className":21857},[247],[212,21859],{"className":21860,"style":369},[251],[212,21862,323],{"className":21863},[256],[212,21865,21867,21907],{"className":21866,"translate":216},[215],[212,21868,21870],{"className":21869},[220],[222,21871,21872],{"xmlns":224},[226,21873,21874,21904],{},[229,21875,21876,21886,21888,21890,21892,21894,21896,21898,21900,21902],{},[7012,21877,21878,21880],{},[232,21879,234],{},[229,21881,21882,21884],{},[307,21883,7018],{"mathvariant":406},[307,21885,7018],{"mathvariant":406},[307,21887,310],{"stretchy":309},[232,21889,966],{},[307,21891,317],{"stretchy":309},[307,21893,320],{},[312,21895,314],{},[232,21897,1138],{"mathvariant":406},[232,21899,966],{},[307,21901,3101],{},[312,21903,323],{},[236,21905,21906],{"encoding":238},"f''(t)=1\u002Ft>0",[212,21908,21910,21967,21988],{"className":21909,"ariaHidden":243},[242],[212,21911,21913,21916,21949,21952,21955,21958,21961,21964],{"className":21912},[247],[212,21914],{"className":21915,"style":7041},[251],[212,21917,21919,21922],{"className":21918},[256],[212,21920,234],{"className":21921,"style":258},[256,257],[212,21923,21925],{"className":21924},[478],[212,21926,21928],{"className":21927},[482],[212,21929,21931],{"className":21930},[487],[212,21932,21934],{"className":21933,"style":7060},[491],[212,21935,21936,21939],{"style":7063},[212,21937],{"className":21938,"style":500},[499],[212,21940,21942],{"className":21941},[504,505,506,507],[212,21943,21945],{"className":21944},[256,507],[212,21946,21948],{"className":21947},[256,507],"′′",[212,21950,310],{"className":21951},[343],[212,21953,966],{"className":21954},[256,257],[212,21956,317],{"className":21957},[350],[212,21959],{"className":21960,"style":355},[354],[212,21962,320],{"className":21963},[359],[212,21965],{"className":21966,"style":355},[354],[212,21968,21970,21973,21976,21979,21982,21985],{"className":21969},[247],[212,21971],{"className":21972,"style":336},[251],[212,21974,8787],{"className":21975},[256],[212,21977,966],{"className":21978},[256,257],[212,21980],{"className":21981,"style":355},[354],[212,21983,3101],{"className":21984},[359],[212,21986],{"className":21987,"style":355},[354],[212,21989,21991,21994],{"className":21990},[247],[212,21992],{"className":21993,"style":369},[251],[212,21995,323],{"className":21996},[256]," 凸。代入模板：",[212,21999,22001],{"className":22000,"translate":216},[377],[212,22002,22004,22107],{"className":22003,"translate":216},[215],[212,22005,22007],{"className":22006},[220],[222,22008,22009],{"xmlns":224,"display":386},[226,22010,22011,22104],{},[229,22012,22013,22019,22021,22023,22025,22027,22029,22031,22033,22035,22037,22043,22045,22047,22053,22055,22057,22059,22061,22063,22065,22067,22069,22075,22077,22079,22081,22083,22094,22096,22098,22100,22102],{},[392,22014,22015,22017],{},[232,22016,396],{},[232,22018,234],{},[307,22020,310],{"stretchy":309},[232,22022,403],{},[232,22024,407],{"mathvariant":406},[232,22026,410],{},[307,22028,317],{"stretchy":309},[307,22030,320],{},[307,22032,1485],{},[232,22034,1141],{},[307,22036,3497],{},[435,22038,22039,22041],{},[232,22040,11],{},[232,22042,1141],{},[232,22044,4298],{},[307,22046,4301],{},[435,22048,22049,22051],{},[232,22050,11],{},[232,22052,1141],{},[1495,22054,1497],{},[232,22056,441],{},[232,22058,971],{},[307,22060,320],{},[307,22062,1485],{},[232,22064,11],{},[232,22066,4298],{},[307,22068,4301],{},[435,22070,22071,22073],{},[232,22072,11],{},[232,22074,1141],{},[1495,22076,1497],{},[232,22078,441],{},[232,22080,971],{},[307,22082,320],{},[392,22084,22085,22087],{},[232,22086,396],{},[229,22088,22089,22091],{},[232,22090,10894],{},[232,22092,22093],{},"L",[307,22095,310],{"stretchy":309},[232,22097,403],{},[232,22099,407],{"mathvariant":406},[232,22101,410],{},[307,22103,317],{"stretchy":309},[236,22105,22106],{"encoding":238},"D_f(P\\|Q)\n=\\int q\\cdot \\frac{p}{q}\\log\\frac{p}{q}\\,dx\n=\\int p\\log\\frac{p}{q}\\,dx\n=D_{KL}(P\\|Q)",[212,22108,22110,22180,22204,22364,22471],{"className":22109,"ariaHidden":243},[242],[212,22111,22113,22116,22156,22159,22162,22165,22168,22171,22174,22177],{"className":22112},[247],[212,22114],{"className":22115,"style":467},[251],[212,22117,22119,22122],{"className":22118},[256],[212,22120,396],{"className":22121,"style":474},[256,257],[212,22123,22125],{"className":22124},[478],[212,22126,22128,22148],{"className":22127},[482,483],[212,22129,22131,22145],{"className":22130},[487],[212,22132,22134],{"className":22133,"style":492},[491],[212,22135,22136,22139],{"style":495},[212,22137],{"className":22138,"style":500},[499],[212,22140,22142],{"className":22141},[504,505,506,507],[212,22143,234],{"className":22144,"style":258},[256,257,507],[212,22146,515],{"className":22147},[514],[212,22149,22151],{"className":22150},[487],[212,22152,22154],{"className":22153,"style":522},[491],[212,22155],{},[212,22157,310],{"className":22158},[343],[212,22160,403],{"className":22161,"style":531},[256,257],[212,22163,407],{"className":22164},[256],[212,22166,410],{"className":22167},[256,257],[212,22169,317],{"className":22170},[350],[212,22172],{"className":22173,"style":355},[354],[212,22175,320],{"className":22176},[359],[212,22178],{"className":22179,"style":355},[354],[212,22181,22183,22186,22189,22192,22195,22198,22201],{"className":22182},[247],[212,22184],{"className":22185,"style":5975},[251],[212,22187,1485],{"className":22188,"style":1685},[1682,1683,1684],[212,22190],{"className":22191,"style":603},[354],[212,22193,1141],{"className":22194,"style":1178},[256,257],[212,22196],{"className":22197,"style":2785},[354],[212,22199,3497],{"className":22200},[2789],[212,22202],{"className":22203,"style":2785},[354],[212,22205,22207,22211,22273,22276,22281,22284,22346,22349,22352,22355,22358,22361],{"className":22206},[247],[212,22208],{"className":22209,"style":22210},[251],"height:1.988em;vertical-align:-0.8804em;",[212,22212,22214,22217,22270],{"className":22213},[256],[212,22215],{"className":22216},[343,638],[212,22218,22220],{"className":22219},[435],[212,22221,22223,22262],{"className":22222},[482,483],[212,22224,22226,22259],{"className":22225},[487],[212,22227,22229,22240,22248],{"className":22228,"style":3752},[491],[212,22230,22231,22234],{"style":654},[212,22232],{"className":22233,"style":658},[499],[212,22235,22237],{"className":22236},[256],[212,22238,1141],{"className":22239,"style":1178},[256,257],[212,22241,22242,22245],{"style":670},[212,22243],{"className":22244,"style":658},[499],[212,22246],{"className":22247,"style":678},[677],[212,22249,22250,22253],{"style":681},[212,22251],{"className":22252,"style":658},[499],[212,22254,22256],{"className":22255},[256],[212,22257,11],{"className":22258},[256,257],[212,22260,515],{"className":22261},[514],[212,22263,22265],{"className":22264},[487],[212,22266,22268],{"className":22267,"style":703},[491],[212,22269],{},[212,22271],{"className":22272},[350,638],[212,22274],{"className":22275,"style":603},[354],[212,22277,4352,22279],{"className":22278},[1682],[212,22280,4356],{"style":4355},[212,22282],{"className":22283,"style":603},[354],[212,22285,22287,22290,22343],{"className":22286},[256],[212,22288],{"className":22289},[343,638],[212,22291,22293],{"className":22292},[435],[212,22294,22296,22335],{"className":22295},[482,483],[212,22297,22299,22332],{"className":22298},[487],[212,22300,22302,22313,22321],{"className":22301,"style":3752},[491],[212,22303,22304,22307],{"style":654},[212,22305],{"className":22306,"style":658},[499],[212,22308,22310],{"className":22309},[256],[212,22311,1141],{"className":22312,"style":1178},[256,257],[212,22314,22315,22318],{"style":670},[212,22316],{"className":22317,"style":658},[499],[212,22319],{"className":22320,"style":678},[677],[212,22322,22323,22326],{"style":681},[212,22324],{"className":22325,"style":658},[499],[212,22327,22329],{"className":22328},[256],[212,22330,11],{"className":22331},[256,257],[212,22333,515],{"className":22334},[514],[212,22336,22338],{"className":22337},[487],[212,22339,22341],{"className":22340,"style":703},[491],[212,22342],{},[212,22344],{"className":22345},[350,638],[212,22347],{"className":22348,"style":603},[354],[212,22350,441],{"className":22351},[256,257],[212,22353,971],{"className":22354},[256,257],[212,22356],{"className":22357,"style":355},[354],[212,22359,320],{"className":22360},[359],[212,22362],{"className":22363,"style":355},[354],[212,22365,22367,22371,22374,22377,22380,22383,22388,22391,22453,22456,22459,22462,22465,22468],{"className":22366},[247],[212,22368],{"className":22369,"style":22370},[251],"height:2.2404em;vertical-align:-0.8804em;",[212,22372,1485],{"className":22373,"style":1685},[1682,1683,1684],[212,22375],{"className":22376,"style":603},[354],[212,22378,11],{"className":22379},[256,257],[212,22381],{"className":22382,"style":603},[354],[212,22384,4352,22386],{"className":22385},[1682],[212,22387,4356],{"style":4355},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KL 散度 ",[212,22542,22544,22576],{"className":22543,"translate":216},[215],[212,22545,22547],{"className":22546},[220],[222,22548,22549],{"xmlns":224},[226,22550,22551,22573],{},[229,22552,22553,22563,22565,22567,22569,22571],{},[392,22554,22555,22557],{},[232,22556,396],{},[229,22558,22559,22561],{},[232,22560,10894],{},[232,22562,22093],{},[307,22564,310],{"stretchy":309},[232,22566,410],{},[232,22568,407],{"mathvariant":406},[232,22570,403],{},[307,22572,317],{"stretchy":309},[236,22574,22575],{"encoding":238},"D_{KL}(Q\\|P)",[212,22577,22579],{"className":22578,"ariaHidden":243},[242],[212,22580,22582,22585,22631,22634,22637,22640,22643],{"className":22581},[247],[212,22583],{"className":22584,"style":336},[251],[212,22586,22588,22591],{"className":22587},[256],[212,22589,396],{"className":22590,"style":474},[256,257],[212,22592,22594],{"className":22593},[478],[212,22595,22597,22623],{"className":22596},[482,483],[212,22598,22600,22620],{"className":22599},[487],[212,22601,22603],{"className":22602,"style":576},[491],[212,22604,22605,22608],{"style":495},[212,22606],{"className":22607,"style":500},[499],[212,22609,22611],{"className":22610},[504,505,506,507],[212,22612,22614,22617],{"className":22613},[256,507],[212,22615,10894],{"className":22616,"style":10982},[256,257,507],[212,22618,22093],{"className":22619},[256,257,507],[212,22621,515],{"className":22622},[514],[212,22624,22626],{"className":22625},[487],[212,22627,22629],{"className":22628,"style":8166},[491],[212,22630],{},[212,22632,310],{"className":22633},[343],[212,22635,410],{"className":22636},[256,257],[212,22638,407],{"className":22639},[256],[212,22641,403],{"className":22642,"style":531},[256,257],[212,22644,317],{"className":22645},[350]," 对应斜共轭 ",[212,22648,22650,22676],{"className":22649,"translate":216},[215],[212,22651,22653],{"className":22652},[220],[222,22654,22655],{"xmlns":224},[226,22656,22657,22673],{},[229,22658,22659,22661,22663,22665,22667,22669,22671],{},[232,22660,966],{},[232,22662,234],{},[307,22664,310],{"stretchy":309},[312,22666,314],{},[232,22668,1138],{"mathvariant":406},[232,22670,966],{},[307,22672,317],{"stretchy":309},[236,22674,22675],{"encoding":238},"t f(1\u002Ft)",[212,22677,22679],{"className":22678,"ariaHidden":243},[242],[212,22680,22682,22685,22688,22691,22694,22697,22700],{"className":22681},[247],[212,22683],{"className":22684,"style":336},[251],[212,22686,966],{"className":22687},[256,257],[212,22689,234],{"className":22690,"style":258},[256,257],[212,22692,310],{"className":22693},[343],[212,22695,8787],{"className":22696},[256],[212,22698,966],{"className":22699},[256,257],[212,22701,317],{"className":22702},[350],[212,22704,22706],{"className":22705,"translate":216},[377],[212,22707,22709,22831],{"className":22708,"translate":216},[215],[212,22710,22712],{"className":22711},[220],[222,22713,22714],{"xmlns":224,"display":386},[226,22715,22716,22828],{},[1441,22717,22718,22752],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,22719,22720,22734],{},[1450,22721,22722],{},[1453,22723,22724],{"scriptlevel":323,"displaystyle":243},[229,22725,22726,22728,22730,22732],{},[232,22727,234],{},[307,22729,310],{"stretchy":309},[232,22731,966],{},[307,22733,317],{"stretchy":309},[1450,22735,22736],{},[1453,22737,22738],{"scriptlevel":323,"displaystyle":243},[229,22739,22740,22742,22744,22746,22748,22750],{},[229,22741],{},[307,22743,320],{},[232,22745,966],{},[232,22747,4298],{},[307,22749,4301],{},[232,22751,966],{},[1447,22753,22754,22760],{},[1450,22755,22756],{},[1453,22757,22758],{"scriptlevel":323,"displaystyle":243},[229,22759],{},[1450,22761,22762],{},[1453,22763,22764],{"scriptlevel":323,"displaystyle":243},[229,22765,22766,22768,22770,22772,22788,22790,22792,22794,22796,22798,22800,22806,22808,22810,22816,22818,22820,22822,22824,22826],{},[229,22767],{},[307,22769,4484],{},[1495,22771,4481],{},[7751,22773,22774,22776,22786],{},[232,22775,234],{},[229,22777,22778,22780,22782,22784],{},[232,22779,7759],{},[232,22781,7762],{},[232,22783,7765],{},[232,22785,7768],{},[307,22787,7771],{"lspace":1445,"rspace":1445},[307,22789,310],{"stretchy":309},[232,22791,966],{},[307,22793,317],{"stretchy":309},[307,22795,320],{},[232,22797,966],{},[307,22799,3497],{},[435,22801,22802,22804],{},[312,22803,314],{},[232,22805,966],{},[232,22807,4298],{},[307,22809,4301],{},[435,22811,22812,22814],{},[312,22813,314],{},[232,22815,966],{},[307,22817,320],{},[307,22819,5011],{},[232,22821,4298],{},[307,22823,4301],{},[232,22825,966],{},[307,22827,748],{"separator":243},[236,22829,22830],{"encoding":238},"\\begin{aligned}\nf(t)&=t\\log t\\\\[2pt]\n&\\Longrightarrow\\ f^{*}_{skew}(t)\n=t\\cdot\\frac1t\\log\\frac1t=-\\log t,\n\\end{aligned}",[212,22832,22834],{"className":22833,"ariaHidden":243},[242],[212,22835,22837,22841],{"className":22836},[247],[212,22838],{"className":22839,"style":22840},[251],"height:3.7074em;vertical-align:-1.6037em;",[212,22842,22844],{"className":22843},[256],[212,22845,22847,22903],{"className":22846},[1441],[212,22848,22850],{"className":22849},[1558],[212,22851,22853,22894],{"className":22852},[482,483],[212,22854,22856,22891],{"className":22855},[487],[212,22857,22860,22882],{"className":22858,"style":22859},[491],"height:2.1037em;",[212,22861,22863,22867],{"style":22862},"top:-4.5852em;",[212,22864],{"className":22865,"style":22866},[499],"height:3.3214em;",[212,22868,22870,22873,22876,22879],{"className":22869},[256],[212,22871,234],{"className":22872,"style":258},[256,257],[212,22874,310],{"className":22875},[343],[212,22877,966],{"className":22878},[256,257],[212,22880,317],{"className":22881},[350],[212,22883,22885,22888],{"style":22884},"top:-2.4037em;",[212,22886],{"className":22887,"style":22866},[499],[212,22889],{"className":22890},[256],[212,22892,515],{"className":22893},[514],[212,22895,22897],{"className":22896},[487],[212,22898,22901],{"className":22899,"style":22900},[491],"height:1.6037em;",[212,22902],{},[212,22904,22906],{"className":22905},[1649],[212,22907,22909,23239],{"className":22908},[482,483],[212,22910,22912,23236],{"className":22911},[487],[212,22913,22915,22952],{"className":22914,"style":22859},[491],[212,22916,22917,22920],{"style":22862},[212,22918],{"className":22919,"style":22866},[499],[212,22921,22923,22926,22929,22932,22935,22938,22941,22946,22949],{"className":22922},[256],[212,22924],{"className":22925},[256],[212,22927],{"className":22928,"style":355},[354],[212,22930,320],{"className":22931},[359],[212,22933],{"className":22934,"style":355},[354],[212,22936,966],{"className":22937},[256,257],[212,22939],{"className":22940,"style":603},[354],[212,22942,4352,22944],{"className":22943},[1682],[212,22945,4356],{"style":4355},[212,22947],{"className":22948,"style":603},[354],[212,22950,966],{"className":22951},[256,257],[212,22953,22954,22957],{"style":22884},[212,22955],{"className":22956,"style":22866},[499],[212,22958,22960,22963,22966,22969,22972,22975,23041,23044,23047,23050,23053,23056,23059,23062,23065,23068,23071,23134,23137,23142,23145,23207,23210,23213,23216,23219,23222,23227,23230,23233],{"className":22959},[256],[212,22961],{"className":22962},[256],[212,22964],{"className":22965,"style":355},[354],[212,22967,4484],{"className":22968},[359],[212,22970,4481],{"className":22971},[354],[212,22973],{"className":22974,"style":355},[354],[212,22976,22978,22981],{"className":22977},[256],[212,22979,234],{"className":22980,"style":258},[256,257],[212,22982,22984],{"className":22983},[478],[212,22985,22987,23033],{"className":22986},[482,483],[212,22988,22990,23030],{"className":22989},[487],[212,22991,22993,23016],{"className":22992,"style":8446},[491],[212,22994,22995,22998],{"style":8449},[212,22996],{"className":22997,"style":500},[499],[212,22999,23001],{"className":23000},[504,505,506,507],[212,23002,23004,23007,23010,23013],{"className":23003},[256,507],[212,23005,7759],{"className":23006},[256,257,507],[212,23008,7762],{"className":23009,"style":8465},[256,257,507],[212,23011,7765],{"className":23012},[256,257,507],[212,23014,7768],{"className":23015,"style":8472},[256,257,507],[212,23017,23018,23021],{"style":8475},[212,23019],{"className":23020,"style":500},[499],[212,23022,23024],{"className":23023},[504,505,506,507],[212,23025,23027],{"className":23026},[256,507],[212,23028,7771],{"className":23029},[256,507],[212,23031,515],{"className":23032},[514],[212,23034,23036],{"className":23035},[487],[212,23037,23039],{"className":23038,"style":8497},[491],[212,23040],{},[212,23042,310],{"className":23043},[343],[212,23045,966],{"className":23046},[256,257],[212,23048,317],{"className":23049},[350],[212,23051],{"className":23052,"style":355},[354],[212,23054,320],{"className":23055},[359],[212,23057],{"className":23058,"style":355},[354],[212,23060,966],{"className":23061},[256,257],[212,23063],{"className":23064,"style":2785},[354],[212,23066,3497],{"className":23067},[2789],[212,23069],{"className":23070,"style":2785},[354],[212,23072,23074,23077,23131],{"className":23073},[256],[212,23075],{"className":23076},[343,638],[212,23078,23080],{"className":23079},[435],[212,23081,23083,23123],{"className":23082},[482,483],[212,23084,23086,23120],{"className":23085},[487],[212,23087,23090,23101,23109],{"className":23088,"style":23089},[491],"height:1.3214em;",[212,23091,23092,23095],{"style":654},[212,23093],{"className":23094,"style":658},[499],[212,23096,23098],{"className":23097},[256],[212,23099,966],{"className":23100},[256,257],[212,23102,23103,23106],{"style":670},[212,23104],{"className":23105,"style":658},[499],[212,23107],{"className":23108,"style":678},[677],[212,23110,23111,23114],{"style":681},[212,23112],{"className":23113,"style":658},[499],[212,23115,23117],{"className":23116},[256],[212,23118,314],{"className":23119},[256],[212,23121,515],{"className":23122},[514],[212,23124,23126],{"className":23125},[487],[212,23127,23129],{"className":23128,"style":3976},[491],[212,23130],{},[212,23132],{"className":23133},[350,638],[212,23135],{"className":23136,"style":603},[354],[212,23138,4352,23140],{"className":23139},[1682],[212,23141,4356],{"style":4355},[212,23143],{"className":23144,"style":603},[354],[212,23146,23148,23151,23204],{"className":23147},[256],[212,23149],{"className":23150},[343,638],[212,23152,23154],{"className":23153},[435],[212,23155,23157,23196],{"className":23156},[482,483],[212,23158,23160,23193],{"className":23159},[487],[212,23161,23163,23174,23182],{"className":23162,"style":23089},[491],[212,23164,23165,23168],{"style":654},[212,23166],{"className":23167,"style":658},[499],[212,23169,23171],{"className":23170},[256],[212,23172,966],{"className":23173},[256,257],[212,23175,23176,23179],{"style":670},[212,23177],{"className":23178,"style":658},[499],[212,23180],{"className":23181,"style":678},[677],[212,23183,23184,23187],{"style":681},[212,23185],{"className":23186,"style":658},[499],[212,23188,23190],{"className":23189},[256],[212,23191,314],{"className":23192},[256],[212,23194,515],{"className":23195},[514],[212,23197,23199],{"className":23198},[487],[212,23200,23202],{"className":23201,"style":3976},[491],[212,23203],{},[212,23205],{"className":23206},[350,638],[212,23208],{"className":23209,"style":355},[354],[212,23211,320],{"className":23212},[359],[212,23214],{"className":23215,"style":355},[354],[212,23217,5011],{"className":23218},[256],[212,23220],{"className":23221,"style":603},[354],[212,23223,4352,23225],{"className":23224},[1682],[212,23226,4356],{"style":4355},[212,23228],{"className":23229,"style":603},[354],[212,23231,966],{"className":23232},[256,257],[212,23234,748],{"className":23235},[770],[212,23237,515],{"className":23238},[514],[212,23240,23242],{"className":23241},[487],[212,23243,23245],{"className":23244,"style":22900},[491],[212,23246],{},[11,23248,23249],{},"所以",[212,23251,23253],{"className":23252,"translate":216},[377],[212,23254,23256,23332],{"className":23255,"translate":216},[215],[212,23257,23259],{"className":23258},[220],[222,23260,23261],{"xmlns":224,"display":386},[226,23262,23263,23329],{},[229,23264,23265,23267,23269,23271,23273,23275,23277,23279,23281,23283,23285,23287,23289,23295,23297,23299,23301,23303,23305,23307,23317,23319,23321,23323,23325,23327],{},[232,23266,234],{},[307,23268,310],{"stretchy":309},[232,23270,966],{},[307,23272,317],{"stretchy":309},[307,23274,320],{},[307,23276,5011],{},[232,23278,4298],{},[307,23280,4301],{},[232,23282,966],{},[1495,23284,4481],{},[307,23286,4484],{},[1495,23288,4481],{},[392,23290,23291,23293],{},[232,23292,396],{},[232,23294,234],{},[307,23296,310],{"stretchy":309},[232,23298,403],{},[232,23300,407],{"mathvariant":406},[232,23302,410],{},[307,23304,317],{"stretchy":309},[307,23306,320],{},[392,23308,23309,23311],{},[232,23310,396],{},[229,23312,23313,23315],{},[232,23314,10894],{},[232,23316,22093],{},[307,23318,310],{"stretchy":309},[232,23320,410],{},[232,23322,407],{"mathvariant":406},[232,23324,403],{},[307,23326,317],{"stretchy":309},[232,23328,4573],{"mathvariant":406},[236,23330,23331],{"encoding":238},"f(t)=-\\log t\n\\ \\Longrightarrow\\ D_f(P\\|Q)=D_{KL}(Q\\|P).",[212,23333,23335,23362,23400,23470],{"className":23334,"ariaHidden":243},[242],[212,23336,23338,23341,23344,23347,23350,23353,23356,23359],{"className":23337},[247],[212,23339],{"className":23340,"style":336},[251],[212,23342,234],{"className":23343,"style":258},[256,257],[212,23345,310],{"className":23346},[343],[212,23348,966],{"className":23349},[256,257],[212,23351,317],{"className":23352},[350],[212,23354],{"className":23355,"style":355},[354],[212,23357,320],{"className":23358},[359],[212,23360],{"className":23361,"style":355},[354],[212,23363,23365,23368,23371,23374,23379,23382,23385,23388,23391,23394,23397],{"className":23364},[247],[212,23366],{"className":23367,"style":252},[251],[212,23369,5011],{"className":23370},[256],[212,23372],{"className":23373,"style":603},[354],[212,23375,4352,23377],{"className":23376},[1682],[212,23378,4356],{"style":4355},[212,23380],{"className":23381,"style":603},[354],[212,23383,966],{"className":23384},[256,257],[212,23386,4481],{"className":23387},[354],[212,23389],{"className":23390,"style":355},[354],[212,23392,4484],{"className":23393},[359],[212,23395,4481],{"className":23396},[354],[212,23398],{"className":23399,"style":355},[354],[212,23401,23403,23406,23446,23449,23452,23455,23458,23461,23464,23467],{"className":23402},[247],[212,23404],{"className":23405,"style":467},[251],[212,23407,23409,23412],{"className":23408},[256],[212,23410,396],{"className":23411,"style":474},[256,257],[212,23413,23415],{"className":23414},[478],[212,23416,23418,23438],{"className":23417},[482,483],[212,23419,23421,23435],{"className":23420},[487],[212,23422,23424],{"className":23423,"style":492},[491],[212,23425,23426,23429],{"style":495},[212,23427],{"className":23428,"style":500},[499],[212,23430,23432],{"className":23431},[504,505,506,507],[212,23433,234],{"className":23434,"style":258},[256,257,507],[212,23436,515],{"className":23437},[514],[212,23439,23441],{"className":23440},[487],[212,23442,23444],{"className":23443,"style":522},[491],[212,23445],{},[212,23447,310],{"className":23448},[343],[212,23450,403],{"className":23451,"style":531},[256,257],[212,23453,407],{"className":23454},[256],[212,23456,410],{"className":23457},[256,257],[212,23459,317],{"className":23460},[350],[212,23462],{"className":23463,"style":355},[354],[212,23465,320],{"className":23466},[359],[212,23468],{"className":23469,"style":355},[354],[212,23471,23473,23476,23522,23525,23528,23531,23534,23537],{"className":23472},[247],[212,23474],{"className":23475,"style":336},[251],[212,23477,23479,23482],{"className":23478},[256],[212,23480,396],{"className":23481,"style":474},[256,257],[212,23483,23485],{"className":23484},[478],[212,23486,23488,23514],{"className":23487},[482,483],[212,23489,23491,23511],{"className":23490},[487],[212,23492,23494],{"className":23493,"style":576},[491],[212,23495,23496,23499],{"style":495},[212,23497],{"className":23498,"style":500},[499],[212,23500,23502],{"className":23501},[504,505,506,507],[212,23503,23505,23508],{"className":23504},[256,507],[212,23506,10894],{"className":23507,"style":10982},[256,257,507],[212,23509,22093],{"className":23510},[256,257,507],[212,23512,515],{"className":23513},[514],[212,23515,23517],{"className":23516},[487],[212,23518,23520],{"className":23519,"style":8166},[491],[212,23521],{},[212,23523,310],{"className":23524},[343],[212,23526,410],{"className":23527},[256,257],[212,23529,407],{"className":23530},[256],[212,23532,403],{"className":23533,"style":531},[256,257],[212,23535,317],{"className":23536},[350],[212,23538,4573],{"className":23539},[256],[11,23541,23542,23545,23546,23664,23665,23730,23731,23824],{},[1194,23543,23544],{},"对称化：Jeffreys 散度。"," 取 ",[212,23547,23549,23587],{"className":23548,"translate":216},[215],[212,23550,23552],{"className":23551},[220],[222,23553,23554],{"xmlns":224},[226,23555,23556,23584],{},[229,23557,23558,23560,23562,23564,23566,23568,23570,23572,23574,23576,23578,23580,23582],{},[232,23559,234],{},[307,23561,310],{"stretchy":309},[232,23563,966],{},[307,23565,317],{"stretchy":309},[307,23567,320],{},[307,23569,310],{"stretchy":309},[232,23571,966],{},[307,23573,5011],{},[312,23575,314],{},[307,23577,317],{"stretchy":309},[232,23579,4298],{},[307,23581,4301],{},[232,23583,966],{},[236,23585,23586],{"encoding":238},"f(t)=(t-1)\\log t",[212,23588,23590,23617,23638],{"className":23589,"ariaHidden":243},[242],[212,23591,23593,23596,23599,23602,23605,23608,23611,23614],{"className":23592},[247],[212,23594],{"className":23595,"style":336},[251],[212,23597,234],{"className":23598,"style":258},[256,257],[212,23600,310],{"className":23601},[343],[212,23603,966],{"className":23604},[256,257],[212,23606,317],{"className":23607},[350],[212,23609],{"className":23610,"style":355},[354],[212,23612,320],{"className":23613},[359],[212,23615],{"className":23616,"style":355},[354],[212,23618,23620,23623,23626,23629,23632,23635],{"className":23619},[247],[212,23621],{"className":23622,"style":336},[251],[212,23624,310],{"className":23625},[343],[212,23627,966],{"className":23628},[256,257],[212,23630],{"className":23631,"style":2785},[354],[212,23633,5011],{"className":23634},[2789],[212,23636],{"className":23637,"style":2785},[354],[212,23639,23641,23644,23647,23650,23653,23658,23661],{"className":23640},[247],[212,23642],{"className":23643,"style":336},[251],[212,23645,314],{"className":23646},[256],[212,23648,317],{"className":23649},[350],[212,23651],{"className":23652,"style":603},[354],[212,23654,4352,23656],{"className":23655},[1682],[212,23657,4356],{"style":4355},[212,23659],{"className":23660,"style":603},[354],[212,23662,966],{"className":23663},[256,257],"（它满足 ",[212,23666,23668,23691],{"className":23667,"translate":216},[215],[212,23669,23671],{"className":23670},[220],[222,23672,23673],{"xmlns":224},[226,23674,23675,23689],{},[229,23676,23677,23679,23681,23683,23685,23687],{},[232,23678,234],{},[307,23680,310],{"stretchy":309},[312,23682,314],{},[307,23684,317],{"stretchy":309},[307,23686,320],{},[312,23688,323],{},[236,23690,326],{"encoding":238},[212,23692,23694,23721],{"className":23693,"ariaHidden":243},[242],[212,23695,23697,23700,23703,23706,23709,23712,23715,23718],{"className":23696},[247],[212,23698],{"className":23699,"style":336},[251],[212,23701,234],{"className":23702,"style":258},[256,257],[212,23704,310],{"className":23705},[343],[212,23707,314],{"className":23708},[256],[212,23710,317],{"className":23711},[350],[212,23713],{"className":23714,"style":355},[354],[212,23716,320],{"className":23717},[359],[212,23719],{"className":23720,"style":355},[354],[212,23722,23724,23727],{"className":23723},[247],[212,23725],{"className":23726,"style":369},[251],[212,23728,323],{"className":23729},[256],"，且 ",[212,23732,23734,23770],{"className":23733,"translate":216},[215],[212,23735,23737],{"className":23736},[220],[222,23738,23739],{"xmlns":224},[226,23740,23741,23767],{},[229,23742,23743,23745,23747,23749,23751,23753,23755,23757,23759,23761,23763,23765],{},[232,23744,966],{},[232,23746,234],{},[307,23748,310],{"stretchy":309},[312,23750,314],{},[232,23752,1138],{"mathvariant":406},[232,23754,966],{},[307,23756,317],{"stretchy":309},[307,23758,320],{},[232,23760,234],{},[307,23762,310],{"stretchy":309},[232,23764,966],{},[307,23766,317],{"stretchy":309},[236,23768,23769],{"encoding":238},"t f(1\u002Ft)=f(t)",[212,23771,23773,23806],{"className":23772,"ariaHidden":243},[242],[212,23774,23776,23779,23782,23785,23788,23791,23794,23797,23800,23803],{"className":23775},[247],[212,23777],{"className":23778,"style":336},[251],[212,23780,966],{"className":23781},[256,257],[212,23783,234],{"className":23784,"style":258},[256,257],[212,23786,310],{"className":23787},[343],[212,23789,8787],{"className":23790},[256],[212,23792,966],{"className":23793},[256,257],[212,23795,317],{"className":23796},[350],[212,23798],{"className":23799,"style":355},[354],[212,23801,320],{"className":23802},[359],[212,23804],{"className":23805,"style":355},[354],[212,23807,23809,23812,23815,23818,23821],{"className":23808},[247],[212,23810],{"className":23811,"style":336},[251],[212,23813,234],{"className":23814,"style":258},[256,257],[212,23816,310],{"className":23817},[343],[212,23819,966],{"className":23820},[256,257],[212,23822,317],{"className":23823},[350],"），则",[212,23826,23828],{"className":23827,"translate":216},[377],[212,23829,23831,23959],{"className":23830,"translate":216},[215],[212,23832,23834],{"className":23833},[220],[222,23835,23836],{"xmlns":224,"display":386},[226,23837,23838,23956],{},[229,23839,23840,23846,23848,23850,23852,23854,23856,23858,23860,23862,23864,23866,23868,23870,23872,23874,23880,23882,23884,23886,23889,23891,23901,23903,23905,23907,23909,23911,23913,23923,23925,23927,23929,23931,23933,23935,23937,23944,23946,23948,23950,23952,23954],{},[392,23841,23842,23844],{},[232,23843,396],{},[232,23845,234],{},[307,23847,310],{"stretchy":309},[232,23849,403],{},[232,23851,407],{"mathvariant":406},[232,23853,410],{},[307,23855,317],{"stretchy":309},[307,23857,320],{},[307,23859,1485],{},[307,23861,310],{"stretchy":309},[232,23863,11],{},[307,23865,5011],{},[232,23867,1141],{},[307,23869,317],{"stretchy":309},[232,23871,4298],{},[307,23873,4301],{},[435,23875,23876,23878],{},[232,23877,11],{},[232,23879,1141],{},[1495,23881,1497],{},[232,23883,441],{},[232,23885,971],{},[354,23887],{"linebreak":23888},"newline",[307,23890,320],{},[392,23892,23893,23895],{},[232,23894,396],{},[229,23896,23897,23899],{},[232,23898,10894],{},[232,23900,22093],{},[307,23902,310],{"stretchy":309},[232,23904,403],{},[232,23906,407],{"mathvariant":406},[232,23908,410],{},[307,23910,317],{"stretchy":309},[307,23912,2668],{},[392,23914,23915,23917],{},[232,23916,396],{},[229,23918,23919,23921],{},[232,23920,10894],{},[232,23922,22093],{},[307,23924,310],{"stretchy":309},[232,23926,410],{},[232,23928,407],{"mathvariant":406},[232,23930,403],{},[307,23932,317],{"stretchy":309},[307,23934,320],{},[307,23936,1214],{},[392,23938,23939,23941],{},[232,23940,396],{},[232,23942,23943],{},"J",[307,23945,310],{"stretchy":309},[232,23947,403],{},[307,23949,748],{"separator":243},[232,23951,410],{},[307,23953,317],{"stretchy":309},[307,23955,748],{"separator":243},[236,23957,23958],{"encoding":238},"D_f(P\\|Q)=\\int (p-q)\\log\\frac{p}{q}\\,dx \\\\\n=D_{KL}(P\\|Q)+D_{KL}(Q\\|P)=:D_J(P,Q),",[212,23960,23962,24032,24056,24150,24153,24165,24241,24318],{"className":23961,"ariaHidden":243},[242],[212,23963,23965,23968,24008,24011,24014,24017,24020,24023,24026,24029],{"className":23964},[247],[212,23966],{"className":23967,"style":467},[251],[212,23969,23971,23974],{"className":23970},[256],[212,23972,396],{"className":23973,"style":474},[256,257],[212,23975,23977],{"className":23976},[478],[212,23978,23980,24000],{"className":23979},[482,483],[212,23981,23983,23997],{"className":23982},[487],[212,23984,23986],{"className":23985,"style":492},[491],[212,23987,23988,23991],{"style":495},[212,23989],{"className":23990,"style":500},[499],[212,23992,23994],{"className":23993},[504,505,506,507],[212,23995,234],{"className":23996,"style":258},[256,257,507],[212,23998,515],{"className":23999},[514],[212,24001,24003],{"className":24002},[487],[212,24004,24006],{"className":24005,"style":522},[491],[212,24007],{},[212,24009,310],{"className":24010},[343],[212,24012,403],{"className":24013,"style":531},[256,257],[212,24015,407],{"className":24016},[256],[212,24018,410],{"className":24019},[256,257],[212,24021,317],{"className":24022},[350],[212,24024],{"className":24025,"style":355},[354],[212,24027,320],{"className":24028},[359],[212,24030],{"className":24031,"style":355},[354],[212,24033,24035,24038,24041,24044,24047,24050,24053],{"className":24034},[247],[212,24036],{"className":24037,"style":5975},[251],[212,24039,1485],{"className":24040,"style":1685},[1682,1683,1684],[212,24042,310],{"className":24043},[343],[212,24045,11],{"className":24046},[256,257],[212,24048],{"className":24049,"style":2785},[354],[212,24051,5011],{"className":24052},[2789],[212,24054],{"className":24055,"style":2785},[354],[212,24057,24059,24062,24065,24068,24071,24076,24079,24141,24144,24147],{"className":24058},[247],[212,24060],{"className":24061,"style":22210},[251],[212,24063,1141],{"className":24064,"style":1178},[256,257],[212,24066,317],{"className":24067},[350],[212,24069],{"className":24070,"style":603},[354],[212,24072,4352,24074],{"className":24073},[1682],[212,24075,4356],{"style":4355},[212,24077],{"className":24078,"style":603},[354],[212,24080,24082,24085,24138],{"className":24081},[256],[212,24083],{"className":24084},[343,638],[212,24086,24088],{"className":24087},[435],[212,24089,24091,24130],{"className":24090},[482,483],[212,24092,24094,24127],{"className":24093},[487],[212,24095,24097,24108,24116],{"className":24096,"style":3752},[491],[212,24098,24099,24102],{"style":654},[212,24100],{"className":24101,"style":658},[499],[212,24103,24105],{"className":24104},[256],[212,24106,1141],{"className":24107,"style":1178},[256,257],[212,24109,24110,24113],{"style":670},[212,24111],{"className":24112,"style":658},[499],[212,24114],{"className":24115,"style":678},[677],[212,24117,24118,24121],{"style":681},[212,24119],{"className":24120,"style":658},[499],[212,24122,24124],{"className":24123},[256],[212,24125,11],{"className":24126},[256,257],[212,24128,515],{"className":24129},[514],[212,24131,24133],{"className":24132},[487],[212,24134,24136],{"className":24135,"style":703},[491],[212,24137],{},[212,24139],{"className":24140},[350,638],[212,24142],{"className":24143,"style":603},[354],[212,24145,441],{"className":24146},[256,257],[212,24148,971],{"className":24149},[256,257],[212,24151],{"className":24152},[354,23888],[212,24154,24156,24159,24162],{"className":24155},[247],[212,24157],{"className":24158,"style":11203},[251],[212,24160,320],{"className":24161},[359],[212,24163],{"className":24164,"style":355},[354],[212,24166,24168,24171,24217,24220,24223,24226,24229,24232,24235,24238],{"className":24167},[247],[212,24169],{"className":24170,"style":336},[251],[212,24172,24174,24177],{"className":24173},[256],[212,24175,396],{"className":24176,"style":474},[256,257],[212,24178,24180],{"className":24179},[478],[212,24181,24183,24209],{"className":24182},[482,483],[212,24184,24186,24206],{"className":24185},[487],[212,24187,24189],{"className":24188,"style":576},[491],[212,24190,24191,24194],{"style":495},[212,24192],{"className":24193,"style":500},[499],[212,24195,24197],{"className":24196},[504,505,506,507],[212,24198,24200,24203],{"className":24199},[256,507],[212,24201,10894],{"className":24202,"style":10982},[256,257,507],[212,24204,22093],{"className":24205},[256,257,507],[212,24207,515],{"className":24208},[514],[212,24210,24212],{"className":24211},[487],[212,24213,24215],{"className":24214,"style":8166},[491],[212,24216],{},[212,24218,310],{"className":24219},[343],[212,24221,403],{"className":24222,"style":531},[256,257],[212,24224,407],{"className":24225},[256],[212,24227,410],{"className":24228},[256,257],[212,24230,317],{"className":24231},[350],[212,24233],{"className":24234,"style":2785},[354],[212,24236,2668],{"className":24237},[2789],[212,24239],{"className":24240,"style":2785},[354],[212,24242,24244,24247,24293,24296,24299,24302,24305,24308,24311,24315],{"className":24243},[247],[212,24245],{"className":24246,"style":336},[251],[212,24248,24250,24253],{"className":24249},[256],[212,24251,396],{"className":24252,"style":474},[256,257],[212,24254,24256],{"className":24255},[478],[212,24257,24259,24285],{"className":24258},[482,483],[212,24260,24262,24282],{"className":24261},[487],[212,24263,24265],{"className":24264,"style":576},[491],[212,24266,24267,24270],{"style":495},[212,24268],{"className":24269,"style":500},[499],[212,24271,24273],{"className":24272},[504,505,506,507],[212,24274,24276,24279],{"className":24275},[256,507],[212,24277,10894],{"className":24278,"style":10982},[256,257,507],[212,24280,22093],{"className":24281},[256,257,507],[212,24283,515],{"className":24284},[514],[212,24286,24288],{"className":24287},[487],[212,24289,24291],{"className":24290,"style":8166},[491],[212,24292],{},[212,24294,310],{"className":24295},[343],[212,24297,410],{"className":24298},[256,257],[212,24300,407],{"className":24301},[256],[212,24303,403],{"className":24304,"style":531},[256,257],[212,24306,317],{"className":24307},[350],[212,24309],{"className":24310,"style":355},[354],[212,24312,24314],{"className":24313},[359],"=:",[212,24316],{"className":24317,"style":355},[354],[212,24319,24321,24324,24365,24368,24371,24374,24377,24380,24383],{"className":24320},[247],[212,24322],{"className":24323,"style":336},[251],[212,24325,24327,24330],{"className":24326},[256],[212,24328,396],{"className":24329,"style":474},[256,257],[212,24331,24333],{"className":24332},[478],[212,24334,24336,24357],{"className":24335},[482,483],[212,24337,24339,24354],{"className":24338},[487],[212,24340,24342],{"className":24341,"style":576},[491],[212,24343,24344,24347],{"style":495},[212,24345],{"className":24346,"style":500},[499],[212,24348,24350],{"className":24349},[504,505,506,507],[212,24351,23943],{"className":24352,"style":24353},[256,257,507],"margin-right:0.0962em;",[212,24355,515],{"className":24356},[514],[212,24358,24360],{"className":24359},[487],[212,24361,24363],{"className":24362,"style":8166},[491],[212,24364],{},[212,24366,310],{"className":24367},[343],[212,24369,403],{"className":24370,"style":531},[256,257],[212,24372,748],{"className":24373},[770],[212,24375],{"className":24376,"style":603},[354],[212,24378,410],{"className":24379},[256,257],[212,24381,317],{"className":24382},[350],[212,24384,748],{"className":24385},[770],[11,24387,24388],{},"这是 KL 的两向之和，也是一个人为构造的对称 f-散度。",[11,24390,24391,24394,24395,24398,24399,24427,24428,24456,24457,24485,24486,24518,24519,24624,24625,24653,24654,24682,24683,24686],{},[1194,24392,24393],{},"意义。"," KL 是最基础的散度，等价于信息论中的",[1194,24396,24397],{},"相对熵","：若真实分布是 ",[212,24400,24402,24415],{"className":24401,"translate":216},[215],[212,24403,24405],{"className":24404},[220],[222,24406,24407],{"xmlns":224},[226,24408,24409,24413],{},[229,24410,24411],{},[232,24412,403],{},[236,24414,403],{"encoding":238},[212,24416,24418],{"className":24417,"ariaHidden":243},[242],[212,24419,24421,24424],{"className":24420},[247],[212,24422],{"className":24423,"style":861},[251],[212,24425,403],{"className":24426,"style":531},[256,257],"、而用 ",[212,24429,24431,24444],{"className":24430,"translate":216},[215],[212,24432,24434],{"className":24433},[220],[222,24435,24436],{"xmlns":224},[226,24437,24438,24442],{},[229,24439,24440],{},[232,24441,410],{},[236,24443,410],{"encoding":238},[212,24445,24447],{"className":24446,"ariaHidden":243},[242],[212,24448,24450,24453],{"className":24449},[247],[212,24451],{"className":24452,"style":763},[251],[212,24454,410],{"className":24455},[256,257]," 去编码来自 ",[212,24458,24460,24473],{"className":24459,"translate":216},[215],[212,24461,24463],{"className":24462},[220],[222,24464,24465],{"xmlns":224},[226,24466,24467,24471],{},[229,24468,24469],{},[232,24470,403],{},[236,24472,403],{"encoding":238},[212,24474,24476],{"className":24475,"ariaHidden":243},[242],[212,24477,24479,24482],{"className":24478},[247],[212,24480],{"className":24481,"style":861},[251],[212,24483,403],{"className":24484,"style":531},[256,257]," 的样本，那么 ",[212,24487,24489,24504],{"className":24488,"translate":216},[215],[212,24490,24492],{"className":24491},[220],[222,24493,24494],{"xmlns":224},[226,24495,24496,24502],{},[229,24497,24498,24500],{},[232,24499,4298],{},[307,24501,4301],{},[236,24503,21783],{"encoding":238},[212,24505,24507],{"className":24506,"ariaHidden":243},[242],[212,24508,24510,24513],{"className":24509},[247],[212,24511],{"className":24512,"style":252},[251],[212,24514,4352,24516],{"className":24515},[1682],[212,24517,4356],{"style":4355}," 以 2 为底时 ",[212,24520,24522,24554],{"className":24521,"translate":216},[215],[212,24523,24525],{"className":24524},[220],[222,24526,24527],{"xmlns":224},[226,24528,24529,24551],{},[229,24530,24531,24541,24543,24545,24547,24549],{},[392,24532,24533,24535],{},[232,24534,396],{},[229,24536,24537,24539],{},[232,24538,10894],{},[232,24540,22093],{},[307,24542,310],{"stretchy":309},[232,24544,403],{},[232,24546,407],{"mathvariant":406},[232,24548,410],{},[307,24550,317],{"stretchy":309},[236,24552,24553],{"encoding":238},"D_{KL}(P\\|Q)",[212,24555,24557],{"className":24556,"ariaHidden":243},[242],[212,24558,24560,24563,24609,24612,24615,24618,24621],{"className":24559},[247],[212,24561],{"className":24562,"style":336},[251],[212,24564,24566,24569],{"className":24565},[256],[212,24567,396],{"className":24568,"style":474},[256,257],[212,24570,24572],{"className":24571},[478],[212,24573,24575,24601],{"className":24574},[482,483],[212,24576,24578,24598],{"className":24577},[487],[212,24579,24581],{"className":24580,"style":576},[491],[212,24582,24583,24586],{"style":495},[212,24584],{"className":24585,"style":500},[499],[212,24587,24589],{"className":24588},[504,505,506,507],[212,24590,24592,24595],{"className":24591},[256,507],[212,24593,10894],{"className":24594,"style":10982},[256,257,507],[212,24596,22093],{"className":24597},[256,257,507],[212,24599,515],{"className":24600},[514],[212,24602,24604],{"className":24603},[487],[212,24605,24607],{"className":24606,"style":8166},[491],[212,24608],{},[212,24610,310],{"className":24611},[343],[212,24613,403],{"className":24614,"style":531},[256,257],[212,24616,407],{"className":24617},[256],[212,24619,410],{"className":24620},[256,257],[212,24622,317],{"className":24623},[350]," 正是用 ",[212,24626,24628,24641],{"className":24627,"translate":216},[215],[212,24629,24631],{"className":24630},[220],[222,24632,24633],{"xmlns":224},[226,24634,24635,24639],{},[229,24636,24637],{},[232,24638,410],{},[236,24640,410],{"encoding":238},[212,24642,24644],{"className":24643,"ariaHidden":243},[242],[212,24645,24647,24650],{"className":24646},[247],[212,24648],{"className":24649,"style":763},[251],[212,24651,410],{"className":24652},[256,257]," 编码比用 ",[212,24655,24657,24670],{"className":24656,"translate":216},[215],[212,24658,24660],{"className":24659},[220],[222,24661,24662],{"xmlns":224},[226,24663,24664,24668],{},[229,24665,24666],{},[232,24667,403],{},[236,24669,403],{"encoding":238},[212,24671,24673],{"className":24672,"ariaHidden":243},[242],[212,24674,24676,24679],{"className":24675},[247],[212,24677],{"className":24678,"style":861},[251],[212,24680,403],{"className":24681,"style":531},[256,257]," 编码",[1194,24684,24685],{},"多付出的比特数","，即",[212,24688,24690],{"className":24689,"translate":216},[377],[212,24691,24693,24835],{"className":24692,"translate":216},[215],[212,24694,24696],{"className":24695},[220],[222,24697,24698],{"xmlns":224,"display":386},[226,24699,24700,24832],{},[1441,24701,24702,24775],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,24703,24704,24730],{},[1450,24705,24706],{},[1453,24707,24708],{"scriptlevel":323,"displaystyle":243},[229,24709,24710,24720,24722,24724,24726,24728],{},[392,24711,24712,24714],{},[232,24713,396],{},[229,24715,24716,24718],{},[232,24717,10894],{},[232,24719,22093],{},[307,24721,310],{"stretchy":309},[232,24723,403],{},[232,24725,407],{"mathvariant":406},[232,24727,410],{},[307,24729,317],{"stretchy":309},[1450,24731,24732],{},[1453,24733,24734],{"scriptlevel":323,"displaystyle":243},[229,24735,24736,24738,24740],{},[229,24737],{},[307,24739,320],{},[6214,24741,24742,24772],{},[6214,24743,24744,24770],{},[229,24745,24746,24752,24754,24756,24758,24760,24762,24764,24766,24768],{},[392,24747,24748,24750],{},[232,24749,420],{"mathvariant":419},[232,24751,403],{},[307,24753,427],{"stretchy":309},[307,24755,5011],{},[232,24757,4298],{},[307,24759,4301],{},[232,24761,1141],{},[307,24763,310],{"stretchy":309},[232,24765,795],{},[307,24767,317],{"stretchy":309},[307,24769,454],{"stretchy":309},[307,24771,6238],{"stretchy":243},[1495,24773,24774],{},"交叉熵",[1447,24776,24777,24783],{},[1450,24778,24779],{},[1453,24780,24781],{"scriptlevel":323,"displaystyle":243},[229,24782],{},[1450,24784,24785],{},[1453,24786,24787],{"scriptlevel":323,"displaystyle":243},[229,24788,24789,24791,24793,24795,24830],{},[229,24790],{},[354,24792],{"width":3460},[307,24794,5011],{},[6214,24796,24797,24827],{},[6214,24798,24799,24825],{},[229,24800,24801,24807,24809,24811,24813,24815,24817,24819,24821,24823],{},[392,24802,24803,24805],{},[232,24804,420],{"mathvariant":419},[232,24806,403],{},[307,24808,427],{"stretchy":309},[307,24810,5011],{},[232,24812,4298],{},[307,24814,4301],{},[232,24816,11],{},[307,24818,310],{"stretchy":309},[232,24820,795],{},[307,24822,317],{"stretchy":309},[307,24824,454],{"stretchy":309},[307,24826,6238],{"stretchy":243},[1495,24828,24829],{},"熵",[232,24831,4573],{"mathvariant":406},[236,24833,24834],{"encoding":238},"\\begin{aligned}\nD_{KL}(P\\|Q)\n&=\\underbrace{\\mathbb E_P[-\\log q(X)]}\n_{\\text{交叉熵}}\\\\[2pt]\n&\\qquad-\\underbrace{\\mathbb E_P[-\\log p(X)]}\n_{\\text{熵}} .\n\\end{aligned}",[212,24836,24838],{"className":24837,"ariaHidden":243},[242],[212,24839,24841,24845],{"className":24840},[247],[212,24842],{"className":24843,"style":24844},[251],"height:5.1327em;vertical-align:-2.3163em;",[212,24846,24848],{"className":24847},[256],[212,24849,24851,24955],{"className":24850},[1441],[212,24852,24854],{"className":24853},[1558],[212,24855,24857,24946],{"className":24856},[482,483],[212,24858,24860,24943],{"className":24859},[487],[212,24861,24864,24934],{"className":24862,"style":24863},[491],"height:2.8163em;",[212,24865,24867,24870],{"style":24866},"top:-4.9763em;",[212,24868],{"className":24869,"style":658},[499],[212,24871,24873,24919,24922,24925,24928,24931],{"className":24872},[256],[212,24874,24876,24879],{"className":24875},[256],[212,24877,396],{"className":24878,"style":474},[256,257],[212,24880,24882],{"className":24881},[478],[212,24883,24885,24911],{"className":24884},[482,483],[212,24886,24888,24908],{"className":24887},[487],[212,24889,24891],{"className":24890,"style":576},[491],[212,24892,24893,24896],{"style":495},[212,24894],{"className":24895,"style":500},[499],[212,24897,24899],{"className":24898},[504,505,506,507],[212,24900,24902,24905],{"className":24901},[256,507],[212,24903,10894],{"className":24904,"style":10982},[256,257,507],[212,24906,22093],{"className":24907},[256,257,507],[212,24909,515],{"className":24910},[514],[212,24912,24914],{"className":24913},[487],[212,24915,24917],{"className":24916,"style":8166},[491],[212,24918],{},[212,24920,310],{"className":24921},[343],[212,24923,403],{"className":24924,"style":531},[256,257],[212,24926,407],{"className":24927},[256],[212,24929,410],{"className":24930},[256,257],[212,24932,317],{"className":24933},[350],[212,24935,24937,24940],{"style":24936},"top:-2.26em;",[212,24938],{"className":24939,"style":658},[499],[212,24941],{"className":24942},[256],[212,24944,515],{"className":24945},[514],[212,24947,24949],{"className":24948},[487],[212,24950,24953],{"className":24951,"style":24952},[491],"height:2.3163em;",[212,24954],{},[212,24956,24958],{"className":24957},[1649],[212,24959,24961,25374],{"className":24960},[482,483],[212,24962,24964,25371],{"className":24963},[487],[212,24965,24967,25167],{"className":24966,"style":24863},[491],[212,24968,24969,24972],{"style":24866},[212,24970],{"className":24971,"style":658},[499],[212,24973,24975,24978,24981,24984,24987],{"className":24974},[256],[212,24976],{"className":24977},[256],[212,24979],{"className":24980,"style":355},[354],[212,24982,320],{"className":24983},[359],[212,24985],{"className":24986,"style":355},[354],[212,24988,24990],{"className":24989},[607,6214],[212,24991,24993,25158],{"className":24992},[482,483],[212,24994,24996,25155],{"className":24995},[487],[212,24997,25000,25018],{"className":24998,"style":24999},[491],"height:0.75em;",[212,25001,25003,25006],{"style":25002},"top:-1.4237em;",[212,25004],{"className":25005,"style":658},[499],[212,25007,25009],{"className":25008},[504,505,506,507],[212,25010,25012],{"className":25011},[256,507],[212,25013,25015],{"className":25014},[256,4796,507],[212,25016,24774],{"className":25017},[256,4800,507],[212,25019,25020,25023],{"style":12063},[212,25021],{"className":25022,"style":658},[499],[212,25024,25026],{"className":25025},[607,6214],[212,25027,25029,25146],{"className":25028},[482,483],[212,25030,25032,25143],{"className":25031},[487],[212,25033,25035,25066],{"className":25034,"style":24999},[491],[212,25036,25039,25042],{"className":25037,"style":25038},[6505],"top:-2.102em;",[212,25040],{"className":25041,"style":658},[499],[212,25043,25045,25052,25059],{"className":25044,"style":6514},[6513],[212,25046,25048],{"className":25047,"style":6519},[6518],[6521,25049,25050],{"xmlns":6523,"width":6524,"height":6525,"viewBox":6526,"preserveAspectRatio":6527},[6529,25051],{"d":6531},[212,25053,25055],{"className":25054,"style":6519},[6535],[6521,25056,25057],{"xmlns":6523,"width":6524,"height":6525,"viewBox":6526,"preserveAspectRatio":6538},[6529,25058],{"d":6541},[212,25060,25062],{"className":25061,"style":6519},[6545],[6521,25063,25064],{"xmlns":6523,"width":6524,"height":6525,"viewBox":6526,"preserveAspectRatio":6548},[6529,25065],{"d":6551},[212,25067,25068,25071],{"style":12063},[212,25069],{"className":25070,"style":658},[499],[212,25072,25074,25114,25117,25120,25123,25128,25131,25134,25137,25140],{"className":25073},[256],[212,25075,25077,25080],{"className":25076},[256],[212,25078,420],{"className":25079},[256,563],[212,25081,25083],{"className":25082},[478],[212,25084,25086,25106],{"className":25085},[482,483],[212,25087,25089,25103],{"className":25088},[487],[212,25090,25092],{"className":25091,"style":576},[491],[212,25093,25094,25097],{"style":579},[212,25095],{"className":25096,"style":500},[499],[212,25098,25100],{"className":25099},[504,505,506,507],[212,25101,403],{"className":25102,"style":531},[256,257,507],[212,25104,515],{"className":25105},[514],[212,25107,25109],{"className":25108},[487],[212,25110,25112],{"className":25111,"style":8166},[491],[212,25113],{},[212,25115,427],{"className":25116},[343],[212,25118,5011],{"className":25119},[256],[212,25121],{"className":25122,"style":603},[354],[212,25124,4352,25126],{"className":25125},[1682],[212,25127,4356],{"style":4355},[212,25129],{"className":25130,"style":603},[354],[212,25132,1141],{"className":25133,"style":1178},[256,257],[212,25135,310],{"className":25136},[343],[212,25138,795],{"className":25139,"style":9085},[256,257],[212,25141,20590],{"className":25142},[350],[212,25144,515],{"className":25145},[514],[212,25147,25149],{"className":25148},[487],[212,25150,25153],{"className":25151,"style":25152},[491],"height:0.898em;",[212,25154],{},[212,25156,515],{"className":25157},[514],[212,25159,25161],{"className":25160},[487],[212,25162,25165],{"className":25163,"style":25164},[491],"height:1.5763em;",[212,25166],{},[212,25168,25169,25172],{"style":24936},[212,25170],{"className":25171,"style":658},[499],[212,25173,25175,25178,25181,25184,25187,25190,25365,25368],{"className":25174},[256],[212,25176],{"className":25177},[256],[212,25179],{"className":25180,"style":3832},[354],[212,25182],{"className":25183,"style":2785},[354],[212,25185,5011],{"className":25186},[2789],[212,25188],{"className":25189,"style":2785},[354],[212,25191,25193],{"className":25192},[607,6214],[212,25194,25196,25357],{"className":25195},[482,483],[212,25197,25199,25354],{"className":25198},[487],[212,25200,25202,25219],{"className":25201,"style":24999},[491],[212,25203,25204,25207],{"style":25002},[212,25205],{"className":25206,"style":658},[499],[212,25208,25210],{"className":25209},[504,505,506,507],[212,25211,25213],{"className":25212},[256,507],[212,25214,25216],{"className":25215},[256,4796,507],[212,25217,24829],{"className":25218},[256,4800,507],[212,25220,25221,25224],{"style":12063},[212,25222],{"className":25223,"style":658},[499],[212,25225,25227],{"className":25226},[607,6214],[212,25228,25230,25346],{"className":25229},[482,483],[212,25231,25233,25343],{"className":25232},[487],[212,25234,25236,25266],{"className":25235,"style":24999},[491],[212,25237,25239,25242],{"className":25238,"style":25038},[6505],[212,25240],{"className":25241,"style":658},[499],[212,25243,25245,25252,25259],{"className":25244,"style":6514},[6513],[212,25246,25248],{"className":25247,"style":6519},[6518],[6521,25249,25250],{"xmlns":6523,"width":6524,"height":6525,"viewBox":6526,"preserveAspectRatio":6527},[6529,25251],{"d":6531},[212,25253,25255],{"className":25254,"style":6519},[6535],[6521,25256,25257],{"xmlns":6523,"width":6524,"height":6525,"viewBox":6526,"preserveAspectRatio":6538},[6529,25258],{"d":6541},[212,25260,25262],{"className":25261,"style":6519},[6545],[6521,25263,25264],{"xmlns":6523,"width":6524,"height":6525,"viewBox":6526,"preserveAspectRatio":6548},[6529,25265],{"d":6551},[212,25267,25268,25271],{"style":12063},[212,25269],{"className":25270,"style":658},[499],[212,25272,25274,25314,25317,25320,25323,25328,25331,25334,25337,25340],{"className":25273},[256],[212,25275,25277,25280],{"className":25276},[256],[212,25278,420],{"className":25279},[256,563],[212,25281,25283],{"className":25282},[478],[212,25284,25286,25306],{"className":25285},[482,483],[212,25287,25289,25303],{"className":25288},[487],[212,25290,25292],{"className":25291,"style":576},[491],[212,25293,25294,25297],{"style":579},[212,25295],{"className":25296,"style":500},[499],[212,25298,25300],{"className":25299},[504,505,506,507],[212,25301,403],{"className":25302,"style":531},[256,257,507],[212,25304,515],{"className":25305},[514],[212,25307,25309],{"className":25308},[487],[212,25310,25312],{"className":25311,"style":8166},[491],[212,25313],{},[212,25315,427],{"className":25316},[343],[212,25318,5011],{"className":25319},[256],[212,25321],{"className":25322,"style":603},[354],[212,25324,4352,25326],{"className":25325},[1682],[212,25327,4356],{"style":4355},[212,25329],{"className":25330,"style":603},[354],[212,25332,11],{"className":25333},[256,257],[212,25335,310],{"className":25336},[343],[212,25338,795],{"className":25339,"style":9085},[256,257],[212,25341,20590],{"className":25342},[350],[212,25344,515],{"className":25345},[514],[212,25347,25349],{"className":25348},[487],[212,25350,25352],{"className":25351,"style":25152},[491],[212,25353],{},[212,25355,515],{"className":25356},[514],[212,25358,25360],{"className":25359},[487],[212,25361,25363],{"className":25362,"style":25164},[491],[212,25364],{},[212,25366],{"className":25367,"style":603},[354],[212,25369,4573],{"className":25370},[256],[212,25372,515],{"className":25373},[514],[212,25375,25377],{"className":25376},[487],[212,25378,25380],{"className":25379,"style":24952},[491],[212,25381],{},[11,25383,25384,25385,25489,25490,4051,25518,25546,25547,25550,25551,25579,25580,25684,25685,4051,25713,25741,25742,25745],{},"在统计中它是最大似然估计的对数似然比的期望，决定了 Stein 引理里第二类错误的最优指数，也是 AIC\u002FBIC 这类模型选择的基石；在机器学习中它是最大似然训练、变分推断与知识蒸馏的目标。它的不对称性带来两种相反的行为：",[212,25386,25388,25419],{"className":25387,"translate":216},[215],[212,25389,25391],{"className":25390},[220],[222,25392,25393],{"xmlns":224},[226,25394,25395,25417],{},[229,25396,25397,25407,25409,25411,25413,25415],{},[392,25398,25399,25401],{},[232,25400,396],{},[229,25402,25403,25405],{},[232,25404,10894],{},[232,25406,22093],{},[307,25408,310],{"stretchy":309},[232,25410,403],{},[232,25412,407],{"mathvariant":406},[232,25414,410],{},[307,25416,317],{"stretchy":309},[236,25418,24553],{"encoding":238},[212,25420,25422],{"className":25421,"ariaHidden":243},[242],[212,25423,25425,25428,25474,25477,25480,25483,25486],{"className":25424},[247],[212,25426],{"className":25427,"style":336},[251],[212,25429,25431,25434],{"className":25430},[256],[212,25432,396],{"className":25433,"style":474},[256,257],[212,25435,25437],{"className":25436},[478],[212,25438,25440,25466],{"className":25439},[482,483],[212,25441,25443,25463],{"className":25442},[487],[212,25444,25446],{"className":25445,"style":576},[491],[212,25447,25448,25451],{"style":495},[212,25449],{"className":25450,"style":500},[499],[212,25452,25454],{"className":25453},[504,505,506,507],[212,25455,25457,25460],{"className":25456},[256,507],[212,25458,10894],{"className":25459,"style":10982},[256,257,507],[212,25461,22093],{"className":25462},[256,257,507],[212,25464,515],{"className":25465},[514],[212,25467,25469],{"className":25468},[487],[212,25470,25472],{"className":25471,"style":8166},[491],[212,25473],{},[212,25475,310],{"className":25476},[343],[212,25478,403],{"className":25479,"style":531},[256,257],[212,25481,407],{"className":25482},[256],[212,25484,410],{"className":25485},[256,257],[212,25487,317],{"className":25488},[350]," 要求 ",[212,25491,25493,25506],{"className":25492,"translate":216},[215],[212,25494,25496],{"className":25495},[220],[222,25497,25498],{"xmlns":224},[226,25499,25500,25504],{},[229,25501,25502],{},[232,25503,410],{},[236,25505,410],{"encoding":238},[212,25507,25509],{"className":25508,"ariaHidden":243},[242],[212,25510,25512,25515],{"className":25511},[247],[212,25513],{"className":25514,"style":763},[251],[212,25516,410],{"className":25517},[256,257],[212,25519,25521,25534],{"className":25520,"translate":216},[215],[212,25522,25524],{"className":25523},[220],[222,25525,25526],{"xmlns":224},[226,25527,25528,25532],{},[229,25529,25530],{},[232,25531,403],{},[236,25533,403],{"encoding":238},[212,25535,25537],{"className":25536,"ariaHidden":243},[242],[212,25538,25540,25543],{"className":25539},[247],[212,25541],{"className":25542,"style":861},[251],[212,25544,403],{"className":25545,"style":531},[256,257]," 有质量处不为零（",[1194,25548,25549],{},"零回避","，mass-covering，倾向覆盖 ",[212,25552,25554,25567],{"className":25553,"translate":216},[215],[212,25555,25557],{"className":25556},[220],[222,25558,25559],{"xmlns":224},[226,25560,25561,25565],{},[229,25562,25563],{},[232,25564,403],{},[236,25566,403],{"encoding":238},[212,25568,25570],{"className":25569,"ariaHidden":243},[242],[212,25571,25573,25576],{"className":25572},[247],[212,25574],{"className":25575,"style":861},[251],[212,25577,403],{"className":25578,"style":531},[256,257]," 的每一个模式），而 ",[212,25581,25583,25614],{"className":25582,"translate":216},[215],[212,25584,25586],{"className":25585},[220],[222,25587,25588],{"xmlns":224},[226,25589,25590,25612],{},[229,25591,25592,25602,25604,25606,25608,25610],{},[392,25593,25594,25596],{},[232,25595,396],{},[229,25597,25598,25600],{},[232,25599,10894],{},[232,25601,22093],{},[307,25603,310],{"stretchy":309},[232,25605,410],{},[232,25607,407],{"mathvariant":406},[232,25609,403],{},[307,25611,317],{"stretchy":309},[236,25613,22575],{"encoding":238},[212,25615,25617],{"className":25616,"ariaHidden":243},[242],[212,25618,25620,25623,25669,25672,25675,25678,25681],{"className":25619},[247],[212,25621],{"className":25622,"style":336},[251],[212,25624,25626,25629],{"className":25625},[256],[212,25627,396],{"className":25628,"style":474},[256,257],[212,25630,25632],{"className":25631},[478],[212,25633,25635,25661],{"className":25634},[482,483],[212,25636,25638,25658],{"className":25637},[487],[212,25639,25641],{"className":25640,"style":576},[491],[212,25642,25643,25646],{"style":495},[212,25644],{"className":25645,"style":500},[499],[212,25647,25649],{"className":25648},[504,505,506,507],[212,25650,25652,25655],{"className":25651},[256,507],[212,25653,10894],{"className":25654,"style":10982},[256,257,507],[212,25656,22093],{"className":25657},[256,257,507],[212,25659,515],{"className":25660},[514],[212,25662,25664],{"className":25663},[487],[212,25665,25667],{"className":25666,"style":8166},[491],[212,25668],{},[212,25670,310],{"className":25671},[343],[212,25673,410],{"className":25674},[256,257],[212,25676,407],{"className":25677},[256],[212,25679,403],{"className":25680,"style":531},[256,257],[212,25682,317],{"className":25683},[350]," 会把 ",[212,25686,25688,25701],{"className":25687,"translate":216},[215],[212,25689,25691],{"className":25690},[220],[222,25692,25693],{"xmlns":224},[226,25694,25695,25699],{},[229,25696,25697],{},[232,25698,410],{},[236,25700,410],{"encoding":238},[212,25702,25704],{"className":25703,"ariaHidden":243},[242],[212,25705,25707,25710],{"className":25706},[247],[212,25708],{"className":25709,"style":763},[251],[212,25711,410],{"className":25712},[256,257],[212,25714,25716,25729],{"className":25715,"translate":216},[215],[212,25717,25719],{"className":25718},[220],[222,25720,25721],{"xmlns":224},[226,25722,25723,25727],{},[229,25724,25725],{},[232,25726,403],{},[236,25728,403],{"encoding":238},[212,25730,25732],{"className":25731,"ariaHidden":243},[242],[212,25733,25735,25738],{"className":25734},[247],[212,25736],{"className":25737,"style":861},[251],[212,25739,403],{"className":25740,"style":531},[256,257]," 为零处压到零（",[1194,25743,25744],{},"零强制","，mode-seeking，倾向锁定单一模式）。GAN 的模式崩塌与变分推断的均值场近似，本质都由这一不对称性决定。",[2509,25747,25749],{"id":25748},"_32-js-散度","3.2 JS 散度",[11,25751,25752,25753,9598],{},"先回顾 JS 散度的定义，令 ",[212,25754,25756,25789],{"className":25755,"translate":216},[215],[212,25757,25759],{"className":25758},[220],[222,25760,25761],{"xmlns":224},[226,25762,25763,25786],{},[229,25764,25765,25768,25770,25776,25778,25780,25782,25784],{},[232,25766,25767],{},"M",[307,25769,320],{},[435,25771,25772,25774],{},[312,25773,314],{},[312,25775,2661],{},[307,25777,310],{"stretchy":309},[232,25779,403],{},[307,25781,2668],{},[232,25783,410],{},[307,25785,317],{"stretchy":309},[236,25787,25788],{"encoding":238},"M=\\frac12(P+Q)",[212,25790,25792,25811,25900],{"className":25791,"ariaHidden":243},[242],[212,25793,25795,25798,25802,25805,25808],{"className":25794},[247],[212,25796],{"className":25797,"style":861},[251],[212,25799,25767],{"className":25800,"style":25801},[256,257],"margin-right:0.109em;",[212,25803],{"className":25804,"style":355},[354],[212,25806,320],{"className":25807},[359],[212,25809],{"className":25810,"style":355},[354],[212,25812,25814,25817,25885,25888,25891,25894,25897],{"className":25813},[247],[212,25815],{"className":25816,"style":2703},[251],[212,25818,25820,25823,25882],{"className":25819},[256],[212,25821],{"className":25822},[343,638],[212,25824,25826],{"className":25825},[435],[212,25827,25829,25874],{"className":25828},[482,483],[212,25830,25832,25871],{"className":25831},[487],[212,25833,25835,25849,25857],{"className":25834,"style":2722},[491],[212,25836,25837,25840],{"style":2725},[212,25838],{"className":25839,"style":658},[499],[212,25841,25843],{"className":25842},[504,505,506,507],[212,25844,25846],{"className":25845},[256,507],[212,25847,2661],{"className":25848},[256,507],[212,25850,25851,25854],{"style":670},[212,25852],{"className":25853,"style":658},[499],[212,25855],{"className":25856,"style":678},[677],[212,25858,25859,25862],{"style":2748},[212,25860],{"className":25861,"style":658},[499],[212,25863,25865],{"className":25864},[504,505,506,507],[212,25866,25868],{"className":25867},[256,507],[212,25869,314],{"className":25870},[256,507],[212,25872,515],{"className":25873},[514],[212,25875,25877],{"className":25876},[487],[212,25878,25880],{"className":25879,"style":2770},[491],[212,25881],{},[212,25883],{"className":25884},[350,638],[212,25886,310],{"className":25887},[343],[212,25889,403],{"className":25890,"style":531},[256,257],[212,25892],{"className":25893,"style":2785},[354],[212,25895,2668],{"className":25896},[2789],[212,25898],{"className":25899,"style":2785},[354],[212,25901,25903,25906,25909],{"className":25902},[247],[212,25904],{"className":25905,"style":336},[251],[212,25907,410],{"className":25908},[256,257],[212,25910,317],{"className":25911},[350],[212,25913,25915],{"className":25914,"translate":216},[377],[212,25916,25918,26017],{"className":25917,"translate":216},[215],[212,25919,25921],{"className":25920},[220],[222,25922,25923],{"xmlns":224,"display":386},[226,25924,25925,26014],{},[229,25926,25927,25938,25940,25942,25944,25946,25948,25950,25956,25966,25968,25980,25982,25988,25998,26000,26012],{},[392,25928,25929,25931],{},[232,25930,396],{},[229,25932,25933,25935],{},[232,25934,23943],{},[232,25936,25937],{},"S",[307,25939,310],{"stretchy":309},[232,25941,403],{},[232,25943,407],{"mathvariant":406},[232,25945,410],{},[307,25947,317],{"stretchy":309},[307,25949,320],{},[435,25951,25952,25954],{},[312,25953,314],{},[312,25955,2661],{},[392,25957,25958,25960],{},[232,25959,396],{},[229,25961,25962,25964],{},[232,25963,10894],{},[232,25965,22093],{},[1495,25967,1502],{},[229,25969,25970,25972,25974,25976,25978],{},[307,25971,310],{"fence":243},[232,25973,403],{},[232,25975,407],{"mathvariant":406},[232,25977,25767],{},[307,25979,317],{"fence":243},[307,25981,2668],{},[435,25983,25984,25986],{},[312,25985,314],{},[312,25987,2661],{},[392,25989,25990,25992],{},[232,25991,396],{},[229,25993,25994,25996],{},[232,25995,10894],{},[232,25997,22093],{},[1495,25999,1502],{},[229,26001,26002,26004,26006,26008,26010],{},[307,26003,310],{"fence":243},[232,26005,410],{},[232,26007,407],{"mathvariant":406},[232,26009,25767],{},[307,26011,317],{"fence":243},[232,26013,4573],{"mathvariant":406},[236,26015,26016],{"encoding":238},"D_{JS}(P\\|Q)=\\frac12 D_{KL}\\!\\left(P\\|M\\right)\n+\\frac12 D_{KL}\\!\\left(Q\\|M\\right).",[212,26018,26020,26097,26245],{"className":26019,"ariaHidden":243},[242],[212,26021,26023,26026,26073,26076,26079,26082,26085,26088,26091,26094],{"className":26022},[247],[212,26024],{"className":26025,"style":336},[251],[212,26027,26029,26032],{"className":26028},[256],[212,26030,396],{"className":26031,"style":474},[256,257],[212,26033,26035],{"className":26034},[478],[212,26036,26038,26065],{"className":26037},[482,483],[212,26039,26041,26062],{"className":26040},[487],[212,26042,26044],{"className":26043,"style":576},[491],[212,26045,26046,26049],{"style":495},[212,26047],{"className":26048,"style":500},[499],[212,26050,26052],{"className":26051},[504,505,506,507],[212,26053,26055,26058],{"className":26054},[256,507],[212,26056,23943],{"className":26057,"style":24353},[256,257,507],[212,26059,25937],{"className":26060,"style":26061},[256,257,507],"margin-right:0.0576em;",[212,26063,515],{"className":26064},[514],[212,26066,26068],{"className":26067},[487],[212,26069,26071],{"className":26070,"style":8166},[491],[212,26072],{},[212,26074,310],{"className":26075},[343],[212,26077,403],{"className":26078,"style":531},[256,257],[212,26080,407],{"className":26081},[256],[212,26083,410],{"className":26084},[256,257],[212,26086,317],{"className":26087},[350],[212,26089],{"className":26090,"style":355},[354],[212,26092,320],{"className":26093},[359],[212,26095],{"className":26096,"style":355},[354],[212,26098,26100,26104,26166,26212,26215,26218,26236,26239,26242],{"className":26099},[247],[212,26101],{"className":26102,"style":26103},[251],"height:2.0074em;vertical-align:-0.686em;",[212,26105,26107,26110,26163],{"className":26106},[256],[212,26108],{"className":26109},[343,638],[212,26111,26113],{"className":26112},[435],[212,26114,26116,26155],{"className":26115},[482,483],[212,26117,26119,26152],{"className":26118},[487],[212,26120,26122,26133,26141],{"className":26121,"style":23089},[491],[212,26123,26124,26127],{"style":654},[212,26125],{"className":26126,"style":658},[499],[212,26128,26130],{"className":26129},[256],[212,26131,2661],{"className":26132},[256],[212,26134,26135,26138],{"style":670},[212,26136],{"className":26137,"style":658},[499],[212,26139],{"className":26140,"style":678},[677],[212,26142,26143,26146],{"style":681},[212,26144],{"className":26145,"style":658},[499],[212,26147,26149],{"className":26148},[256],[212,26150,314],{"className":26151},[256],[212,26153,515],{"className":26154},[514],[212,26156,26158],{"className":26157},[487],[212,26159,26161],{"className":26160,"style":3976},[491],[212,26162],{},[212,26164],{"className":26165},[350,638],[212,26167,26169,26172],{"className":26168},[256],[212,26170,396],{"className":26171,"style":474},[256,257],[212,26173,26175],{"className":26174},[478],[212,26176,26178,26204],{"className":26177},[482,483],[212,26179,26181,26201],{"className":26180},[487],[212,26182,26184],{"className":26183,"style":576},[491],[212,26185,26186,26189],{"style":495},[212,26187],{"className":26188,"style":500},[499],[212,26190,26192],{"className":26191},[504,505,506,507],[212,26193,26195,26198],{"className":26194},[256,507],[212,26196,10894],{"className":26197,"style":10982},[256,257,507],[212,26199,22093],{"className":26200},[256,257,507],[212,26202,515],{"className":26203},[514],[212,26205,26207],{"className":26206},[487],[212,26208,26210],{"className":26209,"style":8166},[491],[212,26211],{},[212,26213],{"className":26214,"style":1710},[354],[212,26216],{"className":26217,"style":603},[354],[212,26219,26221,26224,26227,26230,26233],{"className":26220},[607],[212,26222,310],{"className":26223,"style":612},[343,611],[212,26225,403],{"className":26226,"style":531},[256,257],[212,26228,407],{"className":26229},[256],[212,26231,25767],{"className":26232,"style":25801},[256,257],[212,26234,317],{"className":26235,"style":612},[350,611],[212,26237],{"className":26238,"style":2785},[354],[212,26240,2668],{"className":26241},[2789],[212,26243],{"className":26244,"style":2785},[354],[212,26246,26248,26251,26313,26359,26362,26365,26383,26386],{"className":26247},[247],[212,26249],{"className":26250,"style":26103},[251],[212,26252,26254,26257,26310],{"className":26253},[256],[212,26255],{"className":26256},[343,638],[212,26258,26260],{"className":26259},[435],[212,26261,26263,26302],{"className":26262},[482,483],[212,26264,26266,26299],{"className":26265},[487],[212,26267,26269,26280,26288],{"className":26268,"style":23089},[491],[212,26270,26271,26274],{"style":654},[212,26272],{"className":26273,"style":658},[499],[212,26275,26277],{"className":26276},[256],[212,26278,2661],{"className":26279},[256],[212,26281,26282,26285],{"style":670},[212,26283],{"className":26284,"style":658},[499],[212,26286],{"className":26287,"style":678},[677],[212,26289,26290,26293],{"style":681},[212,26291],{"className":26292,"style":658},[499],[212,26294,26296],{"className":26295},[256],[212,26297,314],{"className":26298},[256],[212,26300,515],{"className":26301},[514],[212,26303,26305],{"className":26304},[487],[212,26306,26308],{"className":26307,"style":3976},[491],[212,26309],{},[212,26311],{"className":26312},[350,638],[212,26314,26316,26319],{"className":26315},[256],[212,26317,396],{"className":26318,"style":474},[256,257],[212,26320,26322],{"className":26321},[478],[212,26323,26325,26351],{"className":26324},[482,483],[212,26326,26328,26348],{"className":26327},[487],[212,26329,26331],{"className":26330,"style":576},[491],[212,26332,26333,26336],{"style":495},[212,26334],{"className":26335,"style":500},[499],[212,26337,26339],{"className":26338},[504,505,506,507],[212,26340,26342,26345],{"className":26341},[256,507],[212,26343,10894],{"className":26344,"style":10982},[256,257,507],[212,26346,22093],{"className":26347},[256,257,507],[212,26349,515],{"className":26350},[514],[212,26352,26354],{"className":26353},[487],[212,26355,26357],{"className":26356,"style":8166},[491],[212,26358],{},[212,26360],{"className":26361,"style":1710},[354],[212,26363],{"className":26364,"style":603},[354],[212,26366,26368,26371,26374,26377,26380],{"className":26367},[607],[212,26369,310],{"className":26370,"style":612},[343,611],[212,26372,410],{"className":26373},[256,257],[212,26375,407],{"className":26376},[256],[212,26378,25767],{"className":26379,"style":25801},[256,257],[212,26381,317],{"className":26382,"style":612},[350,611],[212,26384],{"className":26385,"style":603},[354],[212,26387,4573],{"className":26388},[256],[11,26390,26391,26394,26395,26423,26424,26479,26480,26508,26509,26660],{},[1194,26392,26393],{},"它是单个 f-散度。"," 这一点很容易被误解。我们直接构造 ",[212,26396,26398,26411],{"className":26397,"translate":216},[215],[212,26399,26401],{"className":26400},[220],[222,26402,26403],{"xmlns":224},[226,26404,26405,26409],{},[229,26406,26407],{},[232,26408,234],{},[236,26410,234],{"encoding":238},[212,26412,26414],{"className":26413,"ariaHidden":243},[242],[212,26415,26417,26420],{"className":26416},[247],[212,26418],{"className":26419,"style":252},[251],[212,26421,234],{"className":26422,"style":258},[256,257],"：代入 ",[212,26425,26427,26447],{"className":26426,"translate":216},[215],[212,26428,26430],{"className":26429},[220],[222,26431,26432],{"xmlns":224},[226,26433,26434,26444],{},[229,26435,26436,26438,26440,26442],{},[232,26437,11],{},[307,26439,320],{},[232,26441,966],{},[232,26443,1141],{},[236,26445,26446],{"encoding":238},"p=tq",[212,26448,26450,26468],{"className":26449,"ariaHidden":243},[242],[212,26451,26453,26456,26459,26462,26465],{"className":26452},[247],[212,26454],{"className":26455,"style":2474},[251],[212,26457,11],{"className":26458},[256,257],[212,26460],{"className":26461,"style":355},[354],[212,26463,320],{"className":26464},[359],[212,26466],{"className":26467,"style":355},[354],[212,26469,26471,26475],{"className":26470},[247],[212,26472],{"className":26473,"style":26474},[251],"height:0.8095em;vertical-align:-0.1944em;",[212,26476,26478],{"className":26477,"style":1178},[256,257],"tq","，于是 ",[212,26481,26483,26496],{"className":26482,"translate":216},[215],[212,26484,26486],{"className":26485},[220],[222,26487,26488],{"xmlns":224},[226,26489,26490,26494],{},[229,26491,26492],{},[232,26493,25767],{},[236,26495,25767],{"encoding":238},[212,26497,26499],{"className":26498,"ariaHidden":243},[242],[212,26500,26502,26505],{"className":26501},[247],[212,26503],{"className":26504,"style":861},[251],[212,26506,25767],{"className":26507,"style":25801},[256,257]," 的密度为 ",[212,26510,26512,26547],{"className":26511,"translate":216},[215],[212,26513,26515],{"className":26514},[220],[222,26516,26517],{"xmlns":224},[226,26518,26519,26544],{},[229,26520,26521,26524,26526],{},[232,26522,26523],{},"m",[307,26525,320],{},[435,26527,26528,26542],{},[229,26529,26530,26532,26534,26536,26538,26540],{},[307,26531,310],{"stretchy":309},[232,26533,966],{},[307,26535,2668],{},[312,26537,314],{},[307,26539,317],{"stretchy":309},[232,26541,1141],{},[312,26543,2661],{},[236,26545,26546],{"encoding":238},"m=\\frac{(t+1)q}{2}",[212,26548,26550,26568],{"className":26549,"ariaHidden":243},[242],[212,26551,26553,26556,26559,26562,26565],{"className":26552},[247],[212,26554],{"className":26555,"style":2543},[251],[212,26557,26523],{"className":26558},[256,257],[212,26560],{"className":26561,"style":355},[354],[212,26563,320],{"className":26564},[359],[212,26566],{"className":26567,"style":355},[354],[212,26569,26571,26575],{"className":26570},[247],[212,26572],{"className":26573,"style":26574},[251],"height:1.355em;vertical-align:-0.345em;",[212,26576,26578,26581,26657],{"className":26577},[256],[212,26579],{"className":26580},[343,638],[212,26582,26584],{"className":26583},[435],[212,26585,26587,26649],{"className":26586},[482,483],[212,26588,26590,26646],{"className":26589},[487],[212,26591,26594,26608,26616],{"className":26592,"style":26593},[491],"height:1.01em;",[212,26595,26596,26599],{"style":2725},[212,26597],{"className":26598,"style":658},[499],[212,26600,26602],{"className":26601},[504,505,506,507],[212,26603,26605],{"className":26604},[256,507],[212,26606,2661],{"className":26607},[256,507],[212,26609,26610,26613],{"style":670},[212,26611],{"className":26612,"style":658},[499],[212,26614],{"className":26615,"style":678},[677],[212,26617,26619,26622],{"style":26618},"top:-3.485em;",[212,26620],{"className":26621,"style":658},[499],[212,26623,26625],{"className":26624},[504,505,506,507],[212,26626,26628,26631,26634,26637,26640,26643],{"className":26627},[256,507],[212,26629,310],{"className":26630},[343,507],[212,26632,966],{"className":26633},[256,257,507],[212,26635,2668],{"className":26636},[2789,507],[212,26638,314],{"className":26639},[256,507],[212,26641,317],{"className":26642},[350,507],[212,26644,1141],{"className":26645,"style":1178},[256,257,507],[212,26647,515],{"className":26648},[514],[212,26650,26652],{"className":26651},[487],[212,26653,26655],{"className":26654,"style":2770},[491],[212,26656],{},[212,26658],{"className":26659},[350,638],"，逐项算：",[212,26662,26664],{"className":26663,"translate":216},[377],[212,26665,26667,26729],{"className":26666,"translate":216},[215],[212,26668,26670],{"className":26669},[220],[222,26671,26672],{"xmlns":224,"display":386},[226,26673,26674,26726],{},[229,26675,26676,26682,26684,26700,26702,26704,26710,26712,26724],{},[435,26677,26678,26680],{},[232,26679,11],{},[232,26681,26523],{},[307,26683,320],{},[435,26685,26686,26692],{},[229,26687,26688,26690],{},[312,26689,2661],{},[232,26691,966],{},[229,26693,26694,26696,26698],{},[232,26695,966],{},[307,26697,2668],{},[312,26699,314],{},[307,26701,748],{"separator":243},[354,26703],{"width":3460},[435,26705,26706,26708],{},[232,26707,1141],{},[232,26709,26523],{},[307,26711,320],{},[435,26713,26714,26716],{},[312,26715,2661],{},[229,26717,26718,26720,26722],{},[232,26719,966],{},[307,26721,2668],{},[312,26723,314],{},[307,26725,748],{"separator":243},[236,26727,26728],{"encoding":238},"\\frac{p}{m}=\\frac{2t}{t+1},\\qquad\n\\frac{q}{m}=\\frac{2}{t+1},",[212,26730,26732,26810,26974],{"className":26731,"ariaHidden":243},[242],[212,26733,26735,26739,26801,26804,26807],{"className":26734},[247],[212,26736],{"className":26737,"style":26738},[251],"height:1.7936em;vertical-align:-0.686em;",[212,26740,26742,26745,26798],{"className":26741},[256],[212,26743],{"className":26744},[343,638],[212,26746,26748],{"className":26747},[435],[212,26749,26751,26790],{"className":26750},[482,483],[212,26752,26754,26787],{"className":26753},[487],[212,26755,26757,26768,26776],{"className":26756,"style":3752},[491],[212,26758,26759,26762],{"style":654},[212,26760],{"className":26761,"style":658},[499],[212,26763,26765],{"className":26764},[256],[212,26766,26523],{"className":26767},[256,257],[212,26769,26770,26773],{"style":670},[212,26771],{"className":26772,"style":658},[499],[212,26774],{"className":26775,"style":678},[677],[212,26777,26778,26781],{"style":681},[212,26779],{"className":26780,"style":658},[499],[212,26782,26784],{"className":26783},[256],[212,26785,11],{"className":26786},[256,257],[212,26788,515],{"className":26789},[514],[212,26791,26793],{"className":26792},[487],[212,26794,26796],{"className":26795,"style":3976},[491],[212,26797],{},[212,26799],{"className":26800},[350,638],[212,26802],{"className":26803,"style":355},[354],[212,26805,320],{"className":26806},[359],[212,26808],{"className":26809,"style":355},[354],[212,26811,26813,26817,26894,26897,26900,26903,26965,26968,26971],{"className":26812},[247],[212,26814],{"className":26815,"style":26816},[251],"height:2.0908em;vertical-align:-0.7693em;",[212,26818,26820,26823,26891],{"className":26819},[256],[212,26821],{"className":26822},[343,638],[212,26824,26826],{"className":26825},[435],[212,26827,26829,26883],{"className":26828},[482,483],[212,26830,26832,26880],{"className":26831},[487],[212,26833,26835,26858,26866],{"className":26834,"style":23089},[491],[212,26836,26837,26840],{"style":654},[212,26838],{"className":26839,"style":658},[499],[212,26841,26843,26846,26849,26852,26855],{"className":26842},[256],[212,26844,966],{"className":26845},[256,257],[212,26847],{"className":26848,"style":2785},[354],[212,26850,2668],{"className":26851},[2789],[212,26853],{"className":26854,"style":2785},[354],[212,26856,314],{"className":26857},[256],[212,26859,26860,26863],{"style":670},[212,26861],{"className":26862,"style":658},[499],[212,26864],{"className":26865,"style":678},[677],[212,26867,26868,26871],{"style":681},[212,26869],{"className":26870,"style":658},[499],[212,26872,26874,26877],{"className":26873},[256],[212,26875,2661],{"className":26876},[256],[212,26878,966],{"className":26879},[256,257],[212,26881,515],{"className":26882},[514],[212,26884,26886],{"className":26885},[487],[212,26887,26889],{"className":26888,"style":17215},[491],[212,26890],{},[212,26892],{"className":26893},[350,638],[212,26895,748],{"className":26896},[770],[212,26898],{"className":26899,"style":3832},[354],[212,26901],{"className":26902,"style":603},[354],[212,26904,26906,26909,26962],{"className":26905},[256],[212,26907],{"className":26908},[343,638],[212,26910,26912],{"className":26911},[435],[212,26913,26915,26954],{"className":26914},[482,483],[212,26916,26918,26951],{"className":26917},[487],[212,26919,26921,26932,26940],{"className":26920,"style":3752},[491],[212,26922,26923,26926],{"style":654},[212,26924],{"className":26925,"style":658},[499],[212,26927,26929],{"className":26928},[256],[212,26930,26523],{"className":26931},[256,257],[212,26933,26934,26937],{"style":670},[212,26935],{"className":26936,"style":658},[499],[212,26938],{"className":26939,"style":678},[677],[212,26941,26942,26945],{"style":681},[212,26943],{"className":26944,"style":658},[499],[212,26946,26948],{"className":26947},[256],[212,26949,1141],{"className":26950,"style":1178},[256,257],[212,26952,515],{"className":26953},[514],[212,26955,26957],{"className":26956},[487],[212,26958,26960],{"className":26959,"style":3976},[491],[212,26961],{},[212,26963],{"className":26964},[350,638],[212,26966],{"className":26967,"style":355},[354],[212,26969,320],{"className":26970},[359],[212,26972],{"className":26973,"style":355},[354],[212,26975,26977,26980,27054],{"className":26976},[247],[212,26978],{"className":26979,"style":26816},[251],[212,26981,26983,26986,27051],{"className":26982},[256],[212,26984],{"className":26985},[343,638],[212,26987,26989],{"className":26988},[435],[212,26990,26992,27043],{"className":26991},[482,483],[212,26993,26995,27040],{"className":26994},[487],[212,26996,26998,27021,27029],{"className":26997,"style":23089},[491],[212,26999,27000,27003],{"style":654},[212,27001],{"className":27002,"style":658},[499],[212,27004,27006,27009,27012,27015,27018],{"className":27005},[256],[212,27007,966],{"className":27008},[256,257],[212,27010],{"className":27011,"style":2785},[354],[212,27013,2668],{"className":27014},[2789],[212,27016],{"className":27017,"style":2785},[354],[212,27019,314],{"className":27020},[256],[212,27022,27023,27026],{"style":670},[212,27024],{"className":27025,"style":658},[499],[212,27027],{"className":27028,"style":678},[677],[212,27030,27031,27034],{"style":681},[212,27032],{"className":27033,"style":658},[499],[212,27035,27037],{"className":27036},[256],[212,27038,2661],{"className":27039},[256],[212,27041,515],{"className":27042},[514],[212,27044,27046],{"className":27045},[487],[212,27047,27049],{"className":27048,"style":17215},[491],[212,27050],{},[212,27052],{"className":27053},[350,638],[212,27055,748],{"className":27056},[770],[212,27058,27060],{"className":27059,"translate":216},[377],[212,27061,27063,27203],{"className":27062,"translate":216},[215],[212,27064,27066],{"className":27065},[220],[222,27067,27068],{"xmlns":224,"display":386},[226,27069,27070,27200],{},[1441,27071,27072,27152],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,27073,27074,27100],{},[1450,27075,27076],{},[1453,27077,27078],{"scriptlevel":323,"displaystyle":243},[229,27079,27080,27090,27092,27094,27096,27098],{},[392,27081,27082,27084],{},[232,27083,396],{},[229,27085,27086,27088],{},[232,27087,23943],{},[232,27089,25937],{},[307,27091,310],{"stretchy":309},[232,27093,403],{},[232,27095,407],{"mathvariant":406},[232,27097,410],{},[307,27099,317],{"stretchy":309},[1450,27101,27102],{},[1453,27103,27104],{"scriptlevel":323,"displaystyle":243},[229,27105,27106,27108,27110,27116,27118,27120,27122,27124,27130,27132,27138,27140,27142,27144,27146],{},[229,27107],{},[307,27109,320],{},[435,27111,27112,27114],{},[312,27113,314],{},[312,27115,2661],{},[307,27117,1485],{},[232,27119,11],{},[232,27121,4298],{},[307,27123,4301],{},[435,27125,27126,27128],{},[232,27127,11],{},[232,27129,26523],{},[307,27131,2668],{},[435,27133,27134,27136],{},[312,27135,314],{},[312,27137,2661],{},[307,27139,1485],{},[232,27141,1141],{},[232,27143,4298],{},[307,27145,4301],{},[435,27147,27148,27150],{},[232,27149,1141],{},[232,27151,26523],{},[1447,27153,27154,27160],{},[1450,27155,27156],{},[1453,27157,27158],{"scriptlevel":323,"displaystyle":243},[229,27159],{},[1450,27161,27162],{},[1453,27163,27164],{"scriptlevel":323,"displaystyle":243},[229,27165,27166,27168,27170,27172,27174,27176,27186,27188,27190,27192,27194,27196,27198],{},[229,27167],{},[307,27169,320],{},[307,27171,1485],{},[232,27173,1141],{},[1495,27175,1497],{},[392,27177,27178,27180],{},[232,27179,234],{},[229,27181,27182,27184],{},[232,27183,23943],{},[232,27185,25937],{},[307,27187,310],{"stretchy":309},[232,27189,966],{},[307,27191,317],{"stretchy":309},[1495,27193,1497],{},[232,27195,441],{},[232,27197,971],{},[307,27199,748],{"separator":243},[236,27201,27202],{"encoding":238},"\\begin{aligned}\nD_{JS}(P\\|Q)\n&=\\frac12\\int p\\log\\frac{p}{m}\n+\\frac12\\int q\\log\\frac{q}{m}\\\\[2pt]\n&=\\int q\\,f_{JS}(t)\\,dx,\n\\end{aligned}",[212,27204,27206],{"className":27205,"ariaHidden":243},[242],[212,27207,27209,27213],{"className":27208},[247],[212,27210],{"className":27211,"style":27212},[251],"height:4.7445em;vertical-align:-2.1223em;",[212,27214,27216],{"className":27215},[256],[212,27217,27219,27322],{"className":27218},[1441],[212,27220,27222],{"className":27221},[1558],[212,27223,27225,27313],{"className":27224},[482,483],[212,27226,27228,27310],{"className":27227},[487],[212,27229,27232,27302],{"className":27230,"style":27231},[491],"height:2.6223em;",[212,27233,27235,27238],{"style":27234},"top:-4.6223em;",[212,27236],{"className":27237,"style":6471},[499],[212,27239,27241,27287,27290,27293,27296,27299],{"className":27240},[256],[212,27242,27244,27247],{"className":27243},[256],[212,27245,396],{"className":27246,"style":474},[256,257],[212,27248,27250],{"className":27249},[478],[212,27251,27253,27279],{"className":27252},[482,483],[212,27254,27256,27276],{"className":27255},[487],[212,27257,27259],{"className":27258,"style":576},[491],[212,27260,27261,27264],{"style":495},[212,27262],{"className":27263,"style":500},[499],[212,27265,27267],{"className":27266},[504,505,506,507],[212,27268,27270,27273],{"className":27269},[256,507],[212,27271,23943],{"className":27272,"style":24353},[256,257,507],[212,27274,25937],{"className":27275,"style":26061},[256,257,507],[212,27277,515],{"className":27278},[514],[212,27280,27282],{"className":27281},[487],[212,27283,27285],{"className":27284,"style":8166},[491],[212,27286],{},[212,27288,310],{"className":27289},[343],[212,27291,403],{"className":27292,"style":531},[256,257],[212,27294,407],{"className":27295},[256],[212,27297,410],{"className":27298},[256,257],[212,27300,317],{"className":27301},[350],[212,27303,27304,27307],{"style":2101},[212,27305],{"className":27306,"style":6471},[499],[212,27308],{"className":27309},[256],[212,27311,515],{"className":27312},[514],[212,27314,27316],{"className":27315},[487],[212,27317,27320],{"className":27318,"style":27319},[491],"height:2.1223em;",[212,27321],{},[212,27323,27325],{"className":27324},[1649],[212,27326,27328,27760],{"className":27327},[482,483],[212,27329,27331,27757],{"className":27330},[487],[212,27332,27334,27657],{"className":27333,"style":27231},[491],[212,27335,27336,27339],{"style":27234},[212,27337],{"className":27338,"style":6471},[499],[212,27340,27342,27345,27348,27351,27354,27416,27419,27422,27425,27428,27431,27436,27439,27501,27504,27507,27510,27572,27575,27578,27581,27584,27587,27592,27595],{"className":27341},[256],[212,27343],{"className":27344},[256],[212,27346],{"className":27347,"style":355},[354],[212,27349,320],{"className":27350},[359],[212,27352],{"className":27353,"style":355},[354],[212,27355,27357,27360,27413],{"className":27356},[256],[212,27358],{"className":27359},[343,638],[212,27361,27363],{"className":27362},[435],[212,27364,27366,27405],{"className":27365},[482,483],[212,27367,27369,27402],{"className":27368},[487],[212,27370,27372,27383,27391],{"className":27371,"style":23089},[491],[212,27373,27374,27377],{"style":654},[212,27375],{"className":27376,"style":658},[499],[212,27378,27380],{"className":27379},[256],[212,27381,2661],{"className":27382},[256],[212,27384,27385,27388],{"style":670},[212,27386],{"className":27387,"style":658},[499],[212,27389],{"className":27390,"style":678},[677],[212,27392,27393,27396],{"style":681},[212,27394],{"className":27395,"style":658},[499],[212,27397,27399],{"className":27398},[256],[212,27400,314],{"className":27401},[256],[212,27403,515],{"className":27404},[514],[212,27406,27408],{"className":27407},[487],[212,27409,27411],{"className":27410,"style":3976},[491],[212,27412],{},[212,27414],{"className":27415},[350,638],[212,27417],{"className":27418,"style":603},[354],[212,27420,1485],{"className":27421,"style":1685},[1682,1683,1684],[212,27423],{"className":27424,"style":603},[354],[212,27426,11],{"className":27427},[256,257],[212,27429],{"className":27430,"style":603},[354],[212,27432,4352,27434],{"className":27433},[1682],[212,27435,4356],{"style":4355},[212,27437],{"className":27438,"style":603},[354],[212,27440,27442,27445,27498],{"className":27441},[256],[212,27443],{"className":27444},[343,638],[212,27446,27448],{"className":27447},[435],[212,27449,27451,27490],{"className":27450},[482,483],[212,27452,27454,27487],{"className":27453},[487],[212,27455,27457,27468,27476],{"className":27456,"style":3752},[491],[212,27458,27459,27462],{"style":654},[212,27460],{"className":27461,"style":658},[499],[212,27463,27465],{"className":27464},[256],[212,27466,26523],{"className":27467},[256,257],[212,27469,27470,27473],{"style":670},[212,27471],{"className":27472,"style":658},[499],[212,27474],{"className":27475,"style":678},[677],[212,27477,27478,27481],{"style":681},[212,27479],{"className":27480,"style":658},[499],[212,27482,27484],{"className":27483},[256],[212,27485,11],{"className":27486},[256,257],[212,27488,515],{"className":274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f_{JS}(1\u002Ft)=f_{JS}(t)",[212,29943,29945,30021],{"className":29944,"ariaHidden":243},[242],[212,29946,29948,29951,29954,30000,30003,30006,30009,30012,30015,30018],{"className":29947},[247],[212,29949],{"className":29950,"style":336},[251],[212,29952,966],{"className":29953},[256,257],[212,29955,29957,29960],{"className":29956},[256],[212,29958,234],{"className":29959,"style":258},[256,257],[212,29961,29963],{"className":29962},[478],[212,29964,29966,29992],{"className":29965},[482,483],[212,29967,29969,29989],{"className":29968},[487],[212,29970,29972],{"className":29971,"style":576},[491],[212,29973,29974,29977],{"style":27709},[212,29975],{"className":29976,"style":500},[499],[212,29978,29980],{"className":29979},[504,505,506,507],[212,29981,29983,29986],{"className":29982},[256,507],[212,29984,23943],{"className":29985,"style":24353},[256,257,507],[212,29987,25937],{"className":29988,"style":26061},[256,257,507],[212,29990,515],{"className":29991},[514],[212,29993,29995],{"className":29994},[487],[212,29996,29998],{"className":29997,"style":8166},[491],[212,29999],{},[212,30001,310],{"className":30002},[343],[212,30004,8787],{"className":30005},[256],[212,30007,966],{"className":30008},[256,257],[212,30010,317],{"className":30011},[350],[212,30013],{"className":30014,"style":355},[354],[212,30016,320],{"className":30017},[359],[212,30019],{"className":30020,"style":355},[354],[212,30022,30024,30027,30073,30076,30079],{"className":30023},[247],[212,30025],{"className":30026,"style":336},[251],[212,30028,30030,30033],{"className":30029},[256],[212,30031,234],{"className":30032,"style":258},[256,257],[212,30034,30036],{"className":30035},[478],[212,30037,30039,30065],{"className":30038},[482,483],[212,30040,30042,30062],{"className":30041},[487],[212,30043,30045],{"className":30044,"style":576},[491],[212,30046,30047,30050],{"style":27709},[212,30048],{"className":30049,"style":500},[499],[212,30051,30053],{"className":30052},[504,505,506,507],[212,30054,30056,30059],{"className":30055},[256,507],[212,30057,23943],{"className":30058,"style":24353},[256,257,507],[212,30060,25937],{"className":30061,"style":26061},[256,257,507],[212,30063,515],{"className":30064},[514],[212,30066,30068],{"className":30067},[487],[212,30069,30071],{"className":30070,"style":8166},[491],[212,30072],{},[212,30074,310],{"className":30075},[343],[212,30077,966],{"className":30078},[256,257],[212,30080,317],{"className":30081},[350],"。因此当 ",[212,30084,30086,30103],{"className":30085,"translate":216},[215],[212,30087,30089],{"className":30088},[220],[222,30090,30091],{"xmlns":224},[226,30092,30093,30101],{},[229,30094,30095,30097,30099],{},[232,30096,403],{},[307,30098,911],{},[232,30100,410],{},[236,30102,916],{"encoding":238},[212,30104,30106,30124],{"className":30105,"ariaHidden":243},[242],[212,30107,30109,30112,30115,30118,30121],{"className":30108},[247],[212,30110],{"className":30111,"style":926},[251],[212,30113,403],{"className":30114,"style":531},[256,257],[212,30116],{"className":30117,"style":355},[354],[212,30119,911],{"className":30120},[359],[212,30122],{"className":30123,"style":355},[354],[212,30125,30127,30130],{"className":30126},[247],[212,30128],{"className":30129,"style":763},[251],[212,30131,410],{"className":30132},[256,257]," 时",[212,30135,30137],{"className":30136,"translate":216},[377],[212,30138,30140,30268],{"className":30139,"translate":216},[215],[212,30141,30143],{"className":30142},[220],[222,30144,30145],{"xmlns":224,"display":386},[226,30146,30147,30265],{},[229,30148,30149,30159,30161,30163,30165,30167,30169,30171,30185,30187,30189,30191,30193,30195,30197,30203,30209,30211,30213,30215,30217,30219,30221,30227,30233,30235,30237,30239,30241,30243,30245,30247,30249,30251,30253,30255,30257,30259,30261,30263],{},[392,30150,30151,30153],{},[232,30152,396],{},[229,30154,30155,30157],{},[232,30156,23943],{},[232,30158,25937],{},[307,30160,310],{"stretchy":309},[232,30162,403],{},[232,30164,407],{"mathvariant":406},[232,30166,410],{},[307,30168,317],{"stretchy":309},[307,30170,320],{},[392,30172,30173,30175],{},[232,30174,396],{},[392,30176,30177,30179],{},[232,30178,234],{},[229,30180,30181,30183],{},[232,30182,23943],{},[232,30184,25937],{},[307,30186,310],{"stretchy":309},[232,30188,403],{},[232,30190,407],{"mathvariant":406},[232,30192,410],{},[307,30194,317],{"stretchy":309},[307,30196,320],{},[435,30198,30199,30201],{},[312,30200,314],{},[312,30202,2661],{},[392,30204,30205,30207],{},[232,30206,396],{},[232,30208,234],{},[307,30210,310],{"stretchy":309},[232,30212,403],{},[232,30214,407],{"mathvariant":406},[232,30216,25767],{},[307,30218,317],{"stretchy":309},[307,30220,2668],{},[435,30222,30223,30225],{},[312,30224,314],{},[312,30226,2661],{},[392,30228,30229,30231],{},[232,30230,396],{},[232,30232,234],{},[307,30234,310],{"stretchy":309},[232,30236,410],{},[232,30238,407],{"mathvariant":406},[232,30240,25767],{},[307,30242,317],{"stretchy":309},[307,30244,748],{"separator":243},[354,30246],{"width":3460},[307,30248,310],{"stretchy":309},[232,30250,234],{},[307,30252,320],{},[232,30254,966],{},[232,30256,4298],{},[307,30258,4301],{},[232,30260,966],{},[307,30262,317],{"stretchy":309},[307,30264,748],{"separator":243},[236,30266,30267],{"encoding":238},"D_{JS}(P\\|Q)=D_{f_{JS}}(P\\|Q)\n=\\frac12D_f(P\\|M)\n+\\frac12D_f(Q\\|M),\\qquad(f=t\\log t),",[212,30269,30271,30347,30467,30599,30746],{"className":30270,"ariaHidden":243},[242],[212,30272,30274,30277,30323,30326,30329,30332,30335,30338,30341,30344],{"className":30273},[247],[212,30275],{"className":30276,"style":336},[251],[212,30278,30280,30283],{"className":30279},[256],[212,30281,396],{"className":30282,"style":474},[256,257],[212,30284,30286],{"className":30285},[478],[212,30287,30289,30315],{"className":30288},[482,483],[212,30290,30292,30312],{"className":30291},[487],[212,30293,30295],{"className":30294,"style":576},[491],[212,30296,30297,30300],{"style":495},[212,30298],{"className":30299,"style":500},[499],[212,30301,30303],{"className":30302},[504,505,506,507],[212,30304,30306,30309],{"className":30305},[256,507],[212,30307,23943],{"className":30308,"style":24353},[256,257,507],[212,30310,25937],{"className":30311,"style":26061},[256,257,507],[212,30313,515],{"className":30314},[514],[212,30316,30318],{"className":30317},[487],[212,30319,30321],{"className":30320,"style":8166},[491],[212,30322],{},[212,30324,310],{"className":30325},[343],[212,30327,403],{"className":30328,"style":531},[256,257],[212,30330,407],{"className":30331},[256],[212,30333,410],{"className":30334},[256,257],[212,30336,317],{"className":30337},[350],[212,30339],{"className":30340,"style":355},[354],[212,30342,320],{"className":30343},[359],[212,30345],{"className":30346,"style":355},[354],[212,30348,30350,30353,30443,30446,30449,30452,30455,30458,30461,30464],{"className":30349},[247],[212,30351],{"className":30352,"style":467},[251],[212,30354,30356,30359],{"className":30355},[256],[212,30357,396],{"className":30358,"style":474},[256,257],[212,30360,30362],{"className":30361},[478],[212,30363,30365,30435],{"className":30364},[482,483],[212,30366,30368,30432],{"className":30367},[487],[212,30369,30371],{"className":30370,"style":492},[491],[212,30372,30373,30376],{"style":495},[212,30374],{"className":30375,"style":500},[499],[212,30377,30379],{"className":30378},[504,505,506,507],[212,30380,30382],{"className":30381},[256,507],[212,30383,30385,30388],{"className":30384},[256,507],[212,30386,234],{"className":30387,"style":258},[256,257,507],[212,30389,30391],{"className":30390},[478],[212,30392,30394,30423],{"className":30393},[482,483],[212,30395,30397,30420],{"className":30396},[487],[212,30398,30400],{"className":30399,"style":6296},[491],[212,30401,30403,30407],{"style":30402},"top:-2.3567em;margin-left:-0.1076em;margin-right:0.0714em;",[212,30404],{"className":30405,"style":30406},[499],"height:2.5em;",[212,30408,30411],{"className":30409},[504,30410,9872,507],"reset-size3",[212,30412,30414,30417],{"className":30413},[256,507],[212,30415,23943],{"className":30416,"style":24353},[256,257,507],[212,30418,25937],{"className":30419,"style":26061},[256,257,507],[212,30421,515],{"className":30422},[514],[212,30424,30426],{"className":30425},[487],[212,30427,30430],{"className":30428,"style":30429},[491],"height:0.1433em;",[212,30431],{},[212,30433,515],{"className":30434},[514],[212,30436,30438],{"className":30437},[487],[212,30439,30441],{"className":30440,"style":522},[491],[212,30442],{},[212,30444,310],{"className":30445},[343],[212,30447,403],{"className":30448,"style":531},[256,257],[212,30450,407],{"className":30451},[256],[212,30453,410],{"className":30454},[256,257],[212,30456,317],{"className":30457},[350],[212,30459],{"className":30460,"style":355},[354],[212,30462,320],{"className":30463},[359],[212,30465],{"className":30466,"style":355},[354],[212,30468,30470,30473,30535,30575,30578,30581,30584,30587,30590,30593,30596],{"className":30469},[247],[212,30471],{"className":30472,"style":26103},[251],[212,30474,30476,30479,30532],{"className":30475},[256],[212,30477],{"className":30478},[343,638],[212,30480,30482],{"className":30481},[435],[212,30483,30485,30524],{"className":30484},[482,483],[212,30486,30488,30521],{"className":30487},[487],[212,30489,30491,30502,30510],{"className":30490,"style":23089},[491],[212,30492,30493,30496],{"style":654},[212,30494],{"className":30495,"style":658},[499],[212,30497,30499],{"className":30498},[256],[212,30500,2661],{"className":30501},[256],[212,30503,30504,30507],{"style":670},[212,30505],{"className":30506,"style":658},[499],[212,30508],{"className":30509,"style":678},[677],[212,30511,30512,30515],{"style":681},[212,30513],{"className":30514,"style":658},[499],[212,30516,30518],{"className":30517},[256],[212,30519,314],{"className":30520},[256],[212,30522,515],{"className":30523},[514],[212,30525,30527],{"className":30526},[487],[212,30528,30530],{"className":30529,"style":3976},[491],[212,30531],{},[212,30533],{"className":30534},[350,638],[212,30536,30538,30541],{"className":30537},[256],[212,30539,396],{"className":30540,"style":474},[256,257],[212,30542,30544],{"className":30543},[478],[212,30545,30547,30567],{"className":30546},[482,483],[212,30548,30550,30564],{"className":30549},[487],[212,30551,30553],{"className":30552,"style":492},[491],[212,30554,30555,30558],{"style":495},[212,30556],{"className":30557,"style":500},[499],[212,30559,30561],{"className":30560},[504,505,506,507],[212,30562,234],{"className":30563,"style":258},[256,257,507],[212,30565,515],{"className":30566},[514],[212,30568,30570],{"className":30569},[487],[212,30571,30573],{"className":30572,"style":522},[491],[212,30574],{},[212,30576,310],{"className":30577},[343],[212,30579,403],{"className":30580,"style":531},[256,257],[212,30582,407],{"className":30583},[256],[212,30585,25767],{"className":30586,"style":25801},[256,257],[212,30588,317],{"className":30589},[350],[212,30591],{"className":30592,"style":2785},[354],[212,30594,2668],{"className":30595},[2789],[212,30597],{"className":30598,"style":2785},[354],[212,30600,30602,30605,30667,30707,30710,30713,30716,30719,30722,30725,30728,30731,30734,30737,30740,30743],{"className":30601},[247],[212,30603],{"className":30604,"style":26103},[251],[212,30606,30608,30611,30664],{"className":30607},[256],[212,30609],{"className":30610},[343,638],[212,30612,30614],{"className":30613},[435],[212,30615,30617,30656],{"className":30616},[482,483],[212,30618,30620,30653],{"className":30619},[487],[212,30621,30623,30634,30642],{"className":30622,"style":23089},[491],[212,30624,30625,30628],{"style":654},[212,30626],{"className":30627,"style":658},[499],[212,30629,30631],{"className":30630},[256],[212,30632,2661],{"className":30633},[256],[212,30635,30636,30639],{"style":670},[212,30637],{"className":30638,"style":658},[499],[212,30640],{"className":30641,"style":678},[677],[212,30643,30644,30647],{"style":681},[212,30645],{"className":30646,"style":658},[499],[212,30648,30650],{"className":30649},[256],[212,30651,314],{"className":30652},[256],[212,30654,515],{"className":30655},[514],[212,30657,30659],{"className":30658},[487],[212,30660,30662],{"className":30661,"style":3976},[491],[212,30663],{},[212,30665],{"className":30666},[350,638],[212,30668,30670,30673],{"className":30669},[256],[212,30671,396],{"className":30672,"style":474},[256,257],[212,30674,30676],{"className":30675},[478],[212,30677,30679,30699],{"className":30678},[482,483],[212,30680,30682,30696],{"className":30681},[487],[212,30683,30685],{"className":30684,"style":492},[491],[212,30686,30687,30690],{"style":495},[212,30688],{"className":30689,"style":500},[499],[212,30691,30693],{"className":30692},[504,505,506,507],[212,30694,234],{"className":30695,"style":258},[256,257,507],[212,30697,515],{"className":30698},[514],[212,30700,30702],{"className":30701},[487],[212,30703,30705],{"className":30704,"style":522},[491],[212,30706],{},[212,30708,310],{"className":30709},[343],[212,30711,410],{"className":30712},[256,257],[212,30714,407],{"className":30715},[256],[212,30717,25767],{"className":30718,"style":25801},[256,257],[212,30720,317],{"className":30721},[350],[212,30723,748],{"className":30724},[770],[212,30726],{"className":30727,"style":3832},[354],[212,30729],{"className":30730,"style":603},[354],[212,30732,310],{"className":30733},[343],[212,30735,234],{"className":30736,"style":258},[256,257],[212,30738],{"className":30739,"style":355},[354],[212,30741,320],{"className":30742},[359],[212,30744],{"className":30745,"style":355},[354],[212,30747,30749,30752,30755,30758,30763,30766,30769,30772],{"className":30748},[247],[212,30750],{"className":30751,"style":336},[251],[212,30753,966],{"className":30754},[256,257],[212,30756],{"className":30757,"style":603},[354],[212,30759,4352,30761],{"className":30760},[1682],[212,30762,4356],{"style":4355},[212,30764],{"className":30765,"style":603},[354],[212,30767,966],{"className":30768},[256,257],[212,30770,317],{"className":30771},[350],[212,30773,748],{"className":30774},[770],[11,30776,30777,30778,30806,30807,30876,30877,31012],{},"两种写法完全一致：JS 既是「两个 f-散度（相对 ",[212,30779,30781,30794],{"className":30780,"translate":216},[215],[212,30782,30784],{"className":30783},[220],[222,30785,30786],{"xmlns":224},[226,30787,30788,30792],{},[229,30789,30790],{},[232,30791,25767],{},[236,30793,25767],{"encoding":238},[212,30795,30797],{"className":30796,"ariaHidden":243},[242],[212,30798,30800,30803],{"className":30799},[247],[212,30801],{"className":30802,"style":861},[251],[212,30804,25767],{"className":30805,"style":25801},[256,257],"）的平均」，也是「一个对称 f-散度」。原文「不是单一 ",[212,30808,30810,30827],{"className":30809,"translate":216},[215],[212,30811,30813],{"className":30812},[220],[222,30814,30815],{"xmlns":224},[226,30816,30817,30825],{},[229,30818,30819],{},[392,30820,30821,30823],{},[232,30822,396],{},[232,30824,234],{},[236,30826,4220],{"encoding":238},[212,30828,30830],{"className":30829,"ariaHidden":243},[242],[212,30831,30833,30836],{"className":30832},[247],[212,30834],{"className":30835,"style":4230},[251],[212,30837,30839,30842],{"className":30838},[256],[212,30840,396],{"className":30841,"style":474},[256,257],[212,30843,30845],{"className":30844},[478],[212,30846,30848,30868],{"className":30847},[482,483],[212,30849,30851,30865],{"className":30850},[487],[212,30852,30854],{"className":30853,"style":492},[491],[212,30855,30856,30859],{"style":495},[212,30857],{"className":30858,"style":500},[499],[212,30860,30862],{"className":30861},[504,505,506,507],[212,30863,234],{"className":30864,"style":258},[256,257,507],[212,30866,515],{"className":30867},[514],[212,30869,30871],{"className":30870},[487],[212,30872,30874],{"className":30873,"style":522},[491],[212,30875],{},"」的说法可修正为：",[1194,30878,30879,30880,30930,30931,31011],{},"在 ",[212,30881,30883,30900],{"className":30882,"translate":216},[215],[212,30884,30886],{"className":30885},[220],[222,30887,30888],{"xmlns":224},[226,30889,30890,30898],{},[229,30891,30892,30894,30896],{},[232,30893,403],{},[307,30895,911],{},[232,30897,410],{},[236,30899,916],{"encoding":238},[212,30901,30903,30921],{"className":30902,"ariaHidden":243},[242],[212,30904,30906,30909,30912,30915,30918],{"className":30905},[247],[212,30907],{"className":30908,"style":926},[251],[212,30910,403],{"className":30911,"style":531},[256,257],[212,30913],{"className":30914,"style":355},[354],[212,30916,911],{"className":30917},[359],[212,30919],{"className":30920,"style":355},[354],[212,30922,30924,30927],{"className":30923},[247],[212,30925],{"className":30926,"style":763},[251],[212,30928,410],{"className":30929},[256,257]," 时它是单一 ",[212,30932,30934,30956],{"className":30933,"translate":216},[215],[212,30935,30937],{"className":30936},[220],[222,30938,30939],{"xmlns":224},[226,30940,30941,30953],{},[229,30942,30943],{},[392,30944,30945,30947],{},[232,30946,234],{},[229,30948,30949,30951],{},[232,30950,23943],{},[232,30952,25937],{},[236,30954,30955],{"encoding":238},"f_{JS}",[212,30957,30959],{"className":30958,"ariaHidden":243},[242],[212,30960,30962,30965],{"className":30961},[247],[212,30963],{"className":30964,"style":252},[251],[212,30966,30968,30971],{"className":30967},[256],[212,30969,234],{"className":30970,"style":258},[256,257],[212,30972,30974],{"className":30973},[478],[212,30975,30977,31003],{"className":30976},[482,483],[212,30978,30980,31000],{"className":30979},[487],[212,30981,30983],{"className":30982,"style":576},[491],[212,30984,30985,30988],{"style":27709},[212,30986],{"className":30987,"style":500},[499],[212,30989,30991],{"className":30990},[504,505,506,507],[212,30992,30994,30997],{"className":30993},[256,507],[212,30995,23943],{"className":30996,"style":24353},[256,257,507],[212,30998,25937],{"className":30999,"style":26061},[256,257,507],[212,31001,515],{"className":31002},[514],[212,31004,31006],{"className":31005},[487],[212,31007,31009],{"className":31008,"style":8166},[491],[212,31010],{}," 的 f-散度","；一般情形则用下面的双变量形式。",[11,31014,31015,31018,31019,31060,31061,31176,31177,31180],{},[1194,31016,31017],{},"一般情形的双变量形式."," 当 ",[212,31020,31022,31039],{"className":31021,"translate":216},[215],[212,31023,31025],{"className":31024},[220],[222,31026,31027],{"xmlns":224},[226,31028,31029,31037],{},[229,31030,31031,31033,31035],{},[232,31032,403],{},[307,31034,748],{"separator":243},[232,31036,410],{},[236,31038,753],{"encoding":238},[212,31040,31042],{"className":31041,"ariaHidden":243},[242],[212,31043,31045,31048,31051,31054,31057],{"className":31044},[247],[212,31046],{"className":31047,"style":763},[251],[212,31049,403],{"className":31050,"style":531},[256,257],[212,31052,748],{"className":31053},[770],[212,31055],{"className":31056,"style":603},[354],[212,31058,410],{"className":31059},[256,257]," 支撑集可能分离时，",[212,31062,31064,31100],{"className":31063,"translate":216},[215],[212,31065,31067],{"className":31066},[220],[222,31068,31069],{"xmlns":224},[226,31070,31071,31097],{},[229,31072,31073,31075,31077,31079,31089,31091,31093,31095],{},[307,31074,310],{"stretchy":309},[232,31076,966],{},[307,31078,748],{"separator":243},[392,31080,31081,31083],{},[232,31082,234],{},[229,31084,31085,31087],{},[232,31086,23943],{},[232,31088,25937],{},[307,31090,310],{"stretchy":309},[232,31092,966],{},[307,31094,317],{"stretchy":309},[307,31096,317],{"stretchy":309},[236,31098,31099],{"encoding":238},"(t,f_{JS}(t))",[212,31101,31103],{"className":31102,"ariaHidden":243},[242],[212,31104,31106,31109,31112,31115,31118,31121,31167,31170,31173],{"className":31105},[247],[212,31107],{"className":31108,"style":336},[251],[212,31110,310],{"className":31111},[343],[212,31113,966],{"className":31114},[256,257],[212,31116,748],{"className":31117},[770],[212,31119],{"className":31120,"style":603},[354],[212,31122,31124,31127],{"className":31123},[256],[212,31125,234],{"className":31126,"style":258},[256,257],[212,31128,31130],{"className":31129},[478],[212,31131,31133,31159],{"className":31132},[482,483],[212,31134,31136,31156],{"className":31135},[487],[212,31137,31139],{"className":31138,"style":576},[491],[212,31140,31141,31144],{"style":27709},[212,31142],{"className":31143,"style":500},[499],[212,31145,31147],{"className":31146},[504,505,506,507],[212,31148,31150,31153],{"className":31149},[256,507],[212,31151,23943],{"className":31152,"style":24353},[256,257,507],[212,31154,25937],{"className":31155,"style":26061},[256,257,507],[212,31157,515],{"className":31158},[514],[212,31160,31162],{"className":31161},[487],[212,31163,31165],{"className":31164,"style":8166},[491],[212,31166],{},[212,31168,310],{"className":31169},[343],[212,31171,966],{"className":31172},[256,257],[212,31174,19247],{"className":31175},[350]," 的写法会漏掉奇异项。此时把 JS 写成 Csiszár 的",[1194,31178,31179],{},"双变量（齐次、联合凸）泛函","最稳妥：",[212,31182,31184],{"className":31183,"translate":216},[377],[212,31185,31187,31244],{"className":31186,"translate":216},[215],[212,31188,31190],{"className":31189},[220],[222,31191,31192],{"xmlns":224,"display":386},[226,31193,31194,31241],{},[229,31195,31196,31206,31208,31210,31212,31214,31216,31218,31220,31223,31225,31227,31229,31231,31233,31235,31237,31239],{},[392,31197,31198,31200],{},[232,31199,396],{},[229,31201,31202,31204],{},[232,31203,23943],{},[232,31205,25937],{},[307,31207,310],{"stretchy":309},[232,31209,403],{},[232,31211,407],{"mathvariant":406},[232,31213,410],{},[307,31215,317],{"stretchy":309},[307,31217,320],{},[307,31219,1485],{},[232,31221,31222],{},"φ",[307,31224,310],{"stretchy":309},[232,31226,11],{},[307,31228,748],{"separator":243},[232,31230,1141],{},[307,31232,317],{"stretchy":309},[1495,31234,1497],{},[232,31236,441],{},[232,31238,2562],{},[307,31240,748],{"separator":243},[236,31242,31243],{"encoding":238},"D_{JS}(P\\|Q)=\\int \\varphi(p,q)\\,d\\mu,",[212,31245,31247,31323],{"className":31246,"ariaHidden":243},[242],[212,31248,31250,31253,31299,31302,31305,31308,31311,31314,31317,31320],{"className":31249},[247],[212,31251],{"className":31252,"style":336},[251],[212,31254,31256,31259],{"className":31255},[256],[212,31257,396],{"className":31258,"style":474},[256,257],[212,31260,31262],{"className":31261},[478],[212,31263,31265,31291],{"className":31264},[482,483],[212,31266,31268,31288],{"className":31267},[487],[212,31269,31271],{"className":31270,"style":576},[491],[212,31272,31273,31276],{"style":495},[212,31274],{"className":31275,"style":500},[499],[212,31277,31279],{"className":31278},[504,505,506,507],[212,31280,31282,31285],{"className":31281},[256,507],[212,31283,23943],{"className":31284,"style":24353},[256,257,507],[212,31286,25937],{"className":31287,"style":26061},[256,257,507],[212,31289,515],{"className":31290},[514],[212,31292,31294],{"className":31293},[487],[212,31295,31297],{"className":31296,"style":8166},[491],[212,31298],{},[212,31300,310],{"className":31301},[343],[212,31303,403],{"className":31304,"style":531},[256,257],[212,31306,407],{"className":31307},[256],[212,31309,410],{"className":31310},[256,257],[212,31312,317],{"className":31313},[350],[212,31315],{"className":31316,"style":355},[354],[212,31318,320],{"className":31319},[359],[212,31321],{"className":31322,"style":355},[354],[212,31324,31326,31329,31332,31335,31338,31341,31344,31347,31350,31353,31356,31359,31362,31365],{"className":31325},[247],[212,31327],{"className":31328,"style":5975},[251],[212,31330,1485],{"className":31331,"style":1685},[1682,1683,1684],[212,31333],{"className":31334,"style":603},[354],[212,31336,31222],{"className":31337},[256,257],[212,31339,310],{"className":31340},[343],[212,31342,11],{"className":31343},[256,257],[212,31345,748],{"className":31346},[770],[212,31348],{"className":31349,"style":603},[354],[212,31351,1141],{"className":31352,"style":1178},[256,257],[212,31354,317],{"className":31355},[350],[212,31357],{"className":31358,"style":603},[354],[212,31360,441],{"className":31361},[256,257],[212,31363,2562],{"className":31364},[256,257],[212,31366,748],{"className":31367},[770],[212,31369,31371],{"className":31370,"translate":216},[377],[212,31372,31374,31458],{"className":31373,"translate":216},[215],[212,31375,31377],{"className":31376},[220],[222,31378,31379],{"xmlns":224,"display":386},[226,31380,31381,31455],{},[229,31382,31383,31385,31387,31389,31391,31393,31395,31397,31403,31405,31407,31409,31411,31427,31429,31431,31433,31435,31451,31453],{},[232,31384,31222],{},[307,31386,310],{"stretchy":309},[232,31388,11],{},[307,31390,748],{"separator":243},[232,31392,1141],{},[307,31394,317],{"stretchy":309},[307,31396,320],{},[435,31398,31399,31401],{},[312,31400,314],{},[312,31402,2661],{},[307,31404,427],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[232,31406,11],{},[232,31408,4298],{},[307,31410,4301],{},[435,31412,31413,31419],{},[229,31414,31415,31417],{},[312,31416,2661],{},[232,31418,11],{},[229,31420,31421,31423,31425],{},[232,31422,11],{},[307,31424,2668],{},[232,31426,1141],{},[307,31428,2668],{},[232,31430,1141],{},[232,31432,4298],{},[307,31434,4301],{},[435,31436,31437,31443],{},[229,31438,31439,31441],{},[312,31440,2661],{},[232,31442,1141],{},[229,31444,31445,31447,31449],{},[232,31446,11],{},[307,31448,2668],{},[232,31450,1141],{},[307,31452,454],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[307,31454,748],{"separator":243},[236,31456,31457],{"encoding":238},"\\varphi(p,q)=\\frac12\\Big[\np\\log\\frac{2p}{p+q}+q\\log\\frac{2q}{p+q}\\Big],",[212,31459,31461,31497,31672],{"className":31460,"ariaHidden":243},[242],[212,31462,31464,31467,31470,31473,31476,31479,31482,31485,31488,31491,31494],{"className":31463},[247],[212,31465],{"className":31466,"style":336},[251],[212,31468,31222],{"className":31469},[256,257],[212,31471,310],{"className":31472},[343],[212,31474,11],{"className":31475},[256,257],[212,31477,748],{"className":31478},[770],[212,31480],{"className":31481,"style":603},[354],[212,31483,1141],{"className":31484,"style":1178},[256,257],[212,31486,317],{"className":31487},[350],[212,31489],{"className":31490,"style":355},[354],[212,31492,320],{"className":31493},[359],[212,31495],{"className":31496,"style":355},[354],[212,31498,31500,31504,31566,31572,31575,31578,31583,31586,31663,31666,31669],{"className":31499},[247],[212,31501],{"className":31502,"style":31503},[251],"height:2.2019em;vertical-align:-0.8804em;",[212,31505,31507,31510,31563],{"className":31506},[256],[212,31508],{"className":31509},[343,638],[212,31511,31513],{"className":31512},[435],[212,31514,31516,31555],{"className":31515},[482,483],[212,31517,31519,31552],{"className":31518},[487],[212,31520,31522,31533,31541],{"className":31521,"style":23089},[491],[212,31523,31524,31527],{"style":654},[212,31525],{"className":31526,"style":658},[499],[212,31528,31530],{"className":31529},[256],[212,31531,2661],{"className":31532},[256],[212,31534,31535,31538],{"style":670},[212,31536],{"className":31537,"style":658},[499],[212,31539],{"className":31540,"style":678},[677],[212,31542,31543,31546],{"style":681},[212,31544],{"className":31545,"style":658},[499],[212,31547,31549],{"className":31548},[256],[212,31550,314],{"className":31551},[256],[212,31553,515],{"className":31554},[514],[212,31556,31558],{"className":31557},[487],[212,31559,31561],{"className":31560,"style":3976},[491],[212,31562],{},[212,31564],{"className":31565},[350,638],[212,31567,31569],{"className":31568},[256],[212,31570,427],{"className":31571},[616,3918],[212,31573,11],{"className":31574},[256,257],[212,31576],{"className":31577,"style":603},[354],[212,31579,4352,31581],{"className":31580},[1682],[212,31582,4356],{"style":4355},[212,31584],{"className":31585,"style":603},[354],[212,31587,31589,31592,31660],{"className":31588},[256],[212,31590],{"className":31591},[343,638],[212,31593,31595],{"className":31594},[435],[212,31596,31598,31652],{"className":31597},[482,483],[212,31599,31601,31649],{"className":31600},[487],[212,31602,31604,31627,31635],{"className":31603,"style":23089},[491],[212,31605,31606,31609],{"style":654},[212,31607],{"className":31608,"style":658},[499],[212,31610,31612,31615,31618,31621,31624],{"className":31611},[256],[212,31613,11],{"className":31614},[256,257],[212,31616],{"className":31617,"style":2785},[354],[212,31619,2668],{"className":31620},[2789],[212,31622],{"className":31623,"style":2785},[354],[212,31625,1141],{"className":31626,"style":1178},[256,257],[212,31628,31629,31632],{"style":670},[212,31630],{"className":31631,"style":658},[499],[212,31633],{"className":31634,"style":678},[677],[212,31636,31637,31640],{"style":681},[212,31638],{"className":31639,"style":658},[499],[212,31641,31643,31646],{"className":31642},[256],[212,31644,2661],{"className":31645},[256],[212,31647,11],{"className":31648},[256,257],[212,31650,515],{"className":31651},[514],[212,31653,31655],{"className":31654},[487],[212,31656,31658],{"className":31657,"style":703},[491],[212,31659],{},[212,31661],{"className":31662},[350,638],[212,31664],{"className":31665,"style":2785},[354],[212,31667,2668],{"className":31668},[2789],[212,31670],{"className":31671,"style":2785},[354],[212,31673,31675,31678,31681,31684,31689,31692,31769,31775],{"className":31674},[247],[212,31676],{"className":31677,"style":31503},[251],[212,31679,1141],{"className":31680,"style":1178},[256,257],[212,31682],{"className":31683,"style":603},[354],[212,31685,4352,31687],{"className":31686},[1682],[212,31688,4356],{"style":4355},[212,31690],{"className":31691,"style":603},[354],[212,31693,31695,31698,31766],{"className":31694},[256],[212,31696],{"className":31697},[343,638],[212,31699,31701],{"className":31700},[435],[212,31702,31704,31758],{"className":31703},[482,483],[212,31705,31707,31755],{"className":31706},[487],[212,31708,31710,31733,31741],{"className":31709,"style":23089},[491],[212,31711,31712,31715],{"style":654},[212,31713],{"className":31714,"style":658},[499],[212,31716,31718,31721,31724,31727,31730],{"className":31717},[256],[212,31719,11],{"className":31720},[256,257],[212,31722],{"className":31723,"style":2785},[354],[212,31725,2668],{"className":31726},[2789],[212,31728],{"className":31729,"style":2785},[354],[212,31731,1141],{"className":31732,"style":1178},[256,257],[212,31734,31735,31738],{"style":670},[212,31736],{"className":31737,"style":658},[499],[212,31739],{"className":31740,"style":678},[677],[212,31742,31743,31746],{"style":681},[212,31744],{"className":31745,"style":658},[499],[212,31747,31749,31752],{"className":31748},[256],[212,31750,2661],{"className":31751},[256],[212,31753,1141],{"className":31754,"style":1178},[256,257],[212,31756,515],{"className":31757},[514],[212,31759,31761],{"className":31760},[487],[212,31762,31764],{"className":31763,"style":703},[491],[212,31765],{},[212,31767],{"className":31768},[350,638],[212,31770,31772],{"className":31771},[256],[212,31773,454],{"className":31774},[616,3918],[212,31776,748],{"className":31777},[770],[11,31779,31780,865,31809,31861,31862,31914,31915,32072,32073,32159,32160,32283],{},[212,31781,31783,31797],{"className":31782,"translate":216},[215],[212,31784,31786],{"className":31785},[220],[222,31787,31788],{"xmlns":224},[226,31789,31790,31794],{},[229,31791,31792],{},[232,31793,31222],{},[236,31795,31796],{"encoding":238},"\\varphi",[212,31798,31800],{"className":31799,"ariaHidden":243},[242],[212,31801,31803,31806],{"className":31802},[247],[212,31804],{"className":31805,"style":2474},[251],[212,31807,31222],{"className":31808},[256,257],[212,31810,31812,31834],{"className":31811,"translate":216},[215],[212,31813,31815],{"className":31814},[220],[222,31816,31817],{"xmlns":224},[226,31818,31819,31831],{},[229,31820,31821,31823,31825,31827,31829],{},[307,31822,310],{"stretchy":309},[232,31824,11],{},[307,31826,748],{"separator":243},[232,31828,1141],{},[307,31830,317],{"stretchy":309},[236,31832,31833],{"encoding":238},"(p,q)",[212,31835,31837],{"className":31836,"ariaHidden":243},[242],[212,31838,31840,31843,31846,31849,31852,31855,31858],{"className":31839},[247],[212,31841],{"className":31842,"style":336},[251],[212,31844,310],{"className":31845},[343],[212,31847,11],{"className":31848},[256,257],[212,31850,748],{"className":31851},[770],[212,31853],{"className":31854,"style":603},[354],[212,31856,1141],{"className":31857,"style":1178},[256,257],[212,31859,317],{"className":31860},[350]," 联合凸且一次齐次。在 ",[212,31863,31865,31883],{"className":31864,"translate":216},[215],[212,31866,31868],{"className":31867},[220],[222,31869,31870],{"xmlns":224},[226,31871,31872,31880],{},[229,31873,31874,31876,31878],{},[232,31875,1141],{},[307,31877,3101],{},[312,31879,323],{},[236,31881,31882],{"encoding":238},"q>0",[212,31884,31886,31905],{"className":31885,"ariaHidden":243},[242],[212,31887,31889,31893,31896,31899,31902],{"className":31888},[247],[212,31890],{"className":31891,"style":31892},[251],"height:0.7335em;vertical-align:-0.1944em;",[212,31894,1141],{"className":31895,"style":1178},[256,257],[212,31897],{"className":31898,"style":355},[354],[212,31900,3101],{"className":31901},[359],[212,31903],{"className":31904,"style":355},[354],[212,31906,31908,31911],{"className":31907},[247],[212,31909],{"className":31910,"style":369},[251],[212,31912,323],{"className":31913},[256]," 处 ",[212,31916,31918,31966],{"className":31917,"translate":216},[215],[212,31919,31921],{"className":31920},[220],[222,31922,31923],{"xmlns":224},[226,31924,31925,31963],{},[229,31926,31927,31929,31931,31933,31935,31937,31939,31941,31943,31945,31947,31957,31959,31961],{},[232,31928,31222],{},[307,31930,310],{"stretchy":309},[232,31932,966],{},[232,31934,1141],{},[307,31936,748],{"separator":243},[232,31938,1141],{},[307,31940,317],{"stretchy":309},[307,31942,320],{},[232,31944,1141],{},[1495,31946,1497],{},[392,31948,31949,31951],{},[232,31950,234],{},[229,31952,31953,31955],{},[232,31954,23943],{},[232,31956,25937],{},[307,31958,310],{"stretchy":309},[232,31960,966],{},[307,31962,317],{"stretchy":309},[236,31964,31965],{"encoding":238},"\\varphi(tq,q)=q\\,f_{JS}(t)",[212,31967,31969,32005],{"className":31968,"ariaHidden":243},[242],[212,31970,31972,31975,31978,31981,31984,31987,31990,31993,31996,31999,32002],{"className":31971},[247],[212,31973],{"className":31974,"style":336},[251],[212,31976,31222],{"className":31977},[256,257],[212,31979,310],{"className":31980},[343],[212,31982,26478],{"className":31983,"style":1178},[256,257],[212,31985,748],{"className":31986},[770],[212,31988],{"className":31989,"style":603},[354],[212,31991,1141],{"className":31992,"style":1178},[256,257],[212,31994,317],{"className":31995},[350],[212,31997],{"className":31998,"style":355},[354],[212,32000,320],{"className":32001},[359],[212,32003],{"className":32004,"style":355},[354],[212,32006,32008,32011,32014,32017,32063,32066,32069],{"className":32007},[247],[212,32009],{"className":32010,"style":336},[251],[212,32012,1141],{"className":32013,"style":1178},[256,257],[212,32015],{"className":32016,"style":603},[354],[212,32018,32020,32023],{"className":32019},[256],[212,32021,234],{"className":32022,"style":258},[256,257],[212,32024,32026],{"className":32025},[478],[212,32027,32029,32055],{"className":32028},[482,483],[212,32030,32032,32052],{"className":32031},[487],[212,32033,32035],{"className":32034,"style":576},[491],[212,32036,32037,32040],{"style":27709},[212,32038],{"className":32039,"style":500},[499],[212,32041,32043],{"className":32042},[504,505,506,507],[212,32044,32046,32049],{"className":32045},[256,507],[212,32047,23943],{"className":32048,"style":24353},[256,257,507],[212,32050,25937],{"className":32051,"style":26061},[256,257,507],[212,32053,515],{"className":32054},[514],[212,32056,32058],{"className":32057},[487],[212,32059,32061],{"className":32060,"style":8166},[491],[212,32062],{},[212,32064,310],{"className":32065},[343],[212,32067,966],{"className":32068},[256,257],[212,32070,317],{"className":32071},[350],"，两者一致；在 ",[212,32074,32076,32102],{"className":32075,"translate":216},[215],[212,32077,32079],{"className":32078},[220],[222,32080,32081],{"xmlns":224},[226,32082,32083,32099],{},[229,32084,32085,32087,32089,32091,32093,32095,32097],{},[232,32086,1141],{},[307,32088,320],{},[312,32090,323],{},[307,32092,748],{"separator":243},[232,32094,11],{},[307,32096,3101],{},[312,32098,323],{},[236,32100,32101],{"encoding":238},"q=0,p>0",[212,32103,32105,32123,32150],{"className":32104,"ariaHidden":243},[242],[212,32106,32108,32111,32114,32117,32120],{"className":32107},[247],[212,32109],{"className":32110,"style":2474},[251],[212,32112,1141],{"className":32113,"style":1178},[256,257],[212,32115],{"className":32116,"style":355},[354],[212,32118,320],{"className":32119},[359],[212,32121],{"className":32122,"style":355},[354],[212,32124,32126,32129,32132,32135,32138,32141,32144,32147],{"className":32125},[247],[212,32127],{"className":32128,"style":9556},[251],[212,32130,323],{"className":32131},[256],[212,32133,748],{"className":32134},[770],[212,32136],{"className":32137,"style":603},[354],[212,32139,11],{"className":32140},[256,257],[212,32142],{"className":32143,"style":355},[354],[212,32145,3101],{"className":32146},[359],[212,32148],{"className":32149,"style":355},[354],[212,32151,32153,32156],{"className":32152},[247],[212,32154],{"className":32155,"style":369},[251],[212,32157,323],{"className":32158},[256]," 处奇异项 ",[212,32161,32163,32189],{"className":32162,"translate":216},[215],[212,32164,32166],{"className":32165},[220],[222,32167,32168],{"xmlns":224},[226,32169,32170,32186],{},[229,32171,32172,32178,32180,32182,32184],{},[435,32173,32174,32176],{},[312,32175,314],{},[312,32177,2661],{},[232,32179,11],{},[232,32181,4298],{},[307,32183,4301],{},[312,32185,2661],{},[236,32187,32188],{"encoding":238},"\\frac12 p\\log 2",[212,32190,32192],{"className":32191,"ariaHidden":243},[242],[212,32193,32195,32198,32266,32269,32272,32277,32280],{"className":32194},[247],[212,32196],{"className":32197,"style":2703},[251],[212,32199,32201,32204,32263],{"className":32200},[256],[212,32202],{"className":32203},[343,638],[212,32205,32207],{"className":32206},[435],[212,32208,32210,32255],{"className":32209},[482,483],[212,32211,32213,32252],{"className":32212},[487],[212,32214,32216,32230,32238],{"className":32215,"style":2722},[491],[212,32217,32218,32221],{"style":2725},[212,32219],{"className":32220,"style":658},[499],[212,32222,32224],{"className":32223},[504,505,506,507],[212,32225,32227],{"className":32226},[256,507],[212,32228,2661],{"className":32229},[256,507],[212,32231,32232,32235],{"style":670},[212,32233],{"className":32234,"style":658},[499],[212,32236],{"className":32237,"style":678},[677],[212,32239,32240,32243],{"style":2748},[212,32241],{"className":32242,"style":658},[499],[212,32244,32246],{"className":32245},[504,505,506,507],[212,32247,32249],{"className":32248},[256,507],[212,32250,314],{"className":32251},[256,507],[212,32253,515],{"className":32254},[514],[212,32256,32258],{"className":32257},[487],[212,32259,32261],{"className":32260,"style":2770},[491],[212,32262],{},[212,32264],{"className":32265},[350,638],[212,32267,11],{"className":32268},[256,257],[212,32270],{"className":32271,"style":603},[354],[212,32273,4352,32275],{"className":32274},[1682],[212,32276,4356],{"style":4355},[212,32278],{"className":32279,"style":603},[354],[212,32281,2661],{"className":32282},[256]," 会被保留下来（这正是 1.1 节讨论的「支撑不重叠」约定）。",[11,32285,32286,32289,32290,32369,32370,15995,32373,32424,32425,32658,32659,32687,32688,32716,32717,32905,32906,33001],{},[1194,32287,32288],{},"有界性。"," 注意 ",[212,32291,32293,32314],{"className":32292,"translate":216},[215],[212,32294,32296],{"className":32295},[220],[222,32297,32298],{"xmlns":224},[226,32299,32300,32312],{},[229,32301,32302],{},[392,32303,32304,32306],{},[232,32305,234],{},[229,32307,32308,32310],{},[232,32309,23943],{},[232,32311,25937],{},[236,32313,30955],{"encoding":238},[212,32315,32317],{"className":32316,"ariaHidden":243},[242],[212,32318,32320,32323],{"className":32319},[247],[212,32321],{"className":32322,"style":252},[251],[212,32324,32326,32329],{"className":32325},[256],[212,32327,234],{"className":32328,"style":258},[256,257],[212,32330,32332],{"className":32331},[478],[212,32333,32335,32361],{"className":32334},[482,483],[212,32336,32338,32358],{"className":32337},[487],[212,32339,32341],{"className":32340,"style":576},[491],[212,32342,32343,32346],{"style":27709},[212,32344],{"className":32345,"style":500},[499],[212,32347,32349],{"className":32348},[504,505,506,507],[212,32350,32352,32355],{"className":32351},[256,507],[212,32353,23943],{"className":32354,"style":24353},[256,257,507],[212,32356,25937],{"className":32357,"style":26061},[256,257,507],[212,32359,515],{"className":32360},[514],[212,32362,32364],{"className":32363},[487],[212,32365,32367],{"className":32366,"style":8166},[491],[212,32368],{}," 逐点",[1194,32371,32372],{},"无界",[212,32374,32376,32394],{"className":32375,"translate":216},[215],[212,32377,32379],{"className":32378},[220],[222,32380,32381],{"xmlns":224},[226,32382,32383,32391],{},[229,32384,32385,32387,32389],{},[232,32386,966],{},[307,32388,1228],{},[232,32390,1223],{"mathvariant":406},[236,32392,32393],{"encoding":238},"t\\to\\infty",[212,32395,32397,32415],{"className":32396,"ariaHidden":243},[242],[212,32398,32400,32403,32406,32409,32412],{"className":32399},[247],[212,32401],{"className":32402,"style":5541},[251],[212,32404,966],{"className":32405},[256,257],[212,32407],{"className":32408,"style":355},[354],[212,32410,1228],{"className":32411},[359],[212,32413],{"className":32414,"style":355},[354],[212,32416,32418,32421],{"className":32417},[247],[212,32419],{"className":32420,"style":2543},[251],[212,32422,1223],{"className":32423},[256]," 时 ",[212,32426,32428,32476],{"className":32427,"translate":216},[215],[212,32429,32431],{"className":32430},[220],[222,32432,32433],{"xmlns":224},[226,32434,32435,32473],{},[229,32436,32437,32447,32449,32451,32453,32455,32461,32463,32465,32467,32469,32471],{},[392,32438,32439,32441],{},[232,32440,234],{},[229,32442,32443,32445],{},[232,32444,23943],{},[232,32446,25937],{},[307,32448,310],{"stretchy":309},[232,32450,966],{},[307,32452,317],{"stretchy":309},[307,32454,9067],{},[435,32456,32457,32459],{},[312,32458,314],{},[312,32460,2661],{},[232,32462,966],{},[232,32464,4298],{},[307,32466,4301],{},[312,32468,2661],{},[307,32470,1228],{},[232,32472,1223],{"mathvariant":406},[236,32474,32475],{"encoding":238},"f_{JS}(t)\\sim\\frac12 t\\log 2\\to\\infty",[212,32477,32479,32549,32649],{"className":32478,"ariaHidden":243},[242],[212,32480,32482,32485,32531,32534,32537,32540,32543,32546],{"className":32481},[247],[212,32483],{"className":32484,"style":336},[251],[212,32486,32488,32491],{"className":32487},[256],[212,32489,234],{"className":32490,"style":258},[256,257],[212,32492,32494],{"className":32493},[478],[212,32495,32497,32523],{"className":32496},[482,483],[212,32498,32500,32520],{"className":32499},[487],[212,32501,32503],{"className":32502,"style":576},[491],[212,32504,32505,32508],{"style":27709},[212,32506],{"className":32507,"style":500},[499],[212,32509,32511],{"className":32510},[504,505,506,507],[212,32512,32514,32517],{"className":32513},[256,507],[212,32515,23943],{"className":32516,"style":24353},[256,257,507],[212,32518,25937],{"className":32519,"style":26061},[256,257,507],[212,32521,515],{"className":32522},[514],[212,32524,32526],{"className":32525},[487],[212,32527,32529],{"className":32528,"style":8166},[491],[212,32530],{},[212,32532,310],{"className":32533},[343],[212,32535,966],{"className":32536},[256,257],[212,32538,317],{"className":32539},[350],[212,32541],{"className":32542,"style":355},[354],[212,32544,9067],{"className":32545},[359],[212,32547],{"className":32548,"style":355},[354],[212,32550,32552,32555,32623,32626,32629,32634,32637,32640,32643,32646],{"className":32551},[247],[212,32553],{"className":32554,"style":2703},[251],[212,32556,32558,32561,32620],{"className":32557},[256],[212,32559],{"className":32560},[343,638],[212,32562,32564],{"className":32563},[435],[212,32565,32567,32612],{"className":32566},[482,483],[212,32568,32570,32609],{"className":32569},[487],[212,32571,32573,32587,32595],{"className":32572,"style":2722},[491],[212,32574,32575,32578],{"style":2725},[212,32576],{"className":32577,"style":658},[499],[212,32579,32581],{"className":32580},[504,505,506,507],[212,32582,32584],{"className":32583},[256,507],[212,32585,2661],{"className":32586},[256,507],[212,32588,32589,32592],{"style":670},[212,32590],{"className":32591,"style":658},[499],[212,32593],{"className":32594,"style":678},[677],[212,32596,32597,32600],{"style":2748},[212,32598],{"className":32599,"style":658},[499],[212,32601,32603],{"className":32602},[504,505,506,507],[212,32604,32606],{"className":32605},[256,507],[212,32607,314],{"className":32608},[256,507],[212,32610,515],{"className":32611},[514],[212,32613,32615],{"className":32614},[487],[212,32616,32618],{"className":32617,"style":2770},[491],[212,32619],{},[212,32621],{"className":32622},[350,638],[212,32624,966],{"className":32625},[256,257],[212,32627],{"className":32628,"style":603},[354],[212,32630,4352,32632],{"className":32631},[1682],[212,32633,4356],{"style":4355},[212,32635],{"className":32636,"style":603},[354],[212,32638,2661],{"className":32639},[256],[212,32641],{"className":32642,"style":355},[354],[212,32644,1228],{"className":32645},[359],[212,32647],{"className":32648,"style":355},[354],[212,32650,32652,32655],{"className":32651},[247],[212,32653],{"className":32654,"style":2543},[251],[212,32656,1223],{"className":32657},[256],"），但积分有界，因为 ",[212,32660,32662,32675],{"className":32661,"translate":216},[215],[212,32663,32665],{"className":32664},[220],[222,32666,32667],{"xmlns":224},[226,32668,32669,32673],{},[229,32670,32671],{},[232,32672,966],{},[236,32674,966],{"encoding":238},[212,32676,32678],{"className":32677,"ariaHidden":243},[242],[212,32679,32681,32684],{"className":32680},[247],[212,32682],{"className":32683,"style":5541},[251],[212,32685,966],{"className":32686},[256,257]," 大的地方 ",[212,32689,32691,32704],{"className":32690,"translate":216},[215],[212,32692,32694],{"className":32693},[220],[222,32695,32696],{"xmlns":224},[226,32697,32698,32702],{},[229,32699,32700],{},[232,32701,1141],{},[236,32703,1141],{"encoding":238},[212,32705,32707],{"className":32706,"ariaHidden":243},[242],[212,32708,32710,32713],{"className":32709},[247],[212,32711],{"className":32712,"style":2474},[251],[212,32714,1141],{"className":32715,"style":1178},[256,257]," 小、权重趋于 0。严格地用两 KL 形式：",[212,32718,32720,32778],{"className":32719,"translate":216},[215],[212,32721,32723],{"className":32722},[220],[222,32724,32725],{"xmlns":224},[226,32726,32727,32775],{},[229,32728,32729,32731,32733,32735,32737,32739,32741,32743,32745,32747,32749,32751,32757,32759,32761,32763,32765,32767,32769,32771,32773],{},[312,32730,2661],{},[232,32732,11],{},[232,32734,1138],{"mathvariant":406},[307,32736,310],{"stretchy":309},[232,32738,11],{},[307,32740,2668],{},[232,32742,1141],{},[307,32744,317],{"stretchy":309},[307,32746,10150],{},[312,32748,2661],{},[307,32750,11190],{},[229,32752,32753,32755],{},[232,32754,10894],{"mathvariant":406},[232,32756,22093],{"mathvariant":406},[307,32758,310],{"stretchy":309},[232,32760,403],{},[232,32762,407],{"mathvariant":406},[232,32764,25767],{},[307,32766,317],{"stretchy":309},[307,32768,10150],{},[232,32770,4298],{},[307,32772,4301],{},[312,32774,2661],{},[236,32776,32777],{"encoding":238},"2p\u002F(p+q)\\le 2\\Rightarrow \\mathrm{KL}(P\\|M)\\le\\log2",[212,32779,32781,32811,32832,32850,32888],{"className":32780,"ariaHidden":243},[242],[212,32782,32784,32787,32790,32793,32796,32799,32802,32805,32808],{"className":32783},[247],[212,32785],{"className":32786,"style":336},[251],[212,32788,2661],{"className":32789},[256],[212,32791,11],{"className":32792},[256,257],[212,32794,1138],{"className":32795},[256],[212,32797,310],{"className":32798},[343],[212,32800,11],{"className":32801},[256,257],[212,32803],{"className":32804,"style":2785},[354],[212,32806,2668],{"className":32807},[2789],[212,32809],{"className":32810,"style":2785},[354],[212,32812,32814,32817,32820,32823,32826,32829],{"className":32813},[247],[212,32815],{"className":32816,"style":336},[251],[212,32818,1141],{"className":32819,"style":1178},[256,257],[212,32821,317],{"className":32822},[350],[212,32824],{"className":32825,"style":355},[354],[212,32827,10150],{"className":32828},[359],[212,32830],{"className":32831,"style":355},[354],[212,32833,32835,32838,32841,32844,32847],{"className":32834},[247],[212,32836],{"className":32837,"style":369},[251],[212,32839,2661],{"className":32840},[256],[212,32842],{"className":32843,"style":355},[354],[212,32845,11190],{"className":32846},[359],[212,32848],{"className":32849,"style":355},[354],[212,32851,32853,32856,32864,32867,32870,32873,32876,32879,32882,32885],{"className":32852},[247],[212,32854],{"className":32855,"style":336},[251],[212,32857,32859],{"className":32858},[256],[212,32860,32863],{"className":32861},[256,32862],"mathrm","KL",[212,32865,310],{"className":32866},[343],[212,32868,403],{"className":32869,"style":531},[256,257],[212,32871,407],{"className":32872},[256],[212,32874,25767],{"className":32875,"style":25801},[256,257],[212,32877,317],{"className":32878},[350],[212,32880],{"className":32881,"style":355},[354],[212,32883,10150],{"className":32884},[359],[212,32886],{"className":32887,"style":355},[354],[212,32889,32891,32894,32899,32902],{"className":32890},[247],[212,32892],{"className":32893,"style":252},[251],[212,32895,4352,32897],{"className":32896},[1682],[212,32898,4356],{"style":4355},[212,32900],{"className":32901,"style":603},[354],[212,32903,2661],{"className":32904},[256],"，同理 ",[212,32907,32909,32945],{"className":32908,"translate":216},[215],[212,32910,32912],{"className":32911},[220],[222,32913,32914],{"xmlns":224},[226,32915,32916,32942],{},[229,32917,32918,32924,32926,32928,32930,32932,32934,32936,32938,32940],{},[229,32919,32920,32922],{},[232,32921,10894],{"mathvariant":406},[232,32923,22093],{"mathvariant":406},[307,32925,310],{"stretchy":309},[232,32927,410],{},[232,32929,407],{"mathvariant":406},[232,32931,25767],{},[307,32933,317],{"stretchy":309},[307,32935,10150],{},[232,32937,4298],{},[307,32939,4301],{},[312,32941,2661],{},[236,32943,32944],{"encoding":238},"\\mathrm{KL}(Q\\|M)\\le\\log2",[212,32946,32948,32984],{"className":32947,"ariaHidden":243},[242],[212,32949,32951,32954,32960,32963,32966,32969,32972,32975,32978,32981],{"className":32950},[247],[212,32952],{"className":32953,"style":336},[251],[212,32955,32957],{"className":32956},[256],[212,32958,32863],{"className":32959},[256,32862],[212,32961,310],{"className":32962},[343],[212,32964,410],{"className":32965},[256,257],[212,32967,407],{"className":32968},[256],[212,32970,25767],{"className":32971,"style":25801},[256,257],[212,32973,317],{"className":32974},[350],[212,32976],{"className":32977,"style":355},[354],[212,32979,10150],{"className":32980},[359],[212,32982],{"className":32983,"style":355},[354],[212,32985,32987,32990,32995,32998],{"className":32986},[247],[212,32988],{"className":32989,"style":252},[251],[212,32991,4352,32993],{"className":32992},[1682],[212,32994,4356],{"style":4355},[212,32996],{"className":32997,"style":603},[354],[212,32999,2661],{"className":33000},[256],"，故",[212,33003,33005],{"className":33004,"translate":216},[377],[212,33006,33008,33166],{"className":33007,"translate":216},[215],[212,33009,33011],{"className":33010},[220],[222,33012,33013],{"xmlns":224,"display":386},[226,33014,33015,33163],{},[1441,33016,33017,33105],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,33018,33019,33049],{},[1450,33020,33021],{},[1453,33022,33023],{"scriptlevel":323,"displaystyle":243},[229,33024,33025,33027,33029,33039,33041,33043,33045,33047],{},[312,33026,323],{},[307,33028,10150],{},[392,33030,33031,33033],{},[232,33032,396],{},[229,33034,33035,33037],{},[232,33036,23943],{},[232,33038,25937],{},[307,33040,310],{"stretchy":309},[232,33042,403],{},[232,33044,407],{"mathvariant":406},[232,33046,410],{},[307,33048,317],{"stretchy":309},[1450,33050,33051],{},[1453,33052,33053],{"scriptlevel":323,"displaystyle":243},[229,33054,33055,33057,33059,33065,33071,33073,33075,33077,33079,33081,33083,33089,33095,33097,33099,33101,33103],{},[229,33056],{},[307,33058,320],{},[435,33060,33061,33063],{},[312,33062,314],{},[312,33064,2661],{},[229,33066,33067,33069],{},[232,33068,10894],{"mathvariant":406},[232,33070,22093],{"mathvariant":406},[307,33072,310],{"stretchy":309},[232,33074,403],{},[232,33076,407],{"mathvariant":406},[232,33078,25767],{},[307,33080,317],{"stretchy":309},[307,33082,2668],{},[435,33084,33085,33087],{},[312,33086,314],{},[312,33088,2661],{},[229,33090,33091,33093],{},[232,33092,10894],{"mathvariant":406},[232,33094,22093],{"mathvariant":406},[307,33096,310],{"stretchy":309},[232,33098,410],{},[232,33100,407],{"mathvariant":406},[232,33102,25767],{},[307,33104,317],{"stretchy":309},[1447,33106,33107,33113],{},[1450,33108,33109],{},[1453,33110,33111],{"scriptlevel":323,"displaystyle":243},[229,33112],{},[1450,33114,33115],{},[1453,33116,33117],{"scriptlevel":323,"displaystyle":243},[229,33118,33119,33121,33123,33129,33131,33133,33135,33137,33143,33145,33147,33149,33151,33153,33155,33157,33160],{},[229,33120],{},[307,33122,10150],{},[435,33124,33125,33127],{},[312,33126,314],{},[312,33128,2661],{},[232,33130,4298],{},[307,33132,4301],{},[312,33134,2661],{},[307,33136,2668],{},[435,33138,33139,33141],{},[312,33140,314],{},[312,33142,2661],{},[232,33144,4298],{},[307,33146,4301],{},[312,33148,2661],{},[307,33150,320],{},[232,33152,4298],{},[307,33154,4301],{},[312,33156,2661],{},[307,33158,33159],{},"≈",[312,33161,33162],{},"0.693.",[236,33164,33165],{"encoding":238},"\\begin{aligned}\n0\\le D_{JS}(P\\|Q)\n&=\\frac12\\mathrm{KL}(P\\|M)\n+\\frac12\\mathrm{KL}(Q\\|M)\\\\[2pt]\n&\\le \\frac12\\log 2+\\frac12\\log 2\n=\\log 2\\approx 0.693 .\n\\end{aligned}",[212,33167,33169],{"className":33168,"ariaHidden":243},[242],[212,33170,33172,33176],{"className":33171},[247],[212,33173],{"className":33174,"style":33175},[251],"height:4.3149em;vertical-align:-1.9074em;",[212,33177,33179],{"className":33178},[256],[212,33180,33182,33297],{"className":33181},[1441],[212,33183,33185],{"className":33184},[1558],[212,33186,33188,33288],{"className":33187},[482,483],[212,33189,33191,33285],{"className":33190},[487],[212,33192,33195,33277],{"className":33193,"style":33194},[491],"height:2.4074em;",[212,33196,33198,33201],{"style":33197},"top:-4.4074em;",[212,33199],{"className":33200,"style":22866},[499],[212,33202,33204,33207,33210,33213,33216,33262,33265,33268,33271,33274],{"className":33203},[256],[212,33205,323],{"className":33206},[256],[212,33208],{"className":33209,"style":355},[354],[212,33211,10150],{"className":33212},[359],[212,33214],{"className":33215,"style":355},[354],[212,33217,33219,33222],{"className":33218},[256],[212,33220,396],{"className":33221,"style":474},[256,257],[212,33223,33225],{"className":33224},[478],[212,33226,33228,33254],{"className":33227},[482,483],[212,33229,33231,33251],{"className":33230},[487],[212,33232,33234],{"className":33233,"style":576},[491],[212,33235,33236,33239],{"style":495},[212,33237],{"className":33238,"style":500},[499],[212,33240,33242],{"className":33241},[504,505,506,507],[212,33243,33245,33248],{"className":33244},[256,507],[212,33246,23943],{"className":33247,"style":24353},[256,257,507],[212,33249,25937],{"className":33250,"style":26061},[256,257,507],[212,33252,515],{"className":33253},[514],[212,33255,33257],{"className":33256},[487],[212,33258,33260],{"className":33259,"style":8166},[491],[212,33261],{},[212,33263,310],{"className":33264},[343],[212,33266,403],{"className":33267,"style":531},[256,257],[212,33269,407],{"className":33270},[256],[212,33272,410],{"className":33273},[256,257],[212,33275,317],{"className":33276},[350],[212,33278,33279,33282],{"style":2101},[212,33280],{"className":33281,"style":22866},[499],[212,33283],{"className":33284},[256],[212,33286,515],{"className":33287},[514],[212,33289,33291],{"className":33290},[487],[212,33292,33295],{"className":33293,"style":33294},[491],"height:1.9074em;",[212,33296],{},[212,33298,33300],{"className":33299},[1649],[212,33301,33303,33720],{"className":33302},[482,483],[212,33304,33306,33717],{"className":33305},[487],[212,33307,33309,33504],{"className":33308,"style":33194},[491],[212,33310,33311,33314],{"style":33197},[212,33312],{"className":33313,"style":22866},[499],[212,33315,33317,33320,33323,33326,33329,33391,33397,33400,33403,33406,33409,33412,33415,33418,33421,33483,33489,33492,33495,33498,33501],{"className":33316},[256],[212,33318],{"className":33319},[256],[212,33321],{"className":33322,"style":355},[354],[212,33324,320],{"className":33325},[359],[212,33327],{"className":33328,"style":355},[354],[212,33330,33332,33335,33388],{"className":33331},[256],[212,33333],{"className":33334},[343,638],[212,33336,33338],{"className":33337},[435],[212,33339,33341,33380],{"className":33340},[482,483],[212,33342,33344,33377],{"className":33343},[487],[212,33345,33347,33358,33366],{"className":33346,"style":23089},[491],[212,33348,33349,33352],{"style":654},[212,33350],{"className":33351,"style":658},[499],[212,33353,33355],{"className":33354},[256],[212,33356,2661],{"className":33357},[256],[212,33359,33360,33363],{"style":670},[212,33361],{"className":33362,"style":658},[499],[212,33364],{"className":33365,"style":678},[677],[212,33367,33368,33371],{"style":681},[212,33369],{"className":33370,"style":658},[499],[212,33372,33374],{"className":33373},[256],[212,33375,314],{"className":33376},[256],[212,33378,515],{"className":33379},[514],[212,33381,33383],{"className":33382},[487],[212,33384,33386],{"className":33385,"style":3976},[491],[212,33387],{},[212,33389],{"className":33390},[350,638],[212,33392,33394],{"className":33393},[256],[212,33395,32863],{"className":33396},[256,32862],[212,33398,310],{"className":33399},[343],[212,33401,403],{"className":33402,"style":531},[256,257],[212,33404,407],{"className":33405},[256],[212,33407,25767],{"className":33408,"style":25801},[256,257],[212,33410,317],{"className":33411},[350],[212,33413],{"className":33414,"style":2785},[354],[212,33416,2668],{"className":33417},[2789],[212,33419],{"className":33420,"style":2785},[354],[212,33422,33424,33427,33480],{"className":33423},[256],[212,33425],{"className":33426},[343,638],[212,33428,33430],{"className":33429},[435],[212,33431,33433,33472],{"className":33432},[482,483],[212,33434,33436,33469],{"className":33435},[487],[212,33437,33439,33450,33458],{"className":33438,"style":23089},[491],[212,33440,33441,33444],{"style":654},[212,33442],{"className":33443,"style":658},[499],[212,33445,33447],{"className":33446},[256],[212,33448,2661],{"className":33449},[256],[212,33451,33452,33455],{"style":670},[212,33453],{"className":33454,"style":658},[499],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",[212,33732,33734,33753],{"className":33733,"translate":216},[215],[212,33735,33737],{"className":33736},[220],[222,33738,33739],{"xmlns":224},[226,33740,33741,33750],{},[229,33742,33743,33745,33748],{},[232,33744,403],{},[307,33746,33747],{},"⊥",[232,33749,410],{},[236,33751,33752],{"encoding":238},"P\\perp Q",[212,33754,33756,33774],{"className":33755,"ariaHidden":243},[242],[212,33757,33759,33762,33765,33768,33771],{"className":33758},[247],[212,33760],{"className":33761,"style":12797},[251],[212,33763,403],{"className":33764,"style":531},[256,257],[212,33766],{"className":33767,"style":355},[354],[212,33769,33747],{"className":33770},[359],[212,33772],{"className":33773,"style":355},[354],[212,33775,33777,33780],{"className":33776},[247],[212,33778],{"className":33779,"style":763},[251],[212,33781,410],{"className":33782},[256,257],"（支撑集不重叠）。有界是 JS 相对 KL 的最大优点（梯度消失则是它最大的缺点，二者互为因果）。",[11,33785,33786,33788,33789,33818,33819,33852,33853,33881,33882,33910,33911,33939,33940,33968,33969,2607,33997,34025,34026,9598],{},[1194,33787,24393],{}," JS 有一个很直观的信息论解释：先掷一枚公平硬币 ",[212,33790,33792,33806],{"className":33791,"translate":216},[215],[212,33793,33795],{"className":33794},[220],[222,33796,33797],{"xmlns":224},[226,33798,33799,33804],{},[229,33800,33801],{},[232,33802,33803],{},"Z",[236,33805,33803],{"encoding":238},[212,33807,33809],{"className":33808,"ariaHidden":243},[242],[212,33810,33812,33815],{"className":33811},[247],[212,33813],{"className":33814,"style":861},[251],[212,33816,33803],{"className":33817,"style":10982},[256,257],"（正反面各 ",[212,33820,33822,33840],{"className":33821,"translate":216},[215],[212,33823,33825],{"className":33824},[220],[222,33826,33827],{"xmlns":224},[226,33828,33829,33837],{},[229,33830,33831,33833,33835],{},[312,33832,314],{},[232,33834,1138],{"mathvariant":406},[312,33836,2661],{},[236,33838,33839],{"encoding":238},"1\u002F2",[212,33841,33843],{"className":33842,"ariaHidden":243},[242],[212,33844,33846,33849],{"className":33845},[247],[212,33847],{"className":33848,"style":336},[251],[212,33850,33839],{"className":33851},[256],"），正面时从 ",[212,33854,33856,33869],{"className":33855,"translate":216},[215],[212,33857,33859],{"className":33858},[220],[222,33860,33861],{"xmlns":224},[226,33862,33863,33867],{},[229,33864,33865],{},[232,33866,403],{},[236,33868,403],{"encoding":238},[212,33870,33872],{"className":33871,"ariaHidden":243},[242],[212,33873,33875,33878],{"className":33874},[247],[212,33876],{"className":33877,"style":861},[251],[212,33879,403],{"className":33880,"style":531},[256,257]," 取样、反面时从 ",[212,33883,33885,33898],{"className":33884,"translate":216},[215],[212,33886,33888],{"className":33887},[220],[222,33889,33890],{"xmlns":224},[226,33891,33892,33896],{},[229,33893,33894],{},[232,33895,410],{},[236,33897,410],{"encoding":238},[212,33899,33901],{"className":33900,"ariaHidden":243},[242],[212,33902,33904,33907],{"className":33903},[247],[212,33905],{"className":33906,"style":763},[251],[212,33908,410],{"className":33909},[256,257]," 取样，得到观测 ",[212,33912,33914,33927],{"className":33913,"translate":216},[215],[212,33915,33917],{"className":33916},[220],[222,33918,33919],{"xmlns":224},[226,33920,33921,33925],{},[229,33922,33923],{},[232,33924,795],{},[236,33926,795],{"encoding":238},[212,33928,33930],{"className":33929,"ariaHidden":243},[242],[212,33931,33933,33936],{"className":33932},[247],[212,33934],{"className":33935,"style":861},[251],[212,33937,795],{"className":33938,"style":9085},[256,257],"；则 JS 正是「看一眼 ",[212,33941,33943,33956],{"className":33942,"translate":216},[215],[212,33944,33946],{"className":33945},[220],[222,33947,33948],{"xmlns":224},[226,33949,33950,33954],{},[229,33951,33952],{},[232,33953,795],{},[236,33955,795],{"encoding":238},[212,33957,33959],{"className":33958,"ariaHidden":243},[242],[212,33960,33962,33965],{"className":33961},[247],[212,33963],{"className":33964,"style":861},[251],[212,33966,795],{"className":33967,"style":9085},[256,257]," 能否判断硬币正反」所蕴含的信息量，即 ",[212,33970,33972,33985],{"className":33971,"translate":216},[215],[212,33973,33975],{"className":33974},[220],[222,33976,33977],{"xmlns":224},[226,33978,33979,33983],{},[229,33980,33981],{},[232,33982,33803],{},[236,33984,33803],{"encoding":238},[212,33986,33988],{"className":33987,"ariaHidden":243},[242],[212,33989,33991,33994],{"className":33990},[247],[212,33992],{"className":33993,"style":861},[251],[212,33995,33803],{"className":33996,"style":10982},[256,257],[212,33998,34000,34013],{"className":33999,"translate":216},[215],[212,34001,34003],{"className":34002},[220],[222,34004,34005],{"xmlns":224},[226,34006,34007,34011],{},[229,34008,34009],{},[232,34010,795],{},[236,34012,795],{"encoding":238},[212,34014,34016],{"className":34015,"ariaHidden":243},[242],[212,34017,34019,34022],{"className":34018},[247],[212,34020],{"className":34021,"style":861},[251],[212,34023,795],{"className":34024,"style":9085},[256,257]," 的",[1194,34027,34028],{},"互信息",[212,34030,34032],{"className":34031,"translate":216},[377],[212,34033,34035,34114],{"className":34034,"translate":216},[215],[212,34036,34038],{"className":34037},[220],[222,34039,34040],{"xmlns":224,"display":386},[226,34041,34042,34111],{},[229,34043,34044,34054,34056,34058,34060,34062,34064,34066,34069,34071,34073,34076,34078,34080,34082,34085,34087,34089,34091,34093,34095,34097,34099,34101,34103,34105,34107,34109],{},[392,34045,34046,34048],{},[232,34047,396],{},[229,34049,34050,34052],{},[232,34051,23943],{},[232,34053,25937],{},[307,34055,310],{"stretchy":309},[232,34057,403],{},[232,34059,407],{"mathvariant":406},[232,34061,410],{},[307,34063,317],{"stretchy":309},[307,34065,320],{},[232,34067,34068],{},"I",[307,34070,310],{"stretchy":309},[232,34072,33803],{},[307,34074,34075],{"separator":243},";",[232,34077,795],{},[307,34079,317],{"stretchy":309},[307,34081,320],{},[232,34083,34084],{},"H",[307,34086,310],{"stretchy":309},[232,34088,795],{},[307,34090,317],{"stretchy":309},[307,34092,5011],{},[232,34094,34084],{},[307,34096,310],{"stretchy":309},[232,34098,795],{},[1495,34100,1497],{},[232,34102,5006],{"mathvariant":406},[1495,34104,1497],{},[232,34106,33803],{},[307,34108,317],{"stretchy":309},[232,34110,4573],{"mathvariant":406},[236,34112,34113],{"encoding":238},"D_{JS}(P\\|Q)=I(Z;X)=H(X)-H(X\\,|\\,Z).",[212,34115,34117,34193,34229,34257],{"className":34116,"ariaHidden":243},[242],[212,34118,34120,34123,34169,34172,34175,34178,34181,34184,34187,34190],{"className":34119},[247],[212,34121],{"className":34122,"style":336},[251],[212,34124,34126,34129],{"className":34125},[256],[212,34127,396],{"className":34128,"style":474},[256,257],[212,34130,34132],{"className":34131},[478],[212,34133,34135,34161],{"className":34134},[482,483],[212,34136,34138,34158],{"className":34137},[487],[212,34139,34141],{"className":34140,"style":576},[491],[212,34142,34143,34146],{"style":495},[212,34144],{"className":34145,"style":500},[499],[212,34147,34149],{"className":34148},[504,505,506,507],[212,34150,34152,34155],{"className":34151},[256,507],[212,34153,23943],{"className":34154,"style":24353},[256,257,507],[212,34156,25937],{"className":34157,"style":26061},[256,257,507],[212,34159,515],{"className":34160},[514],[212,34162,34164],{"className":34163},[487],[212,34165,34167],{"className":34166,"style":8166},[491],[212,34168],{},[212,34170,310],{"className":34171},[343],[212,34173,403],{"className":34174,"style":531},[256,257],[212,34176,407],{"className":34177},[256],[212,34179,410],{"className":34180},[256,257],[212,34182,317],{"className":34183},[350],[212,34185],{"className":34186,"style":355},[354],[212,34188,320],{"className":34189},[359],[212,34191],{"className":34192,"style":355},[354],[212,34194,34196,34199,34202,34205,34208,34211,34214,34217,34220,34223,34226],{"className":34195},[247],[212,34197],{"className":34198,"style":336},[251],[212,34200,34068],{"className":34201,"style":9085},[256,257],[212,34203,310],{"className":34204},[343],[212,34206,33803],{"className":34207,"style":10982},[256,257],[212,34209,34075],{"className":34210},[770],[212,34212],{"className":34213,"style":603},[354],[212,34215,795],{"className":34216,"style":9085},[256,257],[212,34218,317],{"className":34219},[350],[212,34221],{"className":34222,"style":355},[354],[212,34224,320],{"className":34225},[359],[212,34227],{"className":34228,"style":355},[354],[212,34230,34232,34235,34239,34242,34245,34248,34251,34254],{"className":34231},[247],[212,34233],{"className":34234,"style":336},[251],[212,34236,34084],{"className":34237,"style":34238},[256,257],"margin-right:0.0813em;",[212,34240,310],{"className":34241},[343],[212,34243,795],{"className":34244,"style":9085},[256,257],[212,34246,317],{"className":34247},[350],[212,34249],{"className":34250,"style":2785},[354],[212,34252,5011],{"className":34253},[2789],[212,34255],{"className":34256,"style":2785},[354],[212,34258,34260,34263,34266,34269,34272,34275,34278,34281,34284,34287],{"className":34259},[247],[212,34261],{"className":34262,"style":336},[251],[212,34264,34084],{"className":34265,"style":34238},[256,257],[212,34267,310],{"className":34268},[343],[212,34270,795],{"className":34271,"style":9085},[256,257],[212,34273],{"className":34274,"style":603},[354],[212,34276,5006],{"className":34277},[256],[212,34279],{"className":34280,"style":603},[354],[212,34282,33803],{"className":34283,"style":10982},[256,257],[212,34285,317],{"className":34286},[350],[212,34288,4573],{"className":34289},[256],[11,34291,34292,34293,34321,34322,34354,34355,34483,34484,34525,34526,34664,34665,34706],{},"由于 ",[212,34294,34296,34309],{"className":34295,"translate":216},[215],[212,34297,34299],{"className":34298},[220],[222,34300,34301],{"xmlns":224},[226,34302,34303,34307],{},[229,34304,34305],{},[232,34306,33803],{},[236,34308,33803],{"encoding":238},[212,34310,34312],{"className":34311,"ariaHidden":243},[242],[212,34313,34315,34318],{"className":34314},[247],[212,34316],{"className":34317,"style":861},[251],[212,34319,33803],{"className":34320,"style":10982},[256,257]," 是概率 ",[212,34323,34325,34342],{"className":34324,"translate":216},[215],[212,34326,34328],{"className":34327},[220],[222,34329,34330],{"xmlns":224},[226,34331,34332,34340],{},[229,34333,34334,34336,34338],{},[312,34335,314],{},[232,34337,1138],{"mathvariant":406},[312,34339,2661],{},[236,34341,33839],{"encoding":238},[212,34343,34345],{"className":34344,"ariaHidden":243},[242],[212,34346,34348,34351],{"className":34347},[247],[212,34349],{"className":34350,"style":336},[251],[212,34352,33839],{"className":34353},[256]," 的伯努利变量，",[212,34356,34358,34400],{"className":34357,"translate":216},[215],[212,34359,34361],{"className":34360},[220],[222,34362,34363],{"xmlns":224},[226,34364,34365,34397],{},[229,34366,34367,34369,34371,34373,34375,34377,34379,34381,34383,34385,34387,34389,34391,34393,34395],{},[232,34368,34068],{},[307,34370,310],{"stretchy":309},[232,34372,33803],{},[307,34374,34075],{"separator":243},[232,34376,795],{},[307,34378,317],{"stretchy":309},[307,34380,10150],{},[232,34382,34084],{},[307,34384,310],{"stretchy":309},[232,34386,33803],{},[307,34388,317],{"stretchy":309},[307,34390,320],{},[232,34392,4298],{},[307,34394,4301],{},[312,34396,2661],{},[236,34398,34399],{"encoding":238},"I(Z;X)\\le H(Z)=\\log 2",[212,34401,34403,34439,34466],{"className":34402,"ariaHidden":243},[242],[212,34404,34406,34409,34412,34415,34418,34421,34424,34427,34430,34433,34436],{"className":34405},[247],[212,34407],{"className":34408,"style":336},[251],[212,34410,34068],{"className":34411,"style":9085},[256,257],[212,34413,310],{"className":34414},[343],[212,34416,33803],{"className":34417,"style":10982},[256,257],[212,34419,34075],{"className":34420},[770],[212,34422],{"className":34423,"style":603},[354],[212,34425,795],{"className":34426,"style":9085},[256,257],[212,34428,317],{"className":34429},[350],[212,34431],{"className":34432,"style":355},[354],[212,34434,10150],{"className":34435},[359],[212,34437],{"className":34438,"style":355},[354],[212,34440,34442,34445,34448,34451,34454,34457,34460,34463],{"className":34441},[247],[212,34443],{"className":34444,"style":336},[251],[212,34446,34084],{"className":34447,"style":34238},[256,257],[212,34449,310],{"className":34450},[343],[212,34452,33803],{"className":34453,"style":10982},[256,257],[212,34455,317],{"className":34456},[350],[212,34458],{"className":34459,"style":355},[354],[212,34461,320],{"className":34462},[359],[212,34464],{"className":34465,"style":355},[354],[212,34467,34469,34472,34477,34480],{"className":34468},[247],[212,34470],{"className":34471,"style":252},[251],[212,34473,4352,34475],{"className":34474},[1682],[212,34476,4356],{"style":4355},[212,34478],{"className":34479,"style":603},[354],[212,34481,2661],{"className":34482},[256],"，有界性由此而来，",[212,34485,34487,34505],{"className":34486,"translate":216},[215],[212,34488,34490],{"className":34489},[220],[222,34491,34492],{"xmlns":224},[226,34493,34494,34502],{},[229,34495,34496,34498,34500],{},[232,34497,4298],{},[307,34499,4301],{},[312,34501,2661],{},[236,34503,34504],{"encoding":238},"\\log 2",[212,34506,34508],{"className":34507,"ariaHidden":243},[242],[212,34509,34511,34514,34519,34522],{"className":34510},[247],[212,34512],{"className":34513,"style":252},[251],[212,34515,4352,34517],{"className":34516},[1682],[212,34518,4356],{"style":4355},[212,34520],{"className":34521,"style":603},[354],[212,34523,2661],{"className":34524},[256]," 恰好对应「最多只能获得 1 比特」这一直觉。JS 对称、有界且 ",[212,34527,34529,34554],{"className":34528,"translate":216},[215],[212,34530,34532],{"className":34531},[220],[222,34533,34534],{"xmlns":224},[226,34535,34536,34551],{},[229,34537,34538],{},[34539,34540,34541],"msqrt",{},[392,34542,34543,34545],{},[232,34544,396],{},[229,34546,34547,34549],{},[232,34548,23943],{},[232,34550,25937],{},[236,34552,34553],{"encoding":238},"\\sqrt{D_{JS}}",[212,34555,34557],{"className":34556,"ariaHidden":243},[242],[212,34558,34560,34564],{"className":34559},[247],[212,34561],{"className":34562,"style":34563},[251],"height:1.04em;vertical-align:-0.1883em;",[212,34565,34568],{"className":34566},[256,34567],"sqrt",[212,34569,34571,34655],{"className":34570},[482,483],[212,34572,34574,34652],{"className":34573},[487],[212,34575,34578,34634],{"className":34576,"style":34577},[491],"height:0.8517em;",[212,34579,34581,34584],{"className":34580,"style":12063},[6505],[212,34582],{"className":34583,"style":658},[499],[212,34585,34588],{"className":34586,"style":34587},[256],"padding-left:0.833em;",[212,34589,34591,34594],{"className":34590},[256],[212,34592,396],{"className":34593,"style":474},[256,257],[212,34595,34597],{"className":34596},[478],[212,34598,34600,34626],{"className":34599},[482,483],[212,34601,34603,34623],{"className":34602},[487],[212,34604,34606],{"className":34605,"style":576},[491],[212,34607,34608,34611],{"style":495},[212,34609],{"className":34610,"style":500},[499],[212,34612,34614],{"className":34613},[504,505,506,507],[212,34615,34617,34620],{"className":34616},[256,507],[212,34618,23943],{"className":34619,"style":24353},[256,257,507],[212,34621,25937],{"className":34622,"style":26061},[256,257,507],[212,34624,515],{"className":34625},[514],[212,34627,34629],{"className":34628},[487],[212,34630,34632],{"className":34631,"style":8166},[491],[212,34633],{},[212,34635,34637,34640],{"style":34636},"top:-2.8117em;",[212,34638],{"className":34639,"style":658},[499],[212,34641,34645],{"className":34642,"style":34644},[34643],"hide-tail","min-width:0.853em;height:1.08em;",[6521,34646,34649],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},"1.08em","0 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",[212,35593,35595,35668],{"className":35594,"translate":216},[215],[212,35596,35598],{"className":35597},[220],[222,35599,35600],{"xmlns":224},[226,35601,35602,35665],{},[229,35603,35604,35614,35616,35618,35620,35622,35624,35626,35643,35645,35647,35649,35651,35653,35655,35657,35659,35661,35663],{},[392,35605,35606,35608],{},[232,35607,396],{},[229,35609,35610,35612],{},[232,35611,5590],{},[232,35613,35050],{},[307,35615,310],{"stretchy":309},[232,35617,403],{},[307,35619,748],{"separator":243},[232,35621,410],{},[307,35623,317],{"stretchy":309},[307,35625,320],{},[392,35627,35628,35635],{},[229,35629,35630,35633],{},[232,35631,35632],{},"sup",[307,35634,4301],{},[229,35636,35637,35639,35641],{},[232,35638,800],{},[307,35640,6107],{},[232,35642,800],{"mathvariant":794},[232,35644,5006],{"mathvariant":406},[232,35646,403],{},[307,35648,310],{"stretchy":309},[232,35650,800],{},[307,35652,317],{"stretchy":309},[307,35654,5011],{},[232,35656,410],{},[307,35658,310],{"stretchy":309},[232,35660,800],{},[307,35662,317],{"stretchy":309},[232,35664,5006],{"mathvariant":406},[236,35666,35667],{"encoding":238},"D_{TV}(P,Q)=\\sup_{A\\in\\mathcal A}|P(A)-Q(A)|",[212,35669,35671,35750,35836],{"className":35670,"ariaHidden":243},[242],[212,35672,35674,35677,35723,35726,35729,35732,35735,35738,35741,35744,35747],{"className":35673},[247],[212,35675],{"className":35676,"style":336},[251],[212,35678,35680,35683],{"className":35679},[256],[212,35681,396],{"className":35682,"style":474},[256,257],[212,35684,35686],{"className":35685},[478],[212,35687,35689,35715],{"className":35688},[482,483],[212,35690,35692,35712],{"className":35691},[487],[212,35693,35695],{"className":35694,"style":576},[491],[212,35696,35697,35700],{"style":495},[212,35698],{"className":35699,"style":500},[499],[212,35701,35703],{"className":35702},[504,505,506,507],[212,35704,35706,35709],{"className":35705},[256,507],[212,35707,5590],{"className":35708,"style":531},[256,257,507],[212,35710,35050],{"className":35711,"style":2785},[256,257,507],[212,35713,515],{"className":35714},[514],[212,35716,35718],{"className":35717},[487],[212,35719,35721],{"className":35720,"style":8166},[491],[212,35722],{},[212,35724,310],{"className":35725},[343],[212,35727,403],{"className":35728,"style":531},[256,257],[212,35730,748],{"className":35731},[770],[212,35733],{"className":35734,"style":603},[354],[212,35736,410],{"className":35737},[256,257],[212,35739,317],{"className":35740},[350],[212,35742],{"className":35743,"style":355},[354],[212,35745,320],{"className":35746},[359],[212,35748],{"className":35749,"style":355},[354],[212,35751,35753,35757,35809,35812,35815,35818,35821,35824,35827,35830,35833],{"className":35752},[247],[212,35754],{"className":35755,"style":35756},[251],"height:1.0215em;vertical-align:-0.2715em;",[212,35758,35760,35763],{"className":35759},[1682],[212,35761,35632],{"className":35762},[1682],[212,35764,35766],{"className":35765},[478],[212,35767,35769,35800],{"className":35768},[482,483],[212,35770,35772,35797],{"className":35771},[487],[212,35773,35776],{"className":35774,"style":35775},[491],"height:0.2342em;",[212,35777,35779,35782],{"style":35778},"top:-2.4559em;margin-right:0.05em;",[212,35780],{"className":35781,"style":500},[499],[212,35783,35785],{"className":35784},[504,505,506,507],[212,35786,35788,35791,35794],{"className":35787},[256,507],[212,35789,800],{"className":35790},[256,257,507],[212,35792,6107],{"className":35793},[359,507],[212,35795,800],{"className":35796},[256,821,507],[212,35798,515],{"className":35799},[514],[212,35801,35803],{"className":35802},[487],[212,35804,35807],{"className":35805,"style":35806},[491],"height:0.2715em;",[212,35808],{},[212,35810],{"className":35811,"style":603},[354],[212,35813,5006],{"className":35814},[256],[212,35816,403],{"className":35817,"style":531},[256,257],[212,35819,310],{"className":35820},[343],[212,35822,800],{"className":35823},[256,257],[212,35825,317],{"className":35826},[350],[212,35828],{"className":35829,"style":2785},[354],[212,35831,5011],{"className":35832},[2789],[212,35834],{"className":35835,"style":2785},[354],[212,35837,35839,35842,35845,35848,35851,35854],{"className":35838},[247],[212,35840],{"className":35841,"style":336},[251],[212,35843,410],{"className":35844},[256,257],[212,35846,310],{"className":35847},[343],[212,35849,800],{"className":35850},[256,257],[212,35852,317],{"className":35853},[350],[212,35855,5006],{"className":35856},[256],"；两个表达式相等（这是全变差的对偶刻画）。注意 ",[212,35859,35861,35895],{"className":35860,"translate":216},[215],[212,35862,35864],{"className":35863},[220],[222,35865,35866],{"xmlns":224},[226,35867,35868,35892],{},[229,35869,35870,35880,35882,35884,35886,35888,35890],{},[392,35871,35872,35874],{},[232,35873,396],{},[229,35875,35876,35878],{},[232,35877,5590],{},[232,35879,35050],{},[307,35881,6107],{},[307,35883,427],{"stretchy":309},[312,35885,323],{},[307,35887,748],{"separator":243},[312,35889,314],{},[307,35891,454],{"stretchy":309},[236,35893,35894],{"encoding":238},"D_{TV}\\in[0,1]",[212,35896,35898,35959],{"className":35897,"ariaHidden":243},[242],[212,35899,35901,35904,35950,35953,35956],{"className":35900},[247],[212,35902],{"className":35903,"style":16161},[251],[212,35905,35907,35910],{"className":35906},[256],[212,35908,396],{"className":35909,"style":474},[256,257],[212,35911,35913],{"className":35912},[478],[212,35914,35916,35942],{"className":35915},[482,483],[212,35917,35919,35939],{"className":35918},[487],[212,35920,35922],{"className":35921,"style":576},[491],[212,35923,35924,35927],{"style":495},[212,35925],{"className":35926,"style":500},[499],[212,35928,35930],{"className":35929},[504,505,506,507],[212,35931,35933,35936],{"className":35932},[256,507],[212,35934,5590],{"className":35935,"style":531},[256,257,507],[212,35937,35050],{"className":35938,"style":2785},[256,257,507],[212,35940,515],{"className":35941},[514],[212,35943,35945],{"className":35944},[487],[212,35946,35948],{"className":35947,"style":8166},[491],[212,35949],{},[212,35951],{"className":35952,"style":355},[354],[212,35954,6107],{"className":35955},[359],[212,35957],{"className":35958,"style":355},[354],[212,35960,35962,35965,35968,35971,35974,35977,35980],{"className":35961},[247],[212,35963],{"className":35964,"style":336},[251],[212,35966,427],{"className":35967},[343],[212,35969,323],{"className":35970},[256],[212,35972,748],{"className":35973},[770],[212,35975],{"className":35976,"style":603},[354],[212,35978,314],{"className":35979},[256],[212,35981,454],{"className":35982},[350],"，总有界。",[11,35985,35986,9598,35989,36375],{},[1194,35987,35988],{},"斜共轭",[212,35990,35992,36056],{"className":35991,"translate":216},[215],[212,35993,35995],{"className":35994},[220],[222,35996,35997],{"xmlns":224},[226,35998,35999,36053],{},[229,36000,36001,36003,36005,36011,36013,36019,36021,36023,36025,36027,36033,36035,36037,36039,36041,36043,36045,36047,36049,36051],{},[232,36002,966],{},[307,36004,3497],{},[435,36006,36007,36009],{},[312,36008,314],{},[312,36010,2661],{},[232,36012,5006],{"mathvariant":406},[435,36014,36015,36017],{},[312,36016,314],{},[232,36018,966],{},[307,36020,5011],{},[312,36022,314],{},[232,36024,5006],{"mathvariant":406},[307,36026,320],{},[435,36028,36029,36031],{},[312,36030,314],{},[312,36032,2661],{},[232,36034,5006],{"mathvariant":406},[312,36036,314],{},[307,36038,5011],{},[232,36040,966],{},[232,36042,5006],{"mathvariant":406},[307,36044,320],{},[232,36046,234],{},[307,36048,310],{"stretchy":309},[232,36050,966],{},[307,36052,317],{"stretchy":309},[236,36054,36055],{"encoding":238},"t\\cdot\\frac12|\\frac1t-1|=\\frac12|1-t|=f(t)",[212,36057,36059,36077,36231,36249,36336,36357],{"className":36058,"ariaHidden":243},[242],[212,36060,36062,36065,36068,36071,36074],{"className":36061},[247],[212,36063],{"className":36064,"style":5541},[251],[212,36066,966],{"className":36067},[256,257],[212,36069],{"className":36070,"style":2785},[354],[212,36072,3497],{"className":36073},[2789],[212,36075],{"className":36076,"style":2785},[354],[212,36078,36080,36083,36151,36154,36222,36225,36228],{"className":36079},[247],[212,36081],{"className":36082,"style":2703},[251],[212,36084,36086,36089,36148],{"className":36085},[256],[212,36087],{"className":36088},[343,638],[212,36090,36092],{"className":36091},[435],[212,36093,36095,36140],{"className":36094},[482,483],[212,36096,36098,36137],{"className":36097},[487],[212,36099,36101,36115,36123],{"className":36100,"style":2722},[491],[212,36102,36103,36106],{"style":2725},[212,36104],{"className":36105,"style":658},[499],[212,36107,36109],{"className":36108},[504,505,506,507],[212,36110,36112],{"className":36111},[256,507],[212,36113,2661],{"className":36114},[256,507],[212,36116,36117,36120],{"style":670},[212,36118],{"className":36119,"style":658},[499],[212,36121],{"className":36122,"style":678},[677],[212,36124,36125,36128],{"style":2748},[212,36126],{"className":36127,"style":658},[499],[212,36129,36131],{"className":36130},[504,505,506,507],[212,36132,36134],{"className":36133},[256,507],[212,36135,314],{"className":36136},[256,507],[212,36138,515],{"className":36139},[514],[212,36141,36143],{"className":36142},[487],[212,36144,36146],{"className":36145,"style":2770},[491],[212,36147],{},[212,36149],{"className":36150},[350,638],[212,36152,5006],{"className":36153},[256],[212,36155,36157,36160,36219],{"className":36156},[256],[212,36158],{"className":36159},[343,638],[212,36161,36163],{"className":36162},[435],[212,36164,36166,36211],{"className":36165},[482,483],[212,36167,36169,36208],{"className":36168},[487],[212,36170,36172,36186,36194],{"className":36171,"style":2722},[491],[212,36173,36174,36177],{"style":2725},[212,36175],{"className":36176,"style":658},[499],[212,36178,36180],{"className":36179},[504,505,506,507],[212,36181,36183],{"className":36182},[256,507],[212,36184,966],{"className":36185},[256,257,507],[212,36187,36188,36191],{"style":670},[212,36189],{"className":36190,"style":658},[499],[212,36192],{"className":36193,"style":678},[677],[212,36195,36196,36199],{"style":2748},[212,36197],{"className":36198,"style":658},[499],[212,36200,36202],{"className":36201},[504,505,506,507],[212,36203,36205],{"className":36204},[256,507],[212,36206,314],{"className":36207},[256,507],[212,36209,515],{"className":36210},[514],[212,36212,36214],{"className":36213},[487],[212,36215,36217],{"className":36216,"style":2770},[491],[212,36218],{},[212,36220],{"className":36221},[350,638],[212,36223],{"className":36224,"style":2785},[354],[212,36226,5011],{"className":36227},[2789],[212,36229],{"className":36230,"style":2785},[354],[212,36232,36234,36237,36240,36243,36246],{"className":36233},[247],[212,36235],{"className":36236,"style":336},[251],[212,36238,34879],{"className":36239},[256],[212,36241],{"className":36242,"style":355},[354],[212,36244,320],{"className":36245},[359],[212,36247],{"className":36248,"style":355},[354],[212,36250,36252,36255,36323,36327,36330,36333],{"className":36251},[247],[212,36253],{"className":36254,"style":2703},[251],[212,36256,36258,36261,36320],{"className":36257},[256],[212,36259],{"className":36260},[343,638],[212,36262,36264],{"className":36263},[435],[212,36265,36267,36312],{"className":36266},[482,483],[212,36268,36270,36309],{"className":36269},[487],[212,36271,36273,36287,36295],{"className":36272,"style":2722},[491],[212,36274,36275,36278],{"style":2725},[212,36276],{"className":36277,"style":658},[499],[212,36279,36281],{"className":36280},[504,505,506,507],[212,36282,36284],{"className":36283},[256,507],[212,36285,2661],{"className":36286},[256,507],[212,36288,36289,36292],{"style":670},[212,36290],{"className":36291,"style":658},[499],[212,36293],{"className":36294,"style":678},[677],[212,36296,36297,36300],{"style":2748},[212,36298],{"className":36299,"style":658},[499],[212,36301,36303],{"className":36302},[504,505,506,507],[212,36304,36306],{"className":36305},[256,507],[212,36307,314],{"className":36308},[256,507],[212,36310,515],{"className":36311},[514],[212,36313,36315],{"className":36314},[487],[212,36316,36318],{"className":36317,"style":2770},[491],[212,36319],{},[212,36321],{"className":36322},[350,638],[212,36324,36326],{"className":36325},[256],"∣1",[212,36328],{"className":36329,"style":2785},[354],[212,36331,5011],{"className":36332},[2789],[212,36334],{"className":36335,"style":2785},[354],[212,36337,36339,36342,36345,36348,36351,36354],{"className":36338},[247],[212,36340],{"className":36341,"style":336},[251],[212,36343,966],{"className":36344},[256,257],[212,36346,5006],{"className":36347},[256],[212,36349],{"className":36350,"style":355},[354],[212,36352,320],{"className":36353},[359],[212,36355],{"className":36356,"style":355},[354],[212,36358,36360,36363,36366,36369,36372],{"className":36359},[247],[212,36361],{"className":36362,"style":336},[251],[212,36364,234],{"className":36365,"style":258},[256,257],[212,36367,310],{"className":36368},[343],[212,36370,966],{"className":36371},[256,257],[212,36373,317],{"className":36374},[350],"，所以 TV 是对称的。",[11,36377,36378,36380,36381,36384],{},[1194,36379,24393],{}," 全变差是概率测度空间上真正的",[1194,36382,36383],{},"度量","（对称、满足三角不等式），它等于两个分布在一件事上能给出的最大概率差：",[212,36386,36388],{"className":36387,"translate":216},[377],[212,36389,36391,36465],{"className":36390,"translate":216},[215],[212,36392,36394],{"className":36393},[220],[222,36395,36396],{"xmlns":224,"display":386},[226,36397,36398,36462],{},[229,36399,36400,36410,36412,36414,36416,36418,36420,36422,36438,36440,36442,36444,36446,36448,36450,36452,36454,36456,36458,36460],{},[392,36401,36402,36404],{},[232,36403,396],{},[229,36405,36406,36408],{},[232,36407,5590],{},[232,36409,35050],{},[307,36411,310],{"stretchy":309},[232,36413,403],{},[307,36415,748],{"separator":243},[232,36417,410],{},[307,36419,317],{"stretchy":309},[307,36421,320],{},[6214,36423,36424,36430],{},[229,36425,36426,36428],{},[232,36427,35632],{},[307,36429,4301],{},[229,36431,36432,36434,36436],{},[232,36433,800],{},[307,36435,6107],{},[232,36437,800],{"mathvariant":794},[307,36439,5006],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,36441,403],{},[307,36443,310],{"stretchy":309},[232,36445,800],{},[307,36447,317],{"stretchy":309},[307,36449,5011],{},[232,36451,410],{},[307,36453,310],{"stretchy":309},[232,36455,800],{},[307,36457,317],{"stretchy":309},[307,36459,5006],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,36461,4573],{"mathvariant":406},[236,36463,36464],{"encoding":238},"D_{TV}(P,Q)\n=\\sup_{A\\in\\mathcal A}\\big|P(A)-Q(A)\\big| .",[212,36466,36468,36547,36673],{"className":36467,"ariaHidden":243},[242],[212,36469,36471,36474,36520,36523,36526,36529,36532,36535,36538,36541,36544],{"className":36470},[247],[212,36472],{"className":36473,"style":336},[251],[212,36475,36477,36480],{"className":36476},[256],[212,36478,396],{"className":36479,"style":474},[256,257],[212,36481,36483],{"className":36482},[478],[212,36484,36486,36512],{"className":36485},[482,483],[212,36487,36489,36509],{"className":36488},[487],[212,36490,36492],{"className":36491,"style":576},[491],[212,36493,36494,36497],{"style":495},[212,36495],{"className":36496,"style":500},[499],[212,36498,36500],{"className":36499},[504,505,506,507],[212,36501,36503,36506],{"className":36502},[256,507],[212,36504,5590],{"className":36505,"style":531},[256,257,507],[212,36507,35050],{"className":36508,"style":2785},[256,257,507],[212,36510,515],{"className":36511},[514],[212,36513,36515],{"className":36514},[487],[212,36516,36518],{"className":36517,"style":8166},[491],[212,36519],{},[212,36521,310],{"className":36522},[343],[212,36524,403],{"className":36525,"style":531},[256,257],[212,36527,748],{"className":36528},[770],[212,36530],{"className":36531,"style":603},[354],[212,36533,410],{"className":36534},[256,257],[212,36536,317],{"className":36537},[350],[212,36539],{"className":36540,"style":355},[354],[212,36542,320],{"className":36543},[359],[212,36545],{"className":36546,"style":355},[354],[212,36548,36550,36554,36609,36612,36652,36655,36658,36661,36664,36667,36670],{"className":36549},[247],[212,36551],{"className":36552,"style":36553},[251],"height:1.8161em;vertical-align:-0.9661em;",[212,36555,36557],{"className":36556},[1682,13916],[212,36558,36560,36600],{"className":36559},[482,483],[212,36561,36563,36597],{"className":36562},[487],[212,36564,36566,36587],{"className":36565,"style":2543},[491],[212,36567,36569,36572],{"style":36568},"top:-2.1612em;margin-left:0em;",[212,36570],{"className":36571,"style":658},[499],[212,36573,36575],{"className":36574},[504,505,506,507],[212,36576,36578,36581,36584],{"className":36577},[256,507],[212,36579,800],{"className":36580},[256,257,507],[212,36582,6107],{"className":36583},[359,507],[212,36585,800],{"className":36586},[256,821,507],[212,36588,36589,36592],{"style":12063},[212,36590],{"className":36591,"style":658},[499],[212,36593,36594],{},[212,36595,35632],{"className":36596},[1682],[212,36598,515],{"className":36599},[514],[212,36601,36603],{"className":36602},[487],[212,36604,36607],{"className":36605,"style":36606},[491],"height:0.9661em;",[212,36608],{},[212,36610],{"className":36611,"style":603},[354],[212,36613,36615],{"className":36614},[256],[212,36616,36618],{"className":36617},[616,15029],[212,36619,36621,36644],{"className":36620},[482,483],[212,36622,36624,36641],{"className":36623},[487],[212,36625,36627],{"className":36626,"style":15039},[491],[212,36628,36629,36632],{"style":15042},[212,36630],{"className":36631,"style":15046},[499],[212,36633,36635],{"style":36634},"width:0.333em;height:1.2em;",[6521,36636,36638],{"xmlns":6523,"width":35251,"height":9648,"viewBox":36637},"0 0 333 1200",[6529,36639],{"d":36640},"M145 15 v585 v0 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v0 v585 h43z",[212,36642,515],{"className":36643},[514],[212,36645,36647],{"className":36646},[487],[212,36648,36650],{"className":36649,"style":15066},[491],[212,36651],{},[212,36653,403],{"className":36654,"style":531},[256,257],[212,36656,310],{"className":36657},[343],[212,36659,800],{"className":36660},[256,257],[212,36662,317],{"className":36663},[350],[212,36665],{"className":36666,"style":2785},[354],[212,36668,5011],{"className":36669},[2789],[212,36671],{"className":36672,"style":2785},[354],[212,36674,36676,36679,36682,36685,36688,36691,36728],{"className":36675},[247],[212,36677],{"className":36678,"style":20763},[251],[212,36680,410],{"className":36681},[256,257],[212,36683,310],{"className":36684},[343],[212,36686,800],{"className":36687},[256,257],[212,36689,317],{"className":36690},[350],[212,36692,36694],{"className":36693},[256],[212,36695,36697],{"className":36696},[616,15029],[212,36698,36700,36720],{"className":36699},[482,483],[212,36701,36703,36717],{"className":36702},[487],[212,36704,36706],{"className":36705,"style":15039},[491],[212,36707,36708,36711],{"style":15042},[212,36709],{"className":36710,"style":15046},[499],[212,36712,36713],{"style":36634},[6521,36714,36715],{"xmlns":6523,"width":35251,"height":9648,"viewBox":36637},[6529,36716],{"d":36640},[212,36718,515],{"className":36719},[514],[212,36721,36723],{"className":36722},[487],[212,36724,36726],{"className":36725,"style":15066},[491],[212,36727],{},[212,36729,4573],{"className":36730},[256],[11,36732,36733,36734,2607,36762,36790,36791,36985,36986,36989,36990,37042,37043,37345],{},"它还有一个判决论解释：在等先验下用最优检验区分 ",[212,36735,36737,36750],{"className":36736,"translate":216},[215],[212,36738,36740],{"className":36739},[220],[222,36741,36742],{"xmlns":224},[226,36743,36744,36748],{},[229,36745,36746],{},[232,36747,403],{},[236,36749,403],{"encoding":238},[212,36751,36753],{"className":36752,"ariaHidden":243},[242],[212,36754,36756,36759],{"className":36755},[247],[212,36757],{"className":36758,"style":861},[251],[212,36760,403],{"className":36761,"style":531},[256,257],[212,36763,36765,36778],{"className":36764,"translate":216},[215],[212,36766,36768],{"className":36767},[220],[222,36769,36770],{"xmlns":224},[226,36771,36772,36776],{},[229,36773,36774],{},[232,36775,410],{},[236,36777,410],{"encoding":238},[212,36779,36781],{"className":36780,"ariaHidden":243},[242],[212,36782,36784,36787],{"className":36783},[247],[212,36785],{"className":36786,"style":763},[251],[212,36788,410],{"className":36789},[256,257]," 时，最小平均错误率为 ",[212,36792,36794,36832],{"className":36793,"translate":216},[215],[212,36795,36797],{"className":36796},[220],[222,36798,36799],{"xmlns":224},[226,36800,36801,36829],{},[229,36802,36803,36811,36813,36815,36817,36827],{},[1453,36804,36805],{"scriptlevel":323,"displaystyle":309},[435,36806,36807,36809],{},[312,36808,314],{},[312,36810,2661],{},[307,36812,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[312,36814,314],{},[307,36816,5011],{},[392,36818,36819,36821],{},[232,36820,396],{},[229,36822,36823,36825],{},[232,36824,5590],{},[232,36826,35050],{},[307,36828,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[236,36830,36831],{"encoding":238},"\\tfrac12\\big(1-D_{TV}\\big)",[212,36833,36835,36927],{"className":36834,"ariaHidden":243},[242],[212,36836,36838,36841,36909,36915,36918,36921,36924],{"className":36837},[247],[212,36839],{"className":36840,"style":20763},[251],[212,36842,36844,36847,36906],{"className":36843},[256],[212,36845],{"className":36846},[343,638],[212,36848,36850],{"className":36849},[435],[212,36851,36853,36898],{"className":36852},[482,483],[212,36854,36856,36895],{"className":36855},[487],[212,36857,36859,36873,36881],{"className":36858,"style":2722},[491],[212,36860,36861,36864],{"style":2725},[212,36862],{"className":36863,"style":658},[499],[212,36865,36867],{"className":36866},[504,505,506,507],[212,36868,36870],{"className":36869},[256,507],[212,36871,2661],{"className":36872},[256,507],[212,36874,36875,36878],{"style":670},[212,36876],{"className":36877,"style":658},[499],[212,36879],{"className":36880,"style":678},[677],[212,36882,36883,36886],{"style":2748},[212,36884],{"className":36885,"style":658},[499],[212,36887,36889],{"className":36888},[504,505,506,507],[212,36890,36892],{"className":36891},[256,507],[212,36893,314],{"className":36894},[256,507],[212,36896,515],{"className":36897},[514],[212,36899,36901],{"className":36900},[487],[212,36902,36904],{"className":36903,"style":2770},[491],[212,36905],{},[212,36907],{"className":36908},[350,638],[212,36910,36912],{"className":36911},[256],[212,36913,310],{"className":36914},[616,9872],[212,36916,314],{"className":36917},[256],[212,36919],{"className":36920,"style":2785},[354],[212,36922,5011],{"className":36923},[2789],[212,36925],{"className":36926,"style":2785},[354],[212,36928,36930,36933,36979],{"className":36929},[247],[212,36931],{"className":36932,"style":20763},[251],[212,36934,36936,36939],{"className":36935},[256],[212,36937,396],{"className":36938,"style":474},[256,257],[212,36940,36942],{"className":36941},[478],[212,36943,36945,36971],{"className":36944},[482,483],[212,36946,36948,36968],{"className":36947},[487],[212,36949,36951],{"className":36950,"style":576},[491],[212,36952,36953,36956],{"style":495},[212,36954],{"className":36955,"style":500},[499],[212,36957,36959],{"className":36958},[504,505,506,507],[212,36960,36962,36965],{"className":36961},[256,507],[212,36963,5590],{"className":36964,"style":531},[256,257,507],[212,36966,35050],{"className":36967,"style":2785},[256,257,507],[212,36969,515],{"className":36970},[514],[212,36972,36974],{"className":36973},[487],[212,36975,36977],{"className":36976,"style":8166},[491],[212,36978],{},[212,36980,36982],{"className":36981},[256],[212,36983,317],{"className":36984},[616,9872],"，因此 TV 直接度量了",[1194,36987,36988],{},"可分性","，「TV 小」就等于「几乎分不开」。TV 是这里所有 f-散度中最「弱」的标尺（总在 ",[212,36991,36993,37015],{"className":36992,"translate":216},[215],[212,36994,36996],{"className":36995},[220],[222,36997,36998],{"xmlns":224},[226,36999,37000,37012],{},[229,37001,37002,37004,37006,37008,37010],{},[307,37003,427],{"stretchy":309},[312,37005,323],{},[307,37007,748],{"separator":243},[312,37009,314],{},[307,37011,454],{"stretchy":309},[236,37013,37014],{"encoding":238},"[0,1]",[212,37016,37018],{"className":37017,"ariaHidden":243},[242],[212,37019,37021,37024,37027,37030,37033,37036,37039],{"className":37020},[247],[212,37022],{"className":37023,"style":336},[251],[212,37025,427],{"className":37026},[343],[212,37028,323],{"className":37029},[256],[212,37031,748],{"className":37032},[770],[212,37034],{"className":37035,"style":603},[354],[212,37037,314],{"className":37038},[256],[212,37040,454],{"className":37041},[350]," 内），但按 Csiszár 定理它与 KL 诱导同一个拓扑，所以常常已经够用；在一维实直线上它退化为 Kolmogorov 距离 ",[212,37044,37046,37111],{"className":37045,"translate":216},[215],[212,37047,37049],{"className":37048},[220],[222,37050,37051],{"xmlns":224},[226,37052,37053,37108],{},[229,37054,37055,37065,37067,37077,37079,37086,37088,37090,37092,37094,37100,37102,37104,37106],{},[392,37056,37057,37059],{},[232,37058,396],{},[229,37060,37061,37063],{},[232,37062,5590],{},[232,37064,35050],{},[307,37066,320],{},[392,37068,37069,37075],{},[229,37070,37071,37073],{},[232,37072,35632],{},[307,37074,4301],{},[232,37076,971],{},[232,37078,5006],{"mathvariant":406},[392,37080,37081,37084],{},[232,37082,37083],{},"F",[232,37085,403],{},[307,37087,310],{"stretchy":309},[232,37089,971],{},[307,37091,317],{"stretchy":309},[307,37093,5011],{},[392,37095,37096,37098],{},[232,37097,37083],{},[232,37099,410],{},[307,37101,310],{"stretchy":309},[232,37103,971],{},[307,37105,317],{"stretchy":309},[232,37107,5006],{"mathvariant":406},[236,37109,37110],{"encoding":238},"D_{TV}=\\sup_x|F_P(x)-F_Q(x)|",[212,37112,37114,37175,37287],{"className":37113,"ariaHidden":243},[242],[212,37115,37117,37120,37166,37169,37172],{"className":37116},[247],[212,37118],{"className":37119,"style":16161},[251],[212,37121,37123,37126],{"className":37122},[256],[212,37124,396],{"className":37125,"style":474},[256,257],[212,37127,37129],{"className":37128},[478],[212,37130,37132,37158],{"className":37131},[482,483],[212,37133,37135,37155],{"className":37134},[487],[212,37136,37138],{"className":37137,"style":576},[491],[212,37139,37140,37143],{"style":495},[212,37141],{"className":37142,"style":500},[499],[212,37144,37146],{"className":37145},[504,505,506,507],[212,37147,37149,37152],{"className":37148},[256,507],[212,37150,5590],{"className":37151,"style":531},[256,257,507],[212,37153,35050],{"className":37154,"style":2785},[256,257,507],[212,37156,515],{"className":37157},[514],[212,37159,37161],{"className":37160},[487],[212,37162,37164],{"className":37163,"style":8166},[491],[212,37165],{},[212,37167],{"className":37168,"style":355},[354],[212,37170,320],{"className":37171},[359],[212,37173],{"className":37174,"style":355},[354],[212,37176,37178,37181,37223,37226,37229,37269,37272,37275,37278,37281,37284],{"className":37177},[247],[212,37179],{"className":37180,"style":336},[251],[212,37182,37184,37187],{"className":37183},[1682],[212,37185,35632],{"className":37186},[1682],[212,37188,37190],{"className":37189},[478],[212,37191,37193,37214],{"className":37192},[482,483],[212,37194,37196,37211],{"className":37195},[487],[212,37197,37200],{"className":37198,"style":37199},[491],"height:0.0573em;",[212,37201,37202,37205],{"style":35778},[212,37203],{"className":37204,"style":500},[499],[212,37206,37208],{"className":37207},[504,505,506,507],[212,37209,971],{"className":37210},[256,257,507],[212,37212,515],{"className":37213},[514],[212,37215,37217],{"className":37216},[487],[212,37218,37221],{"className":37219,"style":37220},[491],"height:0.2441em;",[212,37222],{},[212,37224],{"className":37225,"style":603},[354],[212,37227,5006],{"className":37228},[256],[212,37230,37232,37235],{"className":37231},[256],[212,37233,37083],{"className":37234,"style":531},[256,257],[212,37236,37238],{"className":37237},[478],[212,37239,37241,37261],{"className":37240},[482,483],[212,37242,37244,37258],{"className":37243},[487],[212,37245,37247],{"className":37246,"style":576},[491],[212,37248,37249,37252],{"style":11336},[212,37250],{"className":37251,"style":500},[499],[212,37253,37255],{"className":37254},[504,505,506,507],[212,37256,403],{"className":37257,"style":531},[256,257,507],[212,37259,515],{"className":37260},[514],[212,37262,37264],{"className":37263},[487],[212,37265,37267],{"className":37266,"style":8166},[491],[212,37268],{},[212,37270,310],{"className":37271},[343],[212,37273,971],{"className":37274},[256,257],[212,37276,317],{"className":37277},[350],[212,37279],{"className":37280,"style":2785},[354],[212,37282,5011],{"className":37283},[2789],[212,37285],{"className":37286,"style":2785},[354],[212,37288,37290,37293,37333,37336,37339,37342],{"className":37289},[247],[212,37291],{"className":37292,"style":467},[251],[212,37294,37296,37299],{"className":37295},[256],[212,37297,37083],{"className":37298,"style":531},[256,257],[212,37300,37302],{"className":37301},[478],[212,37303,37305,37325],{"className":37304},[482,483],[212,37306,37308,37322],{"className":37307},[487],[212,37309,37311],{"className":37310,"style":576},[491],[212,37312,37313,37316],{"style":11336},[212,37314],{"className":37315,"style":500},[499],[212,37317,37319],{"className":37318},[504,505,506,507],[212,37320,410],{"className":37321},[256,257,507],[212,37323,515],{"className":37324},[514],[212,37326,37328],{"className":37327},[487],[212,37329,37331],{"className":37330,"style":522},[491],[212,37332],{},[212,37334,310],{"className":37335},[343],[212,37337,971],{"className":37338},[256,257],[212,37340,317],{"className":37341},[350],[212,37343,5006],{"className":37344},[256],"。马尔可夫链的混合时间、耦合构造与统计距离（total variation distance）都以它为核心。",[2509,37347,37349],{"id":37348},"_34-卡方散度","3.4 卡方散度",[11,37351,21673],{},[212,37353,37355],{"className":37354,"translate":216},[377],[212,37356,37358,37394],{"className":37357,"translate":216},[215],[212,37359,37361],{"className":37360},[220],[222,37362,37363],{"xmlns":224,"display":386},[226,37364,37365,37391],{},[229,37366,37367,37369,37371,37373,37375,37377,37379,37381,37383,37385],{},[232,37368,234],{},[307,37370,310],{"stretchy":309},[232,37372,966],{},[307,37374,317],{"stretchy":309},[307,37376,320],{},[307,37378,310],{"stretchy":309},[232,37380,966],{},[307,37382,5011],{},[312,37384,314],{},[7012,37386,37387,37389],{},[307,37388,317],{"stretchy":309},[312,37390,2661],{},[236,37392,37393],{"encoding":238},"f(t)=(t-1)^2",[212,37395,37397,37424,37445],{"className":37396,"ariaHidden":243},[242],[212,37398,37400,37403,37406,37409,37412,37415,37418,37421],{"className":37399},[247],[212,37401],{"className":37402,"style":336},[251],[212,37404,234],{"className":37405,"style":258},[256,257],[212,37407,310],{"className":37408},[343],[212,37410,966],{"className":37411},[256,257],[212,37413,317],{"className":37414},[350],[212,37416],{"className":37417,"style":355},[354],[212,37419,320],{"className":37420},[359],[212,37422],{"className":37423,"style":355},[354],[212,37425,37427,37430,37433,37436,37439,37442],{"className":37426},[247],[212,37428],{"className":37429,"style":336},[251],[212,37431,310],{"className":37432},[343],[212,37434,966],{"className":37435},[256,257],[212,37437],{"className":37438,"style":2785},[354],[212,37440,5011],{"className":37441},[2789],[212,37443],{"className":37444,"style":2785},[354],[212,37446,37448,37452,37455],{"className":37447},[247],[212,37449],{"className":37450,"style":37451},[251],"height:1.1141em;vertical-align:-0.25em;",[212,37453,314],{"className":37454},[256],[212,37456,37458,37461],{"className":37457},[350],[212,37459,317],{"className":37460},[350],[212,37462,37464],{"className":37463},[478],[212,37465,37467],{"className":37466},[482],[212,37468,37470],{"className":37469},[487],[212,37471,37473],{"className":37472,"style":19935},[491],[212,37474,37475,37478],{"style":8475},[212,37476],{"className":37477,"style":500},[499],[212,37479,37481],{"className":37480},[504,505,506,507],[212,37482,2661],{"className":37483},[256,507],[11,37485,34882,37486,37551],{},[212,37487,37489,37512],{"className":37488,"translate":216},[215],[212,37490,37492],{"className":37491},[220],[222,37493,37494],{"xmlns":224},[226,37495,37496,37510],{},[229,37497,37498,37500,37502,37504,37506,37508],{},[232,37499,234],{},[307,37501,310],{"stretchy":309},[312,37503,314],{},[307,37505,317],{"stretchy":309},[307,37507,320],{},[312,37509,323],{},[236,37511,326],{"encoding":238},[212,37513,37515,37542],{"className":37514,"ariaHidden":243},[242],[212,37516,37518,37521,37524,37527,37530,37533,37536,37539],{"className":37517},[247],[212,37519],{"className":37520,"style":336},[251],[212,37522,234],{"className":37523,"style":258},[256,257],[212,37525,310],{"className":37526},[343],[212,37528,314],{"className":37529},[256],[212,37531,317],{"className":37532},[350],[212,37534],{"className":37535,"style":355},[354],[212,37537,320],{"className":37538},[359],[212,37540],{"className":37541,"style":355},[354],[212,37543,37545,37548],{"className":37544},[247],[212,37546],{"className":37547,"style":369},[251],[212,37549,323],{"className":37550},[256],"、凸，代入：",[212,37553,37555],{"className":37554,"translate":216},[377],[212,37556,37558,37665],{"className":37557,"translate":216},[215],[212,37559,37561],{"className":37560},[220],[222,37562,37563],{"xmlns":224,"display":386},[226,37564,37565,37662],{},[229,37566,37567,37573,37575,37577,37579,37581,37583,37585,37587,37589,37609,37611,37613,37615,37617,37637,37639,37641,37643,37645,37652,37654,37656,37658,37660],{},[392,37568,37569,37571],{},[232,37570,396],{},[232,37572,234],{},[307,37574,310],{"stretchy":309},[232,37576,403],{},[232,37578,407],{"mathvariant":406},[232,37580,410],{},[307,37582,317],{"stretchy":309},[307,37584,320],{},[307,37586,1485],{},[232,37588,1141],{},[7012,37590,37591,37607],{},[229,37592,37593,37595,37601,37603,37605],{},[307,37594,310],{"fence":243},[435,37596,37597,37599],{},[232,37598,11],{},[232,37600,1141],{},[307,37602,5011],{},[312,37604,314],{},[307,37606,317],{"fence":243},[312,37608,2661],{},[232,37610,441],{},[232,37612,971],{},[307,37614,320],{},[307,37616,1485],{},[435,37618,37619,37635],{},[229,37620,37621,37623,37625,37627,37629],{},[307,37622,310],{"stretchy":309},[232,37624,11],{},[307,37626,5011],{},[232,37628,1141],{},[7012,37630,37631,37633],{},[307,37632,317],{"stretchy":309},[312,37634,2661],{},[232,37636,1141],{},[1495,37638,1497],{},[232,37640,441],{},[232,37642,971],{},[307,37644,320],{},[7012,37646,37647,37650],{},[232,37648,37649],{},"χ",[312,37651,2661],{},[307,37653,310],{"stretchy":309},[232,37655,403],{},[232,37657,407],{"mathvariant":406},[232,37659,410],{},[307,37661,317],{"stretchy":309},[236,37663,37664],{"encoding":238},"D_f(P\\|Q)=\\int q\\left(\\frac{p}{q}-1\\right)^2dx\n=\\int \\frac{(p-q)^2}{q}\\,dx\n=\\chi^2(P\\|Q)",[212,37666,37668,37738,37892,38030],{"className":37667,"ariaHidden":243},[242],[212,37669,37671,37674,37714,37717,37720,37723,37726,37729,37732,37735],{"className":37670},[247],[212,37672],{"className":37673,"style":467},[251],[212,37675,37677,37680],{"className":37676},[256],[212,37678,396],{"className":37679,"style":474},[256,257],[212,37681,37683],{"className":37682},[478],[212,37684,37686,37706],{"className":37685},[482,483],[212,37687,37689,37703],{"className":37688},[487],[212,37690,37692],{"className":37691,"style":492},[491],[212,37693,37694,37697],{"style":495},[212,37695],{"className":37696,"style":500},[499],[212,37698,37700],{"className":37699},[504,505,506,507],[212,37701,234],{"className":37702,"style":258},[256,257,507],[212,37704,515],{"className":37705},[514],[212,37707,37709],{"className":37708},[487],[212,37710,37712],{"className":37711,"style":522},[491],[212,37713],{},[212,37715,310],{"className":37716},[343],[212,37718,403],{"className":37719,"style":531},[256,257],[212,37721,407],{"className":37722},[256],[212,37724,410],{"className":37725},[256,257],[212,37727,317],{"className":37728},[350],[212,37730],{"className":37731,"style":355},[354],[212,37733,320],{"className":37734},[359],[212,37736],{"className":37737,"style":355},[354],[212,37739,37741,37745,37748,37751,37754,37757,37874,37877,37880,37883,37886,37889],{"className":37740},[247],[212,37742],{"className":37743,"style":37744},[251],"height:2.604em;vertical-align:-0.95em;",[212,37746,1485],{"className":37747,"style":1685},[1682,1683,1684],[212,37749],{"className":37750,"style":603},[354],[212,37752,1141],{"className":37753,"style":1178},[256,257],[212,37755],{"className":37756,"style":603},[354],[212,37758,37760,37849],{"className":37759},[607],[212,37761,37763,37769,37831,37834,37837,37840,37843],{"className":37762},[607],[212,37764,37766],{"className":37765,"style":612},[343,611],[212,37767,310],{"className":37768},[616,506],[212,37770,37772,37775,37828],{"className":37771},[256],[212,37773],{"className":37774},[343,638],[212,37776,37778],{"className":37777},[435],[212,37779,37781,37820],{"className":37780},[482,483],[212,37782,37784,37817],{"className":37783},[487],[212,37785,37787,37798,37806],{"className":37786,"style":3752},[491],[212,37788,37789,37792],{"style":654},[212,37790],{"className":37791,"style":658},[499],[212,37793,37795],{"className":37794},[256],[212,37796,1141],{"className":37797,"style":1178},[256,257],[212,37799,37800,37803],{"style":670},[212,37801],{"className":37802,"style":658},[499],[212,37804],{"className":37805,"style":678},[677],[212,37807,37808,37811],{"style":681},[212,37809],{"className":37810,"style":658},[499],[212,37812,37814],{"className":37813},[256],[212,37815,11],{"className":37816},[256,257],[212,37818,515],{"className":37819},[514],[212,37821,37823],{"className":37822},[487],[212,37824,37826],{"className":37825,"style":703},[491],[212,37827],{},[212,37829],{"className":37830},[350,638],[212,37832],{"className":37833,"style":2785},[354],[212,37835,5011],{"className":37836},[2789],[212,37838],{"className":37839,"style":2785},[354],[212,37841,314],{"className":37842},[256],[212,37844,37846],{"className":37845,"style":612},[350,611],[212,37847,317],{"className":37848},[616,506],[212,37850,37852],{"className":37851},[478],[212,37853,37855],{"className":37854},[482],[212,37856,37858],{"className":37857},[487],[212,37859,37862],{"className":37860,"style":37861},[491],"height:1.654em;",[212,37863,37865,37868],{"style":37864},"top:-3.9029em;margin-right:0.05em;",[212,37866],{"className":37867,"style":500},[499],[212,37869,37871],{"className":37870},[504,505,506,507],[212,37872,2661],{"className":37873},[256,507],[212,37875],{"className":37876,"style":603},[354],[212,37878,441],{"className":37879},[256,257],[212,37881,971],{"className":37882},[256,257],[212,37884],{"className":37885,"style":355},[354],[212,37887,320],{"className":37888},[359],[212,37890],{"className":37891,"style":355},[354],[212,37893,37895,37899,37902,37905,38012,38015,38018,38021,38024,38027],{"className":37894},[247],[212,37896],{"className":37897,"style":37898},[251],"height:2.3715em;vertical-align:-0.8804em;",[212,37900,1485],{"className":37901,"style":1685},[1682,1683,1684],[212,37903],{"className":37904,"style":603},[354],[212,37906,37908,37911,38009],{"className":37907},[256],[212,37909],{"className":37910},[343,638],[212,37912,37914],{"className":37913},[435],[212,37915,37917,38001],{"className":37916},[482,483],[212,37918,37920,37998],{"className":37919},[487],[212,37921,37924,37935,37943],{"className":37922,"style":37923},[491],"height:1.4911em;",[212,37925,37926,37929],{"style":654},[212,37927],{"className":37928,"style":658},[499],[212,37930,37932],{"className":37931},[256],[212,37933,1141],{"className":37934,"style":1178},[256,257],[212,37936,37937,37940],{"style":670},[212,37938],{"className":37939,"style":658},[499],[212,37941],{"className":37942,"style":678},[677],[212,37944,37945,37948],{"style":681},[212,37946],{"className":37947,"style":658},[499],[212,37949,37951,37954,37957,37960,37963,37966,37969],{"className":37950},[256],[212,37952,310],{"className":37953},[343],[212,37955,11],{"className":37956},[256,257],[212,37958],{"className":37959,"style":2785},[354],[212,37961,5011],{"className":37962},[2789],[212,37964],{"className":37965,"style":2785},[354],[212,37967,1141],{"className":37968,"style":1178},[256,257],[212,37970,37972,37975],{"className":37971},[350],[212,37973,317],{"className":37974},[350],[212,37976,37978],{"className":37977},[478],[212,37979,37981],{"className":37980},[482],[212,37982,37984],{"className":37983},[487],[212,37985,37987],{"className":37986,"style":20228},[491],[212,37988,37989,37992],{"style":7063},[212,37990],{"className":37991,"style":500},[499],[212,37993,37995],{"className":37994},[504,505,506,507],[212,37996,2661],{"className":37997},[256,507],[212,37999,515],{"className":38000},[514],[212,38002,38004],{"className":38003},[487],[212,38005,38007],{"className":38006,"style":703},[491],[212,38008],{},[212,38010],{"className":38011},[350,638],[212,38013],{"className":38014,"style":603},[354],[212,38016,441],{"className":38017},[256,257],[212,38019,971],{"className":38020},[256,257],[212,38022],{"className":38023,"style":355},[354],[212,38025,320],{"className":38026},[359],[212,38028],{"className":38029,"style":355},[354],[212,38031,38033,38036,38065,38068,38071,38074,38077],{"className":38032},[247],[212,38034],{"className":38035,"style":37451},[251],[212,38037,38039,38042],{"className":38038},[256],[212,38040,37649],{"className":38041},[256,257],[212,38043,38045],{"className":38044},[478],[212,38046,38048],{"className":38047},[482],[212,38049,38051],{"className":38050},[487],[212,38052,38054],{"className":38053,"style":19935},[491],[212,38055,38056,38059],{"style":8475},[212,38057],{"className":38058,"style":500},[499],[212,38060,38062],{"className":38061},[504,505,506,507],[212,38063,2661],{"className":38064},[256,507],[212,38066,310],{"className":38067},[343],[212,38069,403],{"className":38070,"style":531},[256,257],[212,38072,407],{"className":38073},[256],[212,38075,410],{"className":38076},[256,257],[212,38078,317],{"className":38079},[350],[11,38081,38082,38083,38086],{},"这是",[1194,38084,38085],{},"皮尔逊（Pearson）卡方散度","。它非对称、无界。其斜共轭是",[212,38088,38090],{"className":38089,"translate":216},[377],[212,38091,38093,38169],{"className":38092,"translate":216},[215],[212,38094,38096],{"className":38095},[220],[222,38097,38098],{"xmlns":224,"display":386},[226,38099,38100,38166],{},[229,38101,38102,38104,38106,38108,38110,38112,38114,38116,38118,38120,38122,38142,38144,38164],{},[232,38103,966],{},[1495,38105,1497],{},[232,38107,234],{},[307,38109,310],{"stretchy":309},[312,38111,314],{},[232,38113,1138],{"mathvariant":406},[232,38115,966],{},[307,38117,317],{"stretchy":309},[307,38119,320],{},[232,38121,966],{},[7012,38123,38124,38140],{},[229,38125,38126,38128,38134,38136,38138],{},[307,38127,310],{"fence":243},[435,38129,38130,38132],{},[312,38131,314],{},[232,38133,966],{},[307,38135,5011],{},[312,38137,314],{},[307,38139,317],{"fence":243},[312,38141,2661],{},[307,38143,320],{},[435,38145,38146,38162],{},[229,38147,38148,38150,38152,38154,38156],{},[307,38149,310],{"stretchy":309},[232,38151,966],{},[307,38153,5011],{},[312,38155,314],{},[7012,38157,38158,38160],{},[307,38159,317],{"stretchy":309},[312,38161,2661],{},[232,38163,966],{},[307,38165,748],{"separator":243},[236,38167,38168],{"encoding":238},"t\\,f(1\u002Ft)=t\\left(\\frac1t-1\\right)^2\n=\\frac{(t-1)^2}{t},",[212,38170,38172,38208,38344],{"className":38171,"ariaHidden":243},[242],[212,38173,38175,38178,38181,38184,38187,38190,38193,38196,38199,38202,38205],{"className":38174},[247],[212,38176],{"className":38177,"style":336},[251],[212,38179,966],{"className":38180},[256,257],[212,38182],{"className":38183,"style":603},[354],[212,38185,234],{"className":38186,"style":258},[256,257],[212,38188,310],{"className":38189},[343],[212,38191,8787],{"className":38192},[256],[212,38194,966],{"className":38195},[256,257],[212,38197,317],{"className":38198},[350],[212,38200],{"className":38201,"style":355},[354],[212,38203,320],{"className":38204},[359],[212,38206],{"className":38207,"style":355},[354],[212,38209,38211,38214,38217,38220,38335,38338,38341],{"className":38210},[247],[212,38212],{"className":38213,"style":37744},[251],[212,38215,966],{"className":38216},[256,257],[212,38218],{"className":38219,"style":603},[354],[212,38221,38223,38312],{"className":38222},[607],[212,38224,38226,38232,38294,38297,38300,38303,38306],{"className":38225},[607],[212,38227,38229],{"className":38228,"style":612},[343,611],[212,38230,310],{"className":38231},[616,506],[212,38233,38235,38238,38291],{"className":38234},[256],[212,38236],{"className":38237},[343,638],[212,38239,38241],{"className":38240},[435],[212,38242,38244,38283],{"className":38243},[482,483],[212,38245,38247,38280],{"className":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展开）有 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q)^2\\approx\\frac14\\chi^2",[212,39200,39202,39271,39361],{"className":39201,"ariaHidden":243},[242],[212,39203,39205,39209,39212,39215,39262,39265,39268],{"className":39204},[247],[212,39206],{"className":39207,"style":39208},[251],"height:1.1419em;vertical-align:-0.3369em;",[212,39210,1485],{"className":39211,"style":5815},[1682,1683,5814],[212,39213,310],{"className":39214},[343],[212,39216,39218],{"className":39217},[256,34567],[212,39219,39221,39253],{"className":39220},[482,483],[212,39222,39224,39250],{"className":39223},[487],[212,39225,39228,39237],{"className":39226,"style":39227},[491],"height:0.7031em;",[212,39229,39231,39234],{"className":39230,"style":12063},[6505],[212,39232],{"className":39233,"style":658},[499],[212,39235,11],{"className":39236,"style":34587},[256,257],[212,39238,39240,39243],{"style":39239},"top:-2.6631em;",[212,39241],{"className":39242,"style":658},[499],[212,39244,39246],{"className":39245,"style":34644},[34643],[6521,39247,39248],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,39249],{"d":34651},[212,39251,515],{"className":39252},[514],[212,39254,39256],{"className":39255},[487],[212,39257,39260],{"className":39258,"style":39259},[491],"height:0.3369em;",[212,39261],{},[212,39263],{"className":39264,"style":2785},[354],[212,39266,5011],{"className":39267},[2789],[212,39269],{"className":39270,"style":2785},[354],[212,39272,39274,39278,39323,39352,39355,39358],{"className":39273},[247],[212,39275],{"className":39276,"style":39277},[251],"height:1.151em;vertical-align:-0.3369em;",[212,39279,39281],{"className":39280},[256,34567],[212,39282,39284,39315],{"className":39283},[482,483],[212,39285,39287,39312],{"className":39286},[487],[212,39288,39290,39300],{"className":39289,"style":39227},[491],[212,39291,39293,39296],{"className":39292,"style":12063},[6505],[212,39294],{"className":39295,"style":658},[499],[212,39297,1141],{"className":39298,"style":39299},[256,257],"margin-right:0.0359em;padding-left:0.833em;",[212,39301,39302,39305],{"style":39239},[212,39303],{"className":39304,"style":658},[499],[212,39306,39308],{"className":39307,"style":34644},[34643],[6521,39309,39310],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,39311],{"d":34651},[212,39313,515],{"className":39314},[514],[212,39316,39318],{"className":39317},[487],[212,39319,39321],{"className":39320,"style":39259},[491],[212,39322],{},[212,39324,39326,39329],{"className":39325},[350],[212,39327,317],{"className":39328},[350],[212,39330,39332],{"className":39331},[478],[212,39333,39335],{"className":39334},[482],[212,39336,39338],{"className":39337},[487],[212,39339,39341],{"className":39340,"style":20228},[491],[212,39342,39343,39346],{"style":7063},[212,39344],{"className":39345,"style":500},[499],[212,39347,39349],{"className":39348},[504,505,506,507],[212,39350,2661],{"className":39351},[256,507],[212,39353],{"className":39354,"style":355},[354],[212,39356,33159],{"className":39357},[359],[212,39359],{"className":39360,"style":355},[354],[212,39362,39364,39367,39435],{"className":39363},[247],[212,39365],{"className":39366,"style":2703},[251],[212,39368,39370,39373,39432],{"className":39369},[256],[212,39371],{"className":39372},[343,638],[212,39374,39376],{"className":39375},[435],[212,39377,39379,39424],{"className":39378},[482,483],[212,39380,39382,39421],{"className":39381},[487],[212,39383,39385,39399,39407],{"className":39384,"style":2722},[491],[212,39386,39387,39390],{"style":2725},[212,39388],{"className":39389,"style":658},[499],[212,39391,39393],{"className":39392},[504,505,506,507],[212,39394,39396],{"className":39395},[256,507],[212,39397,39189],{"className":39398},[256,507],[212,39400,39401,39404],{"style":670},[212,39402],{"className":39403,"style":658},[499],[212,39405],{"className":39406,"style":678},[677],[212,39408,39409,39412],{"style":2748},[212,39410],{"className":39411,"style":658},[499],[212,39413,39415],{"className":39414},[504,505,506,507],[212,39416,39418],{"className":39417},[256,507],[212,39419,314],{"className":39420},[256,507],[212,39422,515],{"className":39423},[514],[212,39425,39427],{"className":39426},[487],[212,39428,39430],{"className":39429,"style":2770},[491],[212,39431],{},[212,39433],{"className":39434},[350,638],[212,39436,39438,39441],{"className":39437},[256],[212,39439,37649],{"className":39440},[256,257],[212,39442,39444],{"className":39443},[478],[212,39445,39447],{"className":39446},[482],[212,39448,39450],{"className":39449},[487],[212,39451,39453],{"className":39452,"style":20228},[491],[212,39454,39455,39458],{"style":7063},[212,39456],{"className":39457,"style":500},[499],[212,39459,39461],{"className":39460},[504,505,506,507],[212,39462,2661],{"className":39463},[256,507],"、Bhattacharyya 约定的 ",[212,39466,39468,39513],{"className":39467,"translate":216},[215],[212,39469,39471],{"className":39470},[220],[222,39472,39473],{"xmlns":224},[226,39474,39475,39510],{},[229,39476,39477,39483,39485,39487,39489,39492,39495,39497,39504],{},[7012,39478,39479,39481],{},[232,39480,34084],{},[312,39482,2661],{},[307,39484,320],{},[312,39486,314],{},[307,39488,5011],{},[232,39490,39491],{},"B",[232,39493,39494],{},"C",[307,39496,33159],{},[435,39498,39499,39501],{},[312,39500,314],{},[312,39502,39503],{},"8",[7012,39505,39506,39508],{},[232,39507,37649],{},[312,39509,2661],{},[236,39511,39512],{"encoding":238},"H^2=1-BC\\approx\\frac18\\chi^2",[212,39514,39516,39560,39578,39600],{"className":39515,"ariaHidden":243},[242],[212,39517,39519,39522,39551,39554,39557],{"className":39518},[247],[212,39520],{"className":39521,"style":20228},[251],[212,39523,39525,39528],{"className":39524},[256],[212,39526,34084],{"className":39527,"style":34238},[256,257],[212,39529,39531],{"className":39530},[478],[212,39532,39534],{"className":39533},[482],[212,39535,39537],{"className":39536},[487],[212,39538,39540],{"className":39539,"style":20228},[491],[212,39541,39542,39545],{"style":7063},[212,39543],{"className":39544,"style":500},[499],[212,39546,39548],{"className":39547},[504,505,506,507],[212,39549,2661],{"className":39550},[256,507],[212,39552],{"className":39553,"style":355},[354],[212,39555,320],{"className":39556},[359],[212,39558],{"className":39559,"style":355},[354],[212,39561,39563,39566,39569,39572,39575],{"className":39562},[247],[212,39564],{"className":39565,"style":12778},[251],[212,39567,314],{"className":39568},[256],[212,39570],{"className":39571,"style":2785},[354],[212,39573,5011],{"className":39574},[2789],[212,39576],{"className":39577,"style":2785},[354],[212,39579,39581,39584,39588,39591,39594,39597],{"className":39580},[247],[212,39582],{"className":39583,"style":861},[251],[212,39585,39491],{"className":39586,"style":39587},[256,257],"margin-right:0.0502em;",[212,39589,39494],{"className":39590,"style":10982},[256,257],[212,39592],{"className":39593,"style":355},[354],[212,39595,33159],{"className":39596},[359],[212,39598],{"className":39599,"style":355},[354],[212,39601,39603,39606,39674],{"className":39602},[247],[212,39604],{"className":39605,"style":2703},[251],[212,39607,39609,39612,39671],{"className":39608},[256],[212,39610],{"className":39611},[343,638],[212,39613,39615],{"className":39614},[435],[212,39616,39618,39663],{"className":39617},[482,483],[212,39619,39621,39660],{"className":39620},[487],[212,39622,39624,39638,39646],{"className":39623,"style":2722},[491],[212,39625,39626,39629],{"style":2725},[212,39627],{"className":39628,"style":658},[499],[212,39630,39632],{"className":39631},[504,505,506,507],[212,39633,39635],{"className":39634},[256,507],[212,39636,39503],{"className":39637},[256,507],[212,39639,39640,39643],{"style":670},[212,39641],{"className":39642,"style":658},[499],[212,39644],{"className":39645,"style":678},[677],[212,39647,39648,39651],{"style":2748},[212,39649],{"className":39650,"style":658},[499],[212,39652,39654],{"className":39653},[504,505,506,507],[212,39655,39657],{"className":39656},[256,507],[212,39658,314],{"className":39659},[256,507],[212,39661,515],{"className":39662},[514],[212,39664,39666],{"className":39665},[487],[212,39667,39669],{"className":39668,"style":2770},[491],[212,39670],{},[212,39672],{"className":39673},[350,638],[212,39675,39677,39680],{"className":39676},[256],[212,39678,37649],{"className":39679},[256,257],[212,39681,39683],{"className":39682},[478],[212,39684,39686],{"className":39685},[482],[212,39687,39689],{"className":39688},[487],[212,39690,39692],{"className":39691,"style":20228},[491],[212,39693,39694,39697],{"style":7063},[212,39695],{"className":39696,"style":500},[499],[212,39698,39700],{"className":39699},[504,505,506,507],[212,39701,2661],{"className":39702},[256,507],"（见 4.6 节的局部展开），因此它是所有 f-散度在局部的「公因子」——只是在 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意义下的「单位」不同。",[11,39787,39788,39790,39791,40123,40124,40152,40153,2943,40181,40265,40266,40294,40295,40323,40324,40352,40353,40381,40382,40410,40411,40414,40415,40573,40574,40634],{},[1194,39789,24393],{}," 卡方散度是 Pearson 拟合优度统计量 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的总体（无限样本）版本：把观测频率看作 ",[212,40125,40127,40140],{"className":40126,"translate":216},[215],[212,40128,40130],{"className":40129},[220],[222,40131,40132],{"xmlns":224},[226,40133,40134,40138],{},[229,40135,40136],{},[232,40137,403],{},[236,40139,403],{"encoding":238},[212,40141,40143],{"className":40142,"ariaHidden":243},[242],[212,40144,40146,40149],{"className":40145},[247],[212,40147],{"className":40148,"style":861},[251],[212,40150,403],{"className":40151,"style":531},[256,257],"、期望频率看作 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就是「",[212,40267,40269,40282],{"className":40268,"translate":216},[215],[212,40270,40272],{"className":40271},[220],[222,40273,40274],{"xmlns":224},[226,40275,40276,40280],{},[229,40277,40278],{},[232,40279,403],{},[236,40281,403],{"encoding":238},[212,40283,40285],{"className":40284,"ariaHidden":243},[242],[212,40286,40288,40291],{"className":40287},[247],[212,40289],{"className":40290,"style":861},[251],[212,40292,403],{"className":40293,"style":531},[256,257]," 是否来自 ",[212,40296,40298,40311],{"className":40297,"translate":216},[215],[212,40299,40301],{"className":40300},[220],[222,40302,40303],{"xmlns":224},[226,40304,40305,40309],{},[229,40306,40307],{},[232,40308,410],{},[236,40310,410],{"encoding":238},[212,40312,40314],{"className":40313,"ariaHidden":243},[242],[212,40315,40317,40320],{"className":40316},[247],[212,40318],{"className":40319,"style":763},[251],[212,40321,410],{"className":40322},[256,257],"」的标准化偏差，因此它是独立性检验、拟合优度检验与特征选择的自然尺度。它的分母 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是二次的，判别器梯度不会像 JS 那样饱和；在鲁棒统计与核方法中，",[212,40575,40577,40595],{"className":40576,"translate":216},[215],[212,40578,40580],{"className":40579},[220],[222,40581,40582],{"xmlns":224},[226,40583,40584,40592],{},[229,40585,40586],{},[7012,40587,40588,40590],{},[232,40589,37649],{},[312,40591,2661],{},[236,40593,40594],{"encoding":238},"\\chi^2",[212,40596,40598],{"className":40597,"ariaHidden":243},[242],[212,40599,40601,40605],{"className":40600},[247],[212,40602],{"className":40603,"style":40604},[251],"height:1.0085em;vertical-align:-0.1944em;",[212,40606,40608,40611],{"className":40607},[256],[212,40609,37649],{"className":40610},[256,257],[212,40612,40614],{"className":40613},[478],[212,40615,40617],{"className":40616},[482],[212,40618,40620],{"className":40619},[487],[212,40621,40623],{"className":40622,"style":20228},[491],[212,40624,40625,40628],{"style":7063},[212,40626],{"className":40627,"style":500},[499],[212,40629,40631],{"className":40630},[504,505,506,507],[212,40632,2661],{"className":40633},[256,507]," 距离还给出了带权核的另一种「局部」相似度。",[2509,40636,40638],{"id":40637},"_35-hellinger-平方","3.5 Hellinger 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凸，代入：",[212,41139,41141],{"className":41140,"translate":216},[377],[212,41142,41144,41234],{"className":41143,"translate":216},[215],[212,41145,41147],{"className":41146},[220],[222,41148,41149],{"xmlns":224,"display":386},[226,41150,41151,41231],{},[229,41152,41153,41159,41161,41163,41165,41167,41169,41171,41173,41175,41197,41199,41201,41203,41205,41207,41211,41213,41217,41223,41225,41227,41229],{},[392,41154,41155,41157],{},[232,41156,396],{},[232,41158,234],{},[307,41160,310],{"stretchy":309},[232,41162,403],{},[232,41164,407],{"mathvariant":406},[232,41166,410],{},[307,41168,317],{"stretchy":309},[307,41170,320],{},[307,41172,1485],{},[232,41174,1141],{},[7012,41176,41177,41195],{},[229,41178,41179,41181,41189,41191,41193],{},[307,41180,310],{"fence":243},[34539,41182,41183],{},[435,41184,41185,41187],{},[232,41186,11],{},[232,41188,1141],{},[307,41190,5011],{},[312,41192,314],{},[307,41194,317],{"fence":243},[312,41196,2661],{},[232,41198,441],{},[232,41200,971],{},[307,41202,320],{},[307,41204,1485],{},[307,41206,310],{"stretchy":309},[34539,41208,41209],{},[232,41210,11],{},[307,41212,5011],{},[34539,41214,41215],{},[232,41216,1141],{},[7012,41218,41219,41221],{},[307,41220,317],{"stretchy":309},[312,41222,2661],{},[1495,41224,1497],{},[232,41226,441],{},[232,41228,971],{},[232,41230,4573],{"mathvariant":406},[236,41232,41233],{"encoding":238},"D_f(P\\|Q)\n=\\int q\\left(\\sqrt{\\frac{p}{q}}-1\\right)^2dx\n=\\int (\\sqrt{p}-\\sqrt{q})^2\\,dx 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Bhattacharyya 系数 ",[212,41681,41683,41727],{"className":41682,"translate":216},[215],[212,41684,41686],{"className":41685},[220],[222,41687,41688],{"xmlns":224},[226,41689,41690,41724],{},[229,41691,41692,41694,41696,41698,41700,41702,41704,41706,41708,41710,41718,41720,41722],{},[232,41693,39491],{},[232,41695,39494],{},[307,41697,310],{"stretchy":309},[232,41699,403],{},[307,41701,748],{"separator":243},[232,41703,410],{},[307,41705,317],{"stretchy":309},[307,41707,320],{},[307,41709,1485],{},[34539,41711,41712],{},[229,41713,41714,41716],{},[232,41715,11],{},[232,41717,1141],{},[1495,41719,1497],{},[232,41721,441],{},[232,41723,971],{},[236,41725,41726],{"encoding":238},"BC(P,Q)=\\int\\sqrt{pq}\\,dx",[212,41728,41730,41769],{"className":41729,"ariaHidden":243},[242],[212,41731,41733,41736,41739,41742,41745,41748,41751,41754,41757,41760,41763,41766],{"className":41732},[247],[212,41734],{"className":41735,"style":336},[251],[212,41737,39491],{"className":41738,"style":39587},[256,257],[212,41740,39494],{"className":41741,"style":10982},[256,257],[212,41743,310],{"className":41744},[343],[212,41746,403],{"className":41747,"style":531},[256,257],[212,41749,748],{"className":41750},[770],[212,41752],{"className":41753,"style":603},[354],[212,41755,410],{"className":41756},[256,257],[212,41758,317],{"className":41759},[350],[212,41761],{"className":41762,"style":355},[354],[212,41764,320],{"className":41765},[359],[212,41767],{"className":41768,"style":355},[354],[212,41770,41772,41775,41778,41781,41829,41832,41835],{"className":41771},[247],[212,41773],{"className":41774,"style":39208},[251],[212,41776,1485],{"className":41777,"style":5815},[1682,1683,5814],[212,41779],{"className":41780,"style":603},[354],[212,41782,41784],{"className":41783},[256,34567],[212,41785,41787,41821],{"className":41786},[482,483],[212,41788,41790,41818],{"className":41789},[487],[212,41791,41793,41806],{"className":41792,"style":39227},[491],[212,41794,41796,41799],{"className":41795,"style":12063},[6505],[212,41797],{"className":41798,"style":658},[499],[212,41800,41802],{"className":41801,"style":34587},[256],[212,41803,41805],{"className":41804,"style":1178},[256,257],"pq",[212,41807,41808,41811],{"style":39239},[212,41809],{"className":41810,"style":658},[499],[212,41812,41814],{"className":41813,"style":34644},[34643],[6521,41815,41816],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,41817],{"d":34651},[212,41819,515],{"className":41820},[514],[212,41822,41824],{"className":41823},[487],[212,41825,41827],{"className":41826,"style":39259},[491],[212,41828],{},[212,41830],{"className":41831,"style":603},[354],[212,41833,441],{"className":41834},[256,257],[212,41836,971],{"className":41837},[256,257],"，则",[212,41840,41842],{"className":41841,"translate":216},[377],[212,41843,41845,41921],{"className":41844,"translate":216},[215],[212,41846,41848],{"className":41847},[220],[222,41849,41850],{"xmlns":224,"display":386},[226,41851,41852,41918],{},[229,41853,41854,41856,41858,41862,41864,41868,41874,41876,41878,41880,41882,41884,41886,41888,41890,41892,41900,41902,41904,41906,41908,41910,41912,41914,41916],{},[307,41855,1485],{},[307,41857,310],{"stretchy":309},[34539,41859,41860],{},[232,41861,11],{},[307,41863,5011],{},[34539,41865,41866],{},[232,41867,1141],{},[7012,41869,41870,41872],{},[307,41871,317],{"stretchy":309},[312,41873,2661],{},[307,41875,320],{},[307,41877,1485],{},[232,41879,11],{},[307,41881,2668],{},[307,41883,1485],{},[232,41885,1141],{},[307,41887,5011],{},[312,41889,2661],{},[307,41891,1485],{},[34539,41893,41894],{},[229,41895,41896,41898],{},[232,41897,11],{},[232,41899,1141],{},[307,41901,320],{},[312,41903,2661],{},[307,41905,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[312,41907,314],{},[307,41909,5011],{},[232,41911,39491],{},[232,41913,39494],{},[307,41915,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,41917,4573],{"mathvariant":406},[236,41919,41920],{"encoding":238},"\\int(\\sqrt p-\\sqrt q)^2\n=\\int p+\\int q-2\\int\\sqrt{pq}\n=2\\big(1-BC\\big).",[212,41922,41924,41989,42077,42101,42125,42199,42226],{"className":41923,"ariaHidden":243},[242],[212,41925,41927,41930,41933,41936,41980,41983,41986],{"className":41926},[247],[212,41928],{"className":41929,"style":5975},[251],[212,41931,1485],{"className":41932,"style":1685},[1682,1683,1684],[212,41934,310],{"className":41935},[343],[212,41937,41939],{"className":41938},[256,34567],[212,41940,41942,41972],{"className":41941},[482,483],[212,41943,41945,41969],{"className":41944},[487],[212,41946,41948,41957],{"className":41947,"style":7060},[491],[212,41949,41951,41954],{"className":41950,"style":12063},[6505],[212,41952],{"className":41953,"style":658},[499],[212,41955,11],{"className":41956,"style":34587},[256,257],[212,41958,41959,41962],{"style":41550},[212,41960],{"className":41961,"style":658},[499],[212,41963,41965],{"className":41964,"style":34644},[34643],[6521,41966,41967],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,41968],{"d":34651},[212,41970,515],{"className":41971},[514],[212,41973,41975],{"className":41974},[487],[212,41976,41978],{"className":41977,"style":41570},[491],[212,41979],{},[212,41981],{"className":41982,"style":2785},[354],[212,41984,5011],{"className":41985},[2789],[212,41987],{"className":41988,"style":2785},[354],[212,41990,41992,41995,42039,42068,42071,42074],{"className":41991},[247],[212,41993],{"className":41994,"style":41588},[251],[212,41996,41998],{"className":41997},[256,34567],[212,41999,42001,42031],{"className":42000},[482,483],[212,42002,42004,42028],{"className":42003},[487],[212,42005,42007,42016],{"className":42006,"style":7060},[491],[212,42008,42010,42013],{"className":42009,"style":12063},[6505],[212,42011],{"className":42012,"style":658},[499],[212,42014,1141],{"className":42015,"style":39299},[256,257],[212,42017,42018,42021],{"style":41550},[212,42019],{"className":42020,"style":658},[499],[212,42022,42024],{"className":42023,"style":34644},[34643],[6521,42025,42026],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,42027],{"d":34651},[212,42029,515],{"className":42030},[514],[212,42032,42034],{"className":42033},[487],[212,42035,42037],{"className":42036,"style":41570},[491],[212,42038],{},[212,42040,42042,42045],{"className":42041},[350],[212,42043,317],{"className":42044},[350],[212,42046,42048],{"className":42047},[478],[212,42049,42051],{"className":42050},[482],[212,42052,42054],{"className":42053},[487],[212,42055,42057],{"className":42056,"style":19935},[491],[212,42058,42059,42062],{"style":8475},[212,42060],{"className":42061,"style":500},[499],[212,42063,42065],{"className":42064},[504,505,506,507],[212,42066,2661],{"className":42067},[256,507],[212,42069],{"className":42070,"style":355},[354],[212,42072,320],{"className":42073},[359],[212,42075],{"className":42076,"style":355},[354],[212,42078,42080,42083,42086,42089,42092,42095,42098],{"className":42079},[247],[212,42081],{"className":42082,"style":5975},[251],[212,42084,1485],{"className":42085,"style":1685},[1682,1683,1684],[212,42087],{"className":42088,"style":603},[354],[212,42090,11],{"className":42091},[256,257],[212,42093],{"className":42094,"style":2785},[354],[212,42096,2668],{"className":42097},[2789],[212,42099],{"className":42100,"style":2785},[354],[212,42102,42104,42107,42110,42113,42116,42119,42122],{"className":42103},[247],[212,42105],{"className":42106,"style":5975},[251],[212,42108,1485],{"className":42109,"style":1685},[1682,1683,1684],[212,42111],{"className":42112,"style":603},[354],[212,42114,1141],{"className":42115,"style":1178},[256,257],[212,42117],{"className":42118,"style":2785},[354],[212,42120,5011],{"className":42121},[2789],[212,42123],{"className":42124,"style":2785},[354],[212,42126,42128,42131,42134,42137,42140,42143,42190,42193,42196],{"className":42127},[247],[212,42129],{"className":42130,"style":5975},[251],[212,42132,2661],{"className":42133},[256],[212,42135],{"className":42136,"style":603},[354],[212,42138,1485],{"className":42139,"style":1685},[1682,1683,1684],[212,42141],{"className":42142,"style":603},[354],[212,42144,42146],{"className":42145},[256,34567],[212,42147,42149,42182],{"className":42148},[482,483],[212,42150,42152,42179],{"className":42151},[487],[212,42153,42155,42167],{"className":42154,"style":7060},[491],[212,42156,42158,42161],{"className":42157,"style":12063},[6505],[212,42159],{"className":42160,"style":658},[499],[212,42162,42164],{"className":42163,"style":34587},[256],[212,42165,41805],{"className":42166,"style":1178},[256,257],[212,42168,42169,42172],{"style":41550},[212,42170],{"className":42171,"style":658},[499],[212,42173,42175],{"className":42174,"style":34644},[34643],[6521,42176,42177],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,42178],{"d":34651},[212,42180,515],{"className":42181},[514],[212,42183,42185],{"className":42184},[487],[212,4218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",[212,42251,42253,42271],{"className":42252,"translate":216},[215],[212,42254,42256],{"className":42255},[220],[222,42257,42258],{"xmlns":224},[226,42259,42260,42268],{},[229,42261,42262],{},[7012,42263,42264,42266],{},[232,42265,34084],{},[312,42267,2661],{},[236,42269,42270],{"encoding":238},"H^2",[212,42272,42274],{"className":42273,"ariaHidden":243},[242],[212,42275,42277,42280],{"className":42276},[247],[212,42278],{"className":42279,"style":20228},[251],[212,42281,42283,42286],{"className":42282},[256],[212,42284,34084],{"className":42285,"style":34238},[256,257],[212,42287,42289],{"className":42288},[478],[212,42290,42292],{"className":42291},[482],[212,42293,42295],{"className":42294},[487],[212,42296,42298],{"className":42297,"style":20228},[491],[212,42299,42300,42303],{"style":7063},[212,42301],{"className":42302,"style":500},[499],[212,42304,42306],{"className":42305},[504,505,506,507],[212,42307,2661],{"className":42308},[256,507]," 有两种约定：",[212,42311,42313],{"className":42312,"translate":216},[377],[212,42314,42316,42422],{"className":42315,"translate":216},[215],[212,42317,42319],{"className":42318},[220],[222,42320,42321],{"xmlns":224,"display":386},[226,42322,42323,42419],{},[1441,42324,42325,42360],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,42326,42327,42340],{},[1450,42328,42329],{},[1453,42330,42331],{"scriptlevel":323,"displaystyle":243},[7751,42332,42333,42335,42338],{},[232,42334,34084],{},[1495,42336,42337],{},"Bhattacharyya",[312,42339,2661],{},[1450,42341,42342],{},[1453,42343,42344],{"scriptlevel":323,"displaystyle":243},[229,42345,42346,42348,42350,42352,42354,42356,42358],{},[229,42347],{},[307,42349,320],{},[312,42351,314],{},[307,42353,5011],{},[232,42355,39491],{},[232,42357,39494],{},[307,42359,748],{"separator":243},[1447,42361,42362,42381],{},[1450,42363,42364],{},[1453,42365,42366],{"scriptlevel":323,"displaystyle":243},[7751,42367,42368,42370,42379],{},[232,42369,34084],{},[229,42371,42372,42375,42377],{},[1495,42373,42374],{},"this",[1495,42376,1497],{},[232,42378,234],{},[312,42380,2661],{},[1450,42382,42383],{},[1453,42384,42385],{"scriptlevel":323,"displaystyle":243},[229,42386,42387,42389,42391,42393,42395,42397,42399,42401,42403,42405,42407,42409,42417],{},[229,42388],{},[307,42390,320],{},[312,42392,2661],{},[307,42394,310],{"stretchy":309},[312,42396,314],{},[307,42398,5011],{},[232,42400,39491],{},[232,42402,39494],{},[307,42404,317],{"stretchy":309},[307,42406,320],{},[312,42408,2661],{},[7751,42410,42411,42413,42415],{},[232,42412,34084],{},[1495,42414,42337],{},[312,42416,2661],{},[232,42418,4573],{"mathvariant":406},[236,42420,42421],{"encoding":238},"\\begin{aligned}\nH^2_{\\text{Bhattacharyya}}&=1-BC,\\\\[2pt]\nH^2_{\\text{this}\\,f}&=2(1-BC)\n=2H^2_{\\text{Bhattacharyya}} .\n\\end{aligned}",[212,42423,42425],{"className":42424,"ariaHidden":243},[242],[212,42426,42428,42432],{"className":42427},[247],[212,42429],{"className":42430,"style":42431},[251],"height:2.9713em;vertical-align:-1.2357em;",[212,42433,42435],{"className":42434},[256],[212,42436,42438,42604],{"className":42437},[1441],[212,42439,42441],{"className":42440},[1558],[212,42442,42444,42595],{"className":42443},[482,483],[212,42445,42447,42592],{"className":42446},[487],[212,42448,42451,42519],{"className":42449,"style":42450},[491],"height:1.7357em;",[212,42452,42454,42457],{"style":42453},"top:-3.8716em;",[212,42455],{"className":42456,"style":658},[499],[212,42458,42460],{"className":42459},[256],[212,42461,42463,42466],{"className":42462},[256],[212,42464,34084],{"className":42465,"style":34238},[256,257],[212,42467,42469],{"className":42468},[478],[212,42470,42472,42510],{"className":42471},[482,483],[212,42473,42475,42507],{"className":42474},[487],[212,42476,42478,42496],{"className":42477,"style":19935},[491],[212,42479,42481,42484],{"style":42480},"top:-2.453em;margin-left:-0.0813em;margin-right:0.05em;",[212,42482],{"className":42483,"style":500},[499],[212,42485,42487],{"className":42486},[504,505,506,507],[212,42488,42490],{"className":42489},[256,507],[212,42491,42493],{"className":42492},[256,4796,507],[212,42494,42337],{"className":42495},[256,507],[212,42497,42498,42501],{"style":8475},[212,42499],{"className":42500,"style":500},[499],[212,42502,42504],{"className":42503},[504,505,506,507],[212,42505,2661],{"className":42506},[256,507],[212,42508,515],{"className":42509},[514],[212,42511,42513],{"className":42512},[487],[212,42514,42517],{"className":42515,"style":42516},[491],"height:0.3831em;",[212,42518],{},[212,42520,42522,42525],{"style":42521},"top:-2.1474em;",[212,42523],{"className":42524,"style":658},[499],[212,42526,42528],{"className":42527},[256],[212,42529,42531,42534],{"className":42530},[256],[212,42532,34084],{"className":42533,"style":34238},[256,257],[212,42535,42537],{"className":42536},[478],[212,42538,42540,42584],{"className":42539},[482,483],[212,42541,42543,42581],{"className":42542},[487],[212,42544,42546,42570],{"className":42545,"style":19935},[491],[212,42547,42548,42551],{"style":42480},[212,42549],{"className":42550,"style":500},[499],[212,42552,42554],{"className":42553},[504,505,506,507],[212,42555,42557,42563,42567],{"className":42556},[256,507],[212,42558,42560],{"className":42559},[256,4796,507],[212,42561,42374],{"className":42562},[256,507],[212,42564],{"className":42565,"style":42566},[354,507],"margin-right:0.1952em;",[212,42568,234],{"className":42569,"style":258},[256,257,507],[212,42571,42572,42575],{"style":8475},[212,42573],{"className":42574,"style":500},[499],[212,42576,42578],{"className":42577},[504,505,506,507],[212,42579,2661],{"className":42580},[256,507],[212,42582,515],{"className":42583},[514],[212,42585,42587],{"className":42586},[487],[212,42588,42590],{"className":42589,"style":42516},[491],[212,42591],{},[212,42593,515],{"className":42594},[514],[212,42596,42598],{"className":42597},[487],[212,42599,42602],{"className":42600,"style":42601},[491],"height:1.2357em;",[212,42603],{},[212,42605,42607],{"className":42606},[1649],[212,42608,42610,42779],{"className":42609},[482,483],[212,42611,42613,42776],{"className":42612},[487],[212,42614,42616,42657],{"className":42615,"style":42450},[491],[212,42617,42618,42621],{"style":42453},[212,42619],{"className":42620,"style":658},[499],[212,42622,42624,42627,42630,42633,42636,42639,42642,42645,42648,42651,42654],{"className":42623},[256],[212,42625],{"className":42626},[256],[212,42628],{"className":42629,"style":355},[354],[212,42631,320],{"className":42632},[359],[212,42634],{"className":42635,"style":355},[354],[212,42637,314],{"className":42638},[256],[212,42640],{"className":42641,"style":2785},[354],[212,42643,5011],{"className":42644},[2789],[212,42646],{"className":42647,"style":2785},[354],[212,42649,39491],{"className":42650,"style":39587},[256,257],[212,42652,39494],{"className":42653,"style":10982},[256,257],[212,42655,748],{"className":42656},[770],[212,42658,42659,42662],{"style":42521},[212,42660],{"className":42661,"style":658},[499],[212,42663,42665,42668,42671,42674,42677,42680,42683,42686,42689,42692,42695,42698,42701,42704,42707,42710,42713,42716,42773],{"className":42664},[256],[212,42666],{"className":42667},[256],[212,42669],{"className":42670,"style":355},[354],[212,42672,320],{"className":42673},[359],[212,42675],{"className":42676,"style":355},[354],[212,42678,2661],{"className":42679},[256],[212,42681,310],{"className":42682},[343],[212,42684,314],{"className":42685},[256],[212,42687],{"className":42688,"style":2785},[354],[212,42690,5011],{"className":42691},[2789],[212,42693],{"className":42694,"style":2785},[354],[212,42696,39491],{"className":42697,"style":39587},[256,257],[212,42699,39494],{"className":42700,"style":10982},[256,257],[212,42702,317],{"className":42703}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t-1)^2",[212,42832,42834,42861,42927],{"className":42833,"ariaHidden":243},[242],[212,42835,42837,42840,42843,42846,42849,42852,42855,42858],{"className":42836},[247],[212,42838],{"className":42839,"style":336},[251],[212,42841,234],{"className":42842,"style":258},[256,257],[212,42844,310],{"className":42845},[343],[212,42847,966],{"className":42848},[256,257],[212,42850,317],{"className":42851},[350],[212,42853],{"className":42854,"style":355},[354],[212,42856,320],{"className":42857},[359],[212,42859],{"className":42860,"style":355},[354],[212,42862,42864,42868,42871,42918,42921,42924],{"className":42863},[247],[212,42865],{"className":42866,"style":42867},[251],"height:1.1425em;vertical-align:-0.25em;",[212,42869,310],{"className":42870},[343],[212,42872,42874],{"className":42873},[256,34567],[212,42875,42877,42909],{"className":42876},[482,483],[212,42878,42880,42906],{"className":42879},[487],[212,42881,42884,42893],{"className":42882,"style":42883},[491],"height:0.8925em;",[212,42885,42887,42890],{"className":42886,"style":12063},[6505],[212,42888],{"className":42889,"style":658},[499],[212,42891,966],{"className":42892,"style":34587},[256,257],[212,42894,42896,42899],{"style":42895},"top:-2.8525em;",[212,42897],{"className":42898,"style":658},[499],[212,42900,42902],{"className":42901,"style":34644},[34643],[6521,42903,42904],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,42905],{"d":34651},[212,42907,515],{"className":42908},[514],[212,42910,42912],{"className":42911},[487],[212,42913,42916],{"className":42914,"style":42915},[491],"height:0.1475em;",[212,42917],{},[212,42919],{"className":42920,"style":2785},[354],[212,42922,5011],{"className":42923},[2789],[212,42925],{"className":42926,"style":2785},[354],[212,42928,42930,42933,42936],{"className":42929},[247],[212,42931],{"className":42932,"style":20203},[251],[212,42934,314],{"className":42935},[256],[212,42937,42939,42942],{"className":42938},[350],[212,42940,317],{"className":42941},[350],[212,42943,42945],{"className":42944},[478],[212,42946,42948],{"className":42947},[482],[212,42949,42951],{"className":42950},[487],[212,42952,42954],{"className":42953,"style":20228},[491],[212,42955,42956,42959],{"style":7063},[212,42957],{"className":42958,"style":500},[499],[212,42960,42962],{"className":42961},[504,505,506,507],[212,42963,2661],{"className":42964},[256,507],"，故 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有界（",[212,43361,43363,43379],{"className":43362,"translate":216},[215],[212,43364,43366],{"className":43365},[220],[222,43367,43368],{"xmlns":224},[226,43369,43370,43376],{},[229,43371,43372,43374],{},[307,43373,10150],{},[312,43375,2661],{},[236,43377,43378],{"encoding":238},"\\le 2",[212,43380,43382,43395],{"className":43381,"ariaHidden":243},[242],[212,43383,43385,43389,43392],{"className":43384},[247],[212,43386],{"className":43387,"style":43388},[251],"height:0.7719em;vertical-align:-0.136em;",[212,43390,10150],{"className":43391},[359],[212,43393],{"className":43394,"style":355},[354],[212,43396,43398,43401],{"className":43397},[247],[212,43399],{"className":43400,"style":369},[251],[212,43402,2661],{"className":43403},[256],"）。对称性可直接验算：",[212,43406,43408],{"className":43407,"translate":216},[377],[212,43409,43411,43587],{"className":43410,"translate":216},[215],[212,43412,43414],{"className":43413},[220],[222,43415,43416],{"xmlns":224,"display":386},[226,43417,43418,43584],{},[1441,43419,43420,43478,43522],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,43421,43422,43444],{},[1450,43423,43424],{},[1453,43425,43426],{"scriptlevel":323,"displaystyle":243},[229,43427,43428,43430,43432,43434,43436,43438,43440,43442],{},[232,43429,966],{},[1495,43431,1497],{},[232,43433,234],{},[307,43435,310],{"stretchy":309},[312,43437,314],{},[232,43439,1138],{"mathvariant":406},[232,43441,966],{},[307,43443,317],{"stretchy":309},[1450,43445,43446],{},[1453,43447,43448],{"scriptlevel":323,"displaystyle":243},[229,43449,43450,43452,43454,43456],{},[229,43451],{},[307,43453,320],{},[232,43455,966],{},[7012,43457,43458,43476],{},[229,43459,43460,43462,43470,43472,43474],{},[307,43461,310],{"fence":243},[435,43463,43464,43466],{},[312,43465,314],{},[34539,43467,43468],{},[232,43469,966],{},[307,43471,5011],{},[312,43473,314],{},[307,43475,317],{"fence":243},[312,43477,2661],{},[1447,43479,43480,43486],{},[1450,43481,43482],{},[1453,43483,43484],{"scriptlevel":323,"displaystyle":243},[229,43485],{},[1450,43487,43488],{},[1453,43489,43490],{"scriptlevel":323,"displaystyle":243},[229,43491,43492,43494,43496,43498,43500,43506,43508,43516,43518,43520],{},[229,43493],{},[307,43495,320],{},[232,43497,966],{},[307,43499,310],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[435,43501,43502,43504],{},[312,43503,314],{},[232,43505,966],{},[307,43507,5011],{},[435,43509,43510,43512],{},[312,43511,2661],{},[34539,43513,43514],{},[232,43515,966],{},[307,43517,2668],{},[312,43519,314],{},[307,43521,317],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[1447,43523,43524,43530],{},[1450,43525,43526],{},[1453,43527,43528],{"scriptlevel":323,"displaystyle":243},[229,43529],{},[1450,43531,43532],{},[1453,43533,43534],{"scriptlevel":323,"displaystyle":243},[229,43535,43536,43538,43540,43542,43544,43546,43550,43552,43554,43556,43558,43562,43564,43566,43572,43574,43576,43578,43580,43582],{},[229,43537],{},[307,43539,320],{},[312,43541,314],{},[307,43543,5011],{},[312,43545,2661],{},[34539,43547,43548],{},[232,43549,966],{},[307,43551,2668],{},[232,43553,966],{},[307,43555,320],{},[307,43557,310],{"stretchy":309},[34539,43559,43560],{},[232,43561,966],{},[307,43563,5011],{},[312,43565,314],{},[7012,43567,43568,43570],{},[307,43569,317],{"stretchy":309},[312,43571,2661],{},[307,43573,320],{},[232,43575,234],{},[307,43577,310],{"stretchy":309},[232,43579,966],{},[307,43581,317],{"stretchy":309},[307,43583,748],{"separator":243},[236,43585,43586],{"encoding":238},"\\begin{aligned}\nt\\,f(1\u002Ft)\n&=t\\left(\\frac{1}{\\sqrt t}-1\\right)^2\\\\\n&=t\\Big(\\frac1t-\\frac{2}{\\sqrt t}+1\\Big)\\\\[2pt]\n&=1-2\\sqrt t+t=(\\sqrt t-1)^2=f(t),\n\\end{aligned}",[212,43588,43590],{"className":43589,"ariaHidden":243},[242],[212,43591,43593,43597],{"className":43592},[247],[212,43594],{"className":43595,"style":43596},[251],"height:6.7569em;vertical-align:-3.1284em;",[212,43598,43600],{"className":43599},[256],[212,43601,43603,43677],{"className":43602},[1441],[212,43604,43606],{"className":43605},[1558],[212,43607,43609,43668],{"className":43608},[482,483],[212,43610,43612,43665],{"className":43611},[487],[212,43613,43616,43647,43656],{"className":43614,"style":43615},[491],"height:3.6284em;",[212,43617,43619,43623],{"style":43618},"top:-5.6284em;",[212,43620],{"className":43621,"style":43622},[499],"height:3.654em;",[212,43624,43626,43629,43632,43635,43638,43641,43644],{"className":43625},[256],[212,43627,966],{"className":43628},[256,257],[212,43630],{"className":43631,"style":603},[354],[212,43633,234],{"className":43634,"style":258},[256,257],[212,43636,310],{"className":43637},[343],[212,43639,8787],{"className":43640},[256],[212,43642,966],{"className":43643},[256,257],[212,43645,317],{"className":43646},[350],[212,43648,43650,43653],{"style":43649},"top:-3.057em;",[212,43651],{"className":43652,"style":43622},[499],[212,43654],{"className":43655},[256],[212,43657,43659,43662],{"style":43658},"top:-0.8856em;",[212,43660],{"className":43661,"style":43622},[499],[212,43663],{"className":43664},[256],[212,43666,515],{"className":43667},[514],[212,43669,43671],{"className":43670},[487],[212,43672,43675],{"className":43673,"style":43674},[491],"height:3.1284em;",[212,43676],{},[212,43678,43680],{"className":43679},[1649],[212,43681,43683,44309],{"className":43682},[482,483],[212,43684,43686,44306],{"className":43685},[487],[212,43687,43689,43873,44094],{"className":43688,"style":43615},[491],[212,43690,43691,43694],{"style":43618},[212,43692],{"className":43693,"style":43622},[499],[212,43695,43697,43700,43703,43706,43709,43712,43715],{"className":43696},[256],[212,43698],{"className":43699},[256],[212,43701],{"className":43702,"style":355},[354],[212,43704,320],{"className":43705},[359],[212,43707],{"className":43708,"style":355},[354],[212,43710,966],{"className":43711},[256,257],[212,43713],{"className":43714,"style":603},[354],[212,43716,43718,43850],{"className":43717},[607],[212,43719,43721,43727,43832,43835,43838,43841,43844],{"className":43720},[607],[212,43722,43724],{"className":43723,"style":612},[343,611],[212,43725,310],{"className":43726},[616,506],[212,43728,43730,43733,43829],{"className":43729},[256],[212,43731],{"className":43732},[343,638],[212,43734,43736],{"className":43735},[435],[212,43737,43739,43820],{"className":43738},[482,483],[212,43740,43742,43817],{"className":43741},[487],[212,43743,43745,43798,43806],{"className":43744,"style":23089},[491],[212,43746,43748,43751],{"style":43747},"top:-2.2175em;",[212,43749],{"className":43750,"style":658},[499],[212,43752,43754],{"className":43753},[256],[212,43755,43757],{"className":43756},[256,34567],[212,43758,43760,43790],{"className":43759},[482,483],[212,43761,43763,43787],{"className":43762},[487],[212,43764,43766,43775],{"className":43765,"style":42883},[491],[212,43767,43769,43772],{"className":43768,"style":12063},[6505],[212,43770],{"className":43771,"style":658},[499],[212,43773,966],{"className":43774,"style":34587},[256,257],[212,43776,43777,43780],{"style":42895},[212,43778],{"className":43779,"style":658},[499],[212,43781,43783],{"className":43782,"style":34644},[34643],[6521,43784,43785],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,43786],{"d":34651},[212,43788,515],{"className":43789},[514],[212,43791,43793],{"className":43792},[487],[212,43794,43796],{"className":43795,"style":42915},[491],[212,43797],{},[212,43799,43800,43803],{"style":670},[212,43801],{"className":43802,"style":658},[499],[212,43804],{"className":43805,"style":678},[677],[212,43807,43808,43811],{"style":681},[212,43809],{"className":43810,"style":658},[499],[212,43812,43814],{"className":43813},[256],[212,43815,314],{"className":43816},[256],[212,43818,515],{"className":43819},[514],[212,43821,43823],{"className":43822},[487],[212,43824,43827],{"className":43825,"style":43826},[491],"height:0.93em;",[212,43828],{},[212,43830],{"className":43831},[350,638],[212,43833],{"className":43834,"style":2785},[354],[212,43836,5011],{"className":43837},[2789],[212,43839],{"className":43840,"style":2785},[354],[212,43842,314],{"className":43843},[256],[212,43845,43847],{"className":43846,"style":612},[350,611],[212,43848,317],{"className":43849},[616,506],[212,43851,43853],{"className":43852},[478],[212,43854,43856],{"className":43855},[482],[212,43857,43859],{"className":43858},[487],[212,43860,43862],{"className":43861,"style":37861},[491],[212,43863,43864,43867],{"style":37864},[212,43865],{"className":43866,"style":500},[499],[212,43868,43870],{"className":43869},[504,505,506,507],[212,43871,2661],{"className":43872},[256,507],[212,43874,43875,43878],{"style":43649},[212,43876],{"className":43877,"style":43622},[499],[212,43879,43881,43884,43887,43890,43893,43896,43902,43964,43967,43970,43973,44076,44079,44082,44085,44088],{"className":43880},[256],[212,43882],{"className":43883},[256],[212,43885],{"className":43886,"style":355},[354],[212,43888,320],{"className":43889},[359],[212,43891],{"className":43892,"style":355},[354],[212,43894,966],{"className":43895},[256,257],[212,43897,43899],{"className":43898},[256],[212,43900,310],{"className":43901},[616,3918],[212,43903,43905,43908,43961],{"className":43904},[256],[212,43906],{"className":43907},[343,638],[212,43909,43911],{"className":43910},[435],[212,43912,43914,43953],{"className":43913},[482,483],[212,43915,43917,43950],{"className":43916},[487],[212,43918,43920,43931,43939],{"className":43919,"style":23089},[491],[212,43921,43922,43925],{"style":654},[212,43923],{"className":43924,"style":658},[499],[212,43926,43928],{"className":43927},[256],[212,43929,966],{"className":43930},[256,257],[212,43932,43933,43936],{"style":670},[212,43934],{"className":43935,"style":658},[499],[212,43937],{"className":43938,"style":678},[677],[212,43940,43941,43944],{"style":681},[212,43942],{"className":43943,"style":658},[499],[212,43945,43947],{"className":43946},[256],[212,43948,314],{"className":43949},[256],[212,43951,515],{"className":43952},[514],[212,43954,43956],{"className":43955},[487],[212,43957,43959],{"className":43958,"style":3976},[491],[212,43960],{},[212,43962],{"className":43963},[350,638],[212,43965],{"className":43966,"style":2785},[354],[212,43968,5011],{"className":43969},[2789],[212,43971],{"className":43972,"style":2785},[354],[212,43974,43976,43979,44073],{"className":43975},[256],[212,43977],{"className":43978},[343,638],[212,43980,43982],{"className":43981},[435],[212,43983,43985,44065],{"className":43984},[482,483],[212,43986,43988,44062],{"className":43987},[487],[212,43989,43991,44043,44051],{"className":43990,"style":23089},[491],[212,43992,43993,43996],{"style":43747},[212,43994],{"className":43995,"style":658},[499],[212,43997,43999],{"className":43998},[256],[212,44000,44002],{"className":44001},[256,34567],[212,44003,44005,44035],{"className":44004},[482,483],[212,44006,44008,44032],{"className":44007},[487],[212,44009,44011,44020],{"className":44010,"style":42883},[491],[212,44012,44014,44017],{"className":44013,"style":12063},[6505],[212,44015],{"className":44016,"style":658},[499],[212,44018,966],{"className":44019,"style":34587},[256,257],[212,44021,44022,44025],{"style":42895},[212,44023],{"className":44024,"style":658},[499],[212,44026,44028],{"className":44027,"style":34644},[34643],[6521,44029,44030],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,44031],{"d":34651},[212,44033,515],{"className":44034},[514],[212,44036,44038],{"className":44037},[487],[212,44039,44041],{"className":44040,"style":42915},[491],[212,44042],{},[212,44044,44045,44048],{"style":670},[212,44046],{"className":44047,"style":658},[499],[212,44049],{"className":44050,"style":678},[677],[212,44052,44053,44056],{"style":681},[212,44054],{"className":44055,"style":658},[499],[212,44057,44059],{"className":44058},[256],[212,44060,2661],{"className":44061},[256],[212,44063,515],{"className":44064},[514],[212,44066,44068],{"className":44067},[487],[212,44069,44071],{"className":44070,"style":43826},[491],[212,44072],{},[212,44074],{"className":44075},[350,638],[212,44077],{"className":44078,"style":2785},[354],[212,44080,2668],{"className":44081},[2789],[212,44083],{"className":44084,"style":2785},[354],[212,44086,314],{"className":44087},[256],[212,44089,44091],{"className":44090},[256],[212,44092,317],{"className":44093},[616,3918],[212,44095,44096,44099],{"style":43658},[212,44097],{"className":44098,"style":43622},[499],[212,44100,44102,44105,44108,44111,44114,44117,44120,44123,44126,44129,44173,44176,44179,44182,44185,44188,44191,44194,44197,44241,44244,44247,44250,44253,44282,44285,44288,44291,44294,44297,44300,44303],{"className":44101},[256],[212,44103],{"className":44104},[256],[212,44106],{"className":44107,"style":355},[354],[212,44109,320],{"className":44110},[359],[212,44112],{"className":44113,"style":355},[354],[212,44115,314],{"className":44116},[256],[212,44118],{"className":44119,"style":2785},[354],[212,44121,5011],{"className":44122},[2789],[212,44124],{"className":44125,"style":2785},[354],[212,44127,2661],{"className":44128},[256],[212,44130,44132],{"className":44131},[256,34567],[212,44133,44135,44165],{"className":44134},[482,483],[212,44136,44138,44162],{"className":44137},[487],[212,44139,44141,44150],{"className":44140,"style":40737},[491],[212,44142,44144,44147],{"className":44143,"style":12063},[6505],[212,44145],{"className":44146,"style":658},[499],[212,44148,966],{"className":44149,"style":34587},[256,257],[212,44151,44152,44155],{"style":40752},[212,44153],{"className":44154,"style":658},[499],[212,44156,44158],{"className"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Hellinger",[212,44450,44452,44470],{"className":44451,"translate":216},[215],[212,44453,44455],{"className":44454},[220],[222,44456,44457],{"xmlns":224},[226,44458,44459,44467],{},[229,44460,44461],{},[7012,44462,44463,44465],{},[229,44464],{},[312,44466,2661],{},[236,44468,44469],{"encoding":238},"^2",[212,44471,44473],{"className":44472,"ariaHidden":243},[242],[212,44474,44476,44479],{"className":44475},[247],[212,44477],{"className":44478,"style":20228},[251],[212,44480,44482,44484],{"className":44481},[256],[212,44483],{},[212,44485,44487],{"className":44486},[478],[212,44488,44490],{"className":44489},[482],[212,44491,44493],{"className":44492},[487],[212,44494,44496],{"className":44495,"style":20228},[491],[212,44497,44498,44501],{"style":7063},[212,44499],{"className":44500,"style":500},[499],[212,44502,44504],{"className":44503},[504,505,506,507],[212,44505,2661],{"className":44506},[256,507]," 也满足对称判别准则（4.3 节）。",[11,44509,44510,44512,44513,44627,44628,44631,44632,44688,44689,44745,44746,44904,44905,44933],{},[1194,44511,24393],{}," Hellinger 与 Bhattacharyya 系数 ",[212,44514,44516,44544],{"className":44515,"translate":216},[215],[212,44517,44519],{"className":44518},[220],[222,44520,44521],{"xmlns":224},[226,44522,44523,44541],{},[229,44524,44525,44527,44529,44531,44533],{},[232,44526,39491],{},[232,44528,39494],{},[307,44530,320],{},[307,44532,1485],{},[34539,44534,44535],{},[229,44536,44537,44539],{},[232,44538,11],{},[232,44540,1141],{},[236,44542,44543],{"encoding":238},"BC=\\int\\sqrt{pq}",[212,44545,44547,44568],{"className":44546,"ariaHidden":243},[242],[212,44548,44550,44553,44556,44559,44562,44565],{"className":44549},[247],[212,44551],{"className":44552,"style":861},[251],[212,44554,39491],{"className":44555,"style":39587},[256,257],[212,44557,39494],{"className":44558,"style":10982},[256,257],[212,44560],{"className":44561,"style":355},[354],[212,44563,320],{"className":44564},[359],[212,44566],{"className":44567,"style":355},[354],[212,44569,44571,44574,44577,44580],{"className":44570},[247],[212,44572],{"className":44573,"style":39208},[251],[212,44575,1485],{"className":44576,"style":5815},[1682,1683,5814],[212,44578],{"className":44579,"style":603},[354],[212,44581,44583],{"className":44582},[256,34567],[212,44584,44586,44619],{"className":44585},[482,483],[212,44587,44589,44616],{"className":44588},[487],[212,44590,44592,44604],{"className":44591,"style":39227},[491],[212,44593,44595,44598],{"className":44594,"style":12063},[6505],[212,44596],{"className":44597,"style":658},[499],[212,44599,44601],{"className":44600,"style":34587},[256],[212,44602,41805],{"className":44603,"style":1178},[256,257],[212,44605,44606,44609],{"style":39239},[212,44607],{"className":44608,"style":658},[499],[212,44610,44612],{"className":44611,"style":34644},[34643],[6521,44613,44614],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,44615],{"d":34651},[212,44617,515],{"className":44618},[514],[212,44620,44622],{"className":44621},[487],[212,44623,44625],{"className":44624,"style":39259},[491],[212,44626],{}," 把「两个分布的",[1194,44629,44630],{},"重叠程度","」量化：",[212,44633,44635,44655],{"className":44634,"translate":216},[215],[212,44636,44638],{"className":44637},[220],[222,44639,44640],{"xmlns":224},[226,44641,44642,44652],{},[229,44643,44644,44646,44648,44650],{},[232,44645,39491],{},[232,44647,39494],{},[307,44649,320],{},[312,44651,314],{},[236,44653,44654],{"encoding":238},"BC=1",[212,44656,44658,44679],{"className":44657,"ariaHidden":243},[242],[212,44659,44661,44664,44667,44670,44673,44676],{"className":44660},[247],[212,44662],{"className":44663,"style":861},[251],[212,44665,39491],{"className":44666,"style":39587},[256,257],[212,44668,39494],{"className":44669,"style":10982},[256,257],[212,44671],{"className":44672,"style":355},[354],[212,44674,320],{"className":44675},[359],[212,44677],{"className":44678,"style":355},[354],[212,44680,44682,44685],{"className":44681},[247],[212,44683],{"className":44684,"style":369},[251],[212,44686,314],{"className":44687},[256]," 表示完全重合，",[212,44690,44692,44712],{"className":44691,"translate":216},[215],[212,44693,44695],{"className":44694},[220],[222,44696,44697],{"xmlns":224},[226,44698,44699,44709],{},[229,44700,44701,44703,44705,44707],{},[232,44702,39491],{},[232,44704,39494],{},[307,44706,320],{},[312,44708,323],{},[236,44710,44711],{"encoding":238},"BC=0",[212,44713,44715,44736],{"className":44714,"ariaHidden":243},[242],[212,44716,44718,44721,44724,44727,44730,44733],{"className":44717},[247],[212,44719],{"className":44720,"style":861},[251],[212,44722,39491],{"className":44723,"style":39587},[256,257],[212,44725,39494],{"className":44726,"style":10982},[256,257],[212,44728],{"className":44729,"style":355},[354],[212,44731,320],{"className":44732},[359],[212,44734],{"className":44735,"style":355},[354],[212,44737,44739,44742],{"className":44738},[247],[212,44740],{"className":44741,"style":369},[251],[212,44743,323],{"className":44744},[256]," 表示支撑分离。由它可造出真正的距离 ",[212,44747,44749,44790],{"className":44748,"translate":216},[215],[212,44750,44752],{"className":44751},[220],[222,44753,44754],{"xmlns":224},[226,44755,44756,44787],{},[229,44757,44758,44761,44763,44765,44767,44769,44771,44773],{},[232,44759,44760],{},"ρ",[307,44762,310],{"stretchy":309},[232,44764,403],{},[307,44766,748],{"separator":243},[232,44768,410],{},[307,44770,317],{"stretchy":309},[307,44772,320],{},[34539,44774,44775],{},[229,44776,44777,44779,44781,44783,44785],{},[312,44778,2661],{},[307,44780,5011],{},[312,44782,2661],{},[232,44784,39491],{},[232,44786,39494],{},[236,44788,44789],{"encoding":238},"\\rho(P,Q)=\\sqrt{2-2BC}",[212,44791,44793,44829],{"className":44792,"ariaHidden":243},[242],[212,44794,44796,44799,44802,44805,44808,44811,44814,44817,44820,44823,44826],{"className":44795},[247],[212,44797],{"className":44798,"style":336},[251],[212,44800,44760],{"className":44801},[256,257],[212,44803,310],{"className":44804},[343],[212,44806,403],{"className":44807,"style":531},[256,257],[212,44809,748],{"className":44810},[770],[212,44812],{"className":44813,"style":603},[354],[212,44815,410],{"className":44816},[256,257],[212,44818,317],{"className":44819},[350],[212,44821],{"className":44822,"style":355},[354],[212,44824,320],{"className":44825},[359],[212,44827],{"className":44828,"style":355},[354],[212,44830,44832,44836],{"className":44831},[247],[212,44833],{"className":44834,"style":44835},[251],"height:1.04em;vertical-align:-0.155em;",[212,44837,44839],{"className":44838},[256,34567],[212,44840,44842,44895],{"className":44841},[482,483],[212,44843,44845,44892],{"className":44844},[487],[212,44846,44849,44879],{"className":44847,"style":44848},[491],"height:0.885em;",[212,44850,44852,44855],{"className":44851,"style":12063},[6505],[212,44853],{"className":44854,"style":658},[499],[212,44856,44858,44861,44864,44867,44870,44873,44876],{"className":44857,"style":34587},[256],[212,44859,2661],{"className":44860},[256],[212,44862],{"className":44863,"style":2785},[354],[212,44865,5011],{"className":44866},[2789],[212,44868],{"className":44869,"style":2785},[354],[212,44871,2661],{"className":44872},[256],[212,44874,39491],{"className":44875,"style":39587},[256,257],[212,44877,39494],{"className":44878,"style":10982},[256,257],[212,44880,44882,44885],{"style":44881},"top:-2.845em;",[212,44883],{"className":44884,"style":658},[499],[212,44886,44888],{"className":44887,"style":34644},[34643],[6521,44889,44890],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,44891],{"d":34651},[212,44893,515],{"className":44894},[514],[212,44896,44898],{"className":44897},[487],[212,44899,44902],{"className":44900,"style":44901},[491],"height:0.155em;",[212,44903],{},"，而且它对绝对连续性不作要求，支撑分离时也只取到有限的最大值 ",[212,44906,44908,44921],{"className":44907,"translate":216},[215],[212,44909,44911],{"className":44910},[220],[222,44912,44913],{"xmlns":224},[226,44914,44915,44919],{},[229,44916,44917],{},[312,44918,2661],{},[236,44920,2661],{"encoding":238},[212,44922,44924],{"className":44923,"ariaHidden":243},[242],[212,44925,44927,44930],{"className":44926},[247],[212,44928],{"className":44929,"style":369},[251],[212,44931,2661],{"className":44932},[256],"，不会像 KL 那样发散——这让它在数值与统计上格外稳健。Hellinger 距离与 Fisher 信息度量在无穷小尺度上相容（4.6 节），并在非参数估计的 Le Cam 三点法、量子信息中的保真度（fidelity）、以及 Hellinger–Fisher–Rao 几何里扮演中心角色。",[2509,44935,44937],{"id":44936},"_36-α-散度","3.6 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p^{a}q^{1-a}\\,dx\\right).",[212,45901,45903,45973],{"className":45902,"ariaHidden":243},[242],[212,45904,45906,45909,45949,45952,45955,45958,45961,45964,45967,45970],{"className":45905},[247],[212,45907],{"className":45908,"style":336},[251],[212,45910,45912,45915],{"className":45911},[256],[212,45913,396],{"className":45914,"style":474},[256,257],[212,45916,45918],{"className":45917},[478],[212,45919,45921,45941],{"className":45920},[482,483],[212,45922,45924,45938],{"className":45923},[487],[212,45925,45927],{"className":45926,"style":45129},[491],[212,45928,45929,45932],{"style":495},[212,45930],{"className":45931,"style":500},[499],[212,45933,45935],{"className":45934},[504,505,506,507],[212,45936,44954],{"className":45937,"style":44984},[256,257,507],[212,45939,515],{"className":45940},[514],[212,45942,45944],{"className":45943},[487],[212,45945,45947],{"className":45946,"style":8166},[491],[212,45948],{},[212,45950,310],{"className":45951},[343],[212,45953,403],{"className":45954,"style":531},[256,257],[212,45956,407],{"className":45957},[256],[212,45959,410],{"className":45960},[256,257],[212,45962,317],{"className":45963},[350],[212,45965],{"className":45966,"style":355},[354],[212,45968,320],{"className":45969},[359],[212,45971],{"className":45972,"style":355},[354],[212,45974,45976,45979,46062,46065,46178,46181],{"className":45975},[247],[212,45977],{"className":45978,"style":556},[251],[212,45980,45982,45985,46059],{"className":45981},[256],[212,45983],{"className":45984},[343,638],[212,45986,45988],{"className":45987},[435],[212,45989,45991,46051],{"className":45990},[482,483],[212,45992,45994,46048],{"className":45993},[487],[212,45995,45997,46029,46037],{"className":45996,"style":23089},[491],[212,45998,45999,46002],{"style":654},[212,46000],{"className":46001,"style":658},[499],[212,46003,46005,46008,46011,46014,46017,46020,46023,46026],{"className":46004},[256],[212,46006,15],{"className":46007},[256,257],[212,46009,310],{"className":46010},[343],[212,46012,314],{"className":46013},[256],[212,46015],{"className":46016,"style":2785},[354],[212,46018,5011],{"className":46019},[2789],[212,46021],{"className":46022,"style":2785},[354],[212,46024,15],{"className":46025},[256,257],[212,46027,317],{"className":46028},[350],[212,46030,46031,46034],{"style":670},[212,46032],{"className":46033,"style":658},[499],[212,46035],{"className":46036,"style":678},[677],[212,46038,46039,46042],{"style":681},[212,46040],{"className":46041,"style":658},[499],[212,46043,46045],{"className":46044},[256],[212,46046,314],{"className":46047},[256],[212,46049,515],{"className":46050},[514],[212,46052,46054],{"className":46053},[487],[212,46055,46057],{"className":46056,"style":1799},[491],[212,46058],{},[212,46060],{"className":46061},[350,638],[212,46063],{"className":46064,"style":603},[354],[212,46066,46068,46074,46077,46080,46083,46086,46089,46092,46125,46163,46166,46169,46172],{"className":46067},[607],[212,46069,46071],{"className":46070,"style":612},[343,611],[212,46072,310],{"className":46073},[616,506],[212,46075,314],{"className":46076},[256],[212,46078],{"className":46079,"style":2785},[354],[212,46081,5011],{"className":46082},[2789],[212,46084],{"className":46085,"style":2785},[354],[212,46087,1485],{"className":46088,"style":1685},[1682,1683,1684],[212,46090],{"className":46091,"style":603},[354],[212,46093,46095,46098],{"className":46094},[256],[212,46096,11],{"className":46097},[256,257],[212,46099,46101],{"className":46100},[478],[212,46102,46104],{"className":46103},[482],[212,46105,46107],{"className":46106},[487],[212,46108,46111],{"className":46109,"style":46110},[491],"height:0.7144em;",[212,46112,46113,46116],{"style":8475},[212,46114],{"className":46115,"style":500},[499],[212,46117,46119],{"className":46118},[504,505,506,507],[212,46120,46122],{"className":46121},[256,507],[212,46123,15],{"className":46124},[256,257,507],[212,46126,46128,46131],{"className":46127},[256],[212,46129,1141],{"className":46130,"style":1178},[256,257],[212,46132,46134],{"className":46133},[478],[212,46135,46137],{"className":46136},[482],[212,46138,46140],{"className":46139},[487],[212,46141,46143],{"className":46142,"style":19935},[491],[212,46144,46145,46148],{"style":8475},[212,46146],{"className":46147,"style":500},[499],[212,46149,46151],{"className":46150},[504,505,506,507],[212,46152,46154,46157,46160],{"className":46153},[256,507],[212,46155,314],{"className":46156},[256,507],[212,46158,5011],{"className":46159},[2789,507],[212,46161,15],{"className":46162},[256,257,507],[212,46164],{"className":46165,"style":603},[354],[212,46167,441],{"className":46168},[256,257],[212,46170,971],{"className":46171},[256,257],[212,46173,46175],{"className":46174,"style":612},[350,611],[212,46176,317],{"className":46177},[616,506],[212,46179],{"className":46180,"style":603},[354],[212,46182,4573],{"className":46183},[256],[11,46185,46186,46187,46190,46191,32424,46246,9598],{},"这正是 Csiszár \u002F Amari 的 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是 Hellinger 型散度。两个端点极限要小心：",[212,46720,46722,46740],{"className":46721,"translate":216},[215],[212,46723,46725],{"className":46724},[220],[222,46726,46727],{"xmlns":224},[226,46728,46729,46737],{},[229,46730,46731],{},[392,46732,46733,46735],{},[232,46734,234],{},[232,46736,44954],{},[236,46738,46739],{"encoding":238},"f_\\alpha",[212,46741,46743],{"className":46742,"ariaHidden":243},[242],[212,46744,46746,46749],{"className":46745},[247],[212,46747],{"className":46748,"style":252},[251],[212,46750,46752,46755],{"className":46751},[256],[212,46753,234],{"className":46754,"style":258},[256,257],[212,46756,46758],{"className":46757},[478],[212,46759,46761,46781],{"className":46760},[482,483],[212,46762,46764,46778],{"className":46763},[487],[212,46765,46767],{"className":46766,"style":45129},[491],[212,46768,46769,46772],{"style":27709},[212,46770],{"className":46771,"style":500},[499],[212,46773,46775],{"className":46774},[504,505,506,507],[212,46776,44954],{"className":46777,"style":44984},[256,257,507],[212,46779,515],{"className":46780},[514],[212,46782,46784],{"className":46783},[487],[212,46785,46787],{"className":46786,"style":8166},[491],[212,46788],{},[212,46790,46792,46813],{"className":46791,"translate":216},[215],[212,46793,46795],{"className":46794},[220],[222,46796,46797],{"xmlns":224},[226,46798,46799,46810],{},[229,46800,46801,46803,46805,46808],{},[232,46802,44954],{},[307,46804,1228],{},[307,46806,46807],{},"±",[312,46809,314],{},[236,46811,46812],{"encoding":238},"\\alpha\\to\\pm1",[212,46814,46816,46834],{"className":46815,"ariaHidden":243},[242],[212,46817,46819,46822,46825,46828,46831],{"className":46818},[247],[212,46820],{"className":46821,"style":2543},[251],[212,46823,44954],{"className":46824,"style":44984},[256,257],[212,46826],{"className":46827,"style":355},[354],[212,46829,1228],{"className":46830},[359],[212,46832],{"className":46833,"style":355},[354],[212,46835,46837,46840,46843],{"className":46836},[247],[212,46838],{"className":46839,"style":12778},[251],[212,46841,46807],{"className":46842},[256],[212,46844,314],{"className":46845},[256]," 时逐点发散，但",[1194,46848,46849],{},"散度值","收敛到 KL：",[212,46852,46854],{"className":46853,"translate":216},[377],[212,46855,46857,46986],{"className":46856,"translate":216},[215],[212,46858,46860],{"className":46859},[220],[222,46861,46862],{"xmlns":224,"display":386},[226,46863,46864,46983],{},[229,46865,46866,46883,46889,46891,46893,46895,46897,46899,46901,46911,46913,46915,46917,46919,46921,46923,46925,46943,46949,46951,46953,46955,46957,46959,46961,46971,46973,46975,46977,46979,46981],{},[6214,46867,46868,46875],{},[229,46869,46870,46873],{},[232,46871,46872],{},"lim",[307,46874,4301],{},[229,46876,46877,46879,46881],{},[232,46878,44954],{},[307,46880,1228],{},[312,46882,314],{},[392,46884,46885,46887],{},[232,46886,396],{},[232,46888,44954],{},[307,46890,310],{"stretchy":309},[232,46892,403],{},[232,46894,407],{"mathvariant":406},[232,46896,410],{},[307,46898,317],{"stretchy":309},[307,46900,320],{},[392,46902,46903,46905],{},[232,46904,396],{},[229,46906,46907,46909],{},[232,46908,10894],{},[232,46910,22093],{},[307,46912,310],{"stretchy":309},[232,46914,403],{},[232,46916,407],{"mathvariant":406},[232,46918,410],{},[307,46920,317],{"stretchy":309},[307,46922,748],{"separator":243},[354,46924],{"width":3460},[6214,46926,46927,46933],{},[229,46928,46929,46931],{},[232,46930,46872],{},[307,46932,4301],{},[229,46934,46935,46937,46939,46941],{},[232,46936,44954],{},[307,46938,1228],{},[307,46940,5011],{},[312,46942,314],{},[392,46944,46945,46947],{},[232,46946,396],{},[232,46948,44954],{},[307,46950,310],{"stretchy":309},[232,46952,403],{},[232,46954,407],{"mathvariant":406},[232,46956,410],{},[307,46958,317],{"stretchy":309},[307,46960,320],{},[392,46962,46963,46965],{},[232,46964,396],{},[229,46966,46967,46969],{},[232,46968,10894],{},[232,46970,22093],{},[307,46972,310],{"stretchy":309},[232,46974,410],{},[232,46976,407],{"mathvariant":406},[232,46978,403],{},[307,46980,317],{"stretchy":309},[232,46982,4573],{"mathvariant":406},[236,46984,46985],{"encoding":238},"\\lim_{\\alpha\\to1}D_\\alpha(P\\|Q)=D_{KL}(P\\|Q),\n\\qquad\n\\lim_{\\alpha\\to-1}D_\\alpha(P\\|Q)=D_{KL}(Q\\|P).",[212,46987,46989,47118,47319],{"className":46988,"ariaHidden":243},[242],[212,46990,46992,46996,47051,47054,47094,47097,47100,47103,47106,47109,47112,47115],{"className":46991},[247],[212,46993],{"className":46994,"style":46995},[251],"height:1.4671em;vertical-align:-0.7171em;",[212,46997,46999],{"className":46998},[1682,13916],[212,47000,47002,47042],{"className":47001},[482,483],[212,47003,47005,47039],{"className":47004},[487],[212,47006,47008,47029],{"className":47007,"style":12797},[491],[212,47009,47011,47014],{"style":47010},"top:-2.3829em;margin-left:0em;",[212,47012],{"className":47013,"style":658},[499],[212,47015,47017],{"className":47016},[504,505,506,507],[212,47018,47020,47023,47026],{"className":47019},[256,507],[212,47021,44954],{"className":47022,"style":44984},[256,257,507],[212,47024,1228],{"className":47025},[359,507],[212,47027,314],{"className":47028},[256,507],[212,47030,47031,47034],{"style":12063},[212,47032],{"className":47033,"style":658},[499],[212,47035,47036],{},[212,47037,46872],{"className":47038},[1682],[212,47040,515],{"className":47041},[514],[212,47043,47045],{"className":47044},[487],[212,47046,47049],{"className":47047,"style":47048},[491],"height:0.7171em;",[212,47050],{},[212,47052],{"className":47053,"style":603},[354],[212,47055,47057,47060],{"className":47056},[256],[212,47058,396],{"className":47059,"style":474},[256,257],[212,47061,47063],{"className":47062},[478],[212,47064,47066,47086],{"className":47065},[482,483],[212,47067,47069,47083],{"className":47068},[487],[212,47070,47072],{"className":47071,"style":45129},[491],[212,47073,47074,47077],{"style":495},[212,47075],{"className":47076,"style":500},[499],[212,47078,47080],{"className":47079},[504,505,506,507],[212,47081,44954],{"className":47082,"style":44984},[256,257,507],[212,47084,515],{"className":47085},[514],[212,47087,47089],{"className":47088},[487],[212,47090,47092],{"className":47091,"style":8166},[491],[212,47093],{},[212,47095,310],{"className":47096},[343],[212,47098,403],{"className":47099,"style":531},[256,257],[212,47101,407],{"className":47102},[256],[212,47104,410],{"className":47105},[256,257],[212,47107,317],{"className":47108},[350],[212,47110],{"className":47111,"style":355},[354],[212,47113,320],{"className":47114},[359],[212,47116],{"className":47117,"style":355},[354],[212,47119,47121,47125,47171,47174,47177,47180,47183,47186,47189,47192,47195,47252,47255,47295,47298,47301,47304,47307,47310,47313,47316],{"className":47120},[247],[212,47122],{"className":47123,"style":47124},[251],"height:1.5254em;vertical-align:-0.7754em;",[212,47126,47128,47131],{"className":47127},[256],[212,47129,396],{"className":47130,"style":474},[256,257],[212,47132,47134],{"className":47133},[478],[212,47135,47137,47163],{"className":47136},[482,483],[212,47138,47140,47160],{"className":47139},[487],[212,47141,47143],{"className":47142,"style":576},[491],[212,47144,47145,47148]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0v40h399900v-40z",[212,49104,49106,49109],{"style":49105},"top:-2.0919em;",[212,49107],{"className":49108,"style":500},[499],[212,49110,49112],{"className":49111},[504,505,506,507,49081],[212,49113,49115,49118,49121],{"className":49114},[256,507],[212,49116,15912],{"className":49117,"style":15961},[256,257,507],[212,49119,1228],{"className":49120},[359,507],[212,49122,323],{"className":49123},[256,507],[212,49125,515],{"className":49126},[514],[212,49128,49130],{"className":49129},[487],[212,49131,49134],{"className":49132,"style":49133},[491],"height:0.6081em;",[212,49135],{},[212,49137],{"className":49138,"style":355},[354],[212,49140,49142,49145],{"className":49141},[256],[212,49143,396],{"className":49144,"style":474},[256,257],[212,49146,49148],{"className":49147},[478],[212,49149,49151,49177],{"className":49150},[482,483],[212,49152,49154,49174],{"className":49153},[487],[212,49155,49157],{"className":49156,"style":576},[491],[212,49158,49159,49162],{"style":495},[212,49160],{"className":49161,"style":500},[499],[212,49163,49165],{"className":49164},[504,505,506,507],[212,49166,49168,49171],{"className":49167},[256,507],[212,49169,10894],{"className":49170,"style":10982},[256,257,507],[212,49172,22093],{"className":49173},[256,257,507],[212,49175,515],{"className":49176},[514],[212,49178,49180],{"className":49179},[487],[212,49181,49183],{"className":49182,"style":8166},[491],[212,49184],{},[212,49186,310],{"className":49187},[343],[212,49189,403],{"className":49190,"style":531},[256,257],[212,49192,407],{"className":49193},[256],[212,49195,410],{"className":49196},[256,257],[212,49198,317],{"className":49199},[350],[212,49201,4573],{"className":49202},[256],[212,49204,515],{"className":49205},[514],[212,49207,49209],{"className":49208},[487],[212,49210,49212],{"className":49211,"style":48671},[491],[212,49213],{},[11,49215,49216,49272,49273,49302],{},[212,49217,49219,49239],{"className":49218,"translate":216},[215],[212,49220,49222],{"className":49221},[220],[222,49223,49224],{"xmlns":224},[226,49225,49226,49236],{},[229,49227,49228,49230,49232,49234],{},[232,49229,44954],{},[307,49231,1228],{},[307,49233,5011],{},[312,49235,314],{},[236,49237,49238],{"encoding":238},"\\alpha\\to-1",[212,49240,49242,49260],{"className":49241,"ariaHidden":243},[242],[212,49243,49245,49248,49251,49254,49257],{"className":49244},[247],[212,49246],{"className":49247,"style":2543},[251],[212,49249,44954],{"className":49250,"style":44984},[256,257],[212,49252],{"className":49253,"style":355},[354],[212,49255,1228],{"className":49256},[359],[212,49258],{"className":49259,"style":355},[354],[212,49261,49263,49266,49269],{"className":49262},[247],[212,49264],{"className":49265,"style":12778},[251],[212,49267,5011],{"className":49268},[256],[212,49270,314],{"className":49271},[256]," 对称地给出反向 KL。所以 α-散度把 KL（两个方向）与 Hellinger 连成一条曲线，",[212,49274,49276,49290],{"className":49275,"translate":216},[215],[212,49277,49279],{"className":49278},[220],[222,49280,49281],{"xmlns":224},[226,49282,49283,49287],{},[229,49284,49285],{},[232,49286,44954],{},[236,49288,49289],{"encoding":238},"\\alpha",[212,49291,49293],{"className":49292,"ariaHidden":243},[242],[212,49294,49296,49299],{"className":49295},[247],[212,49297],{"className":49298,"style":2543},[251],[212,49300,44954],{"className":49301,"style":44984},[256,257]," 是「在对称与不对称之间连续插值」的旋钮。",[11,49304,49305,49307,49308,49336,49337,49371,49372,49400,49401,49451,49452,49455,49456,49484,49485,49513,49514,49542,49543,49571],{},[1194,49306,24393],{}," α-散度的价值在于它把「方向」与「强度」一并参数化：",[212,49309,49311,49324],{"className":49310,"translate":216},[215],[212,49312,49314],{"className":49313},[220],[222,49315,49316],{"xmlns":224},[226,49317,49318,49322],{},[229,49319,49320],{},[232,49321,44954],{},[236,49323,49289],{"encoding":238},[212,49325,49327],{"className":49326,"ariaHidden":243},[242],[212,49328,49330,49333],{"className":49329},[247],[212,49331],{"className":49332,"style":2543},[251],[212,49334,44954],{"className":49335,"style":44984},[256,257]," 从 ",[212,49338,49340,49356],{"className":49339,"translate":216},[215],[212,49341,49343],{"className":49342},[220],[222,49344,49345],{"xmlns":224},[226,49346,49347,49353],{},[229,49348,49349,49351],{},[307,49350,5011],{},[312,49352,314],{},[236,49354,49355],{"encoding":238},"-1",[212,49357,49359],{"className":49358,"ariaHidden":243},[242],[212,49360,49362,49365,49368],{"className":49361},[247],[212,49363],{"className":49364,"style":12778},[251],[212,49366,5011],{"className":49367},[256],[212,49369,314],{"className":49370},[256]," 扫到 ",[212,49373,49375,49388],{"className":49374,"translate":216},[215],[212,49376,49378],{"className":49377},[220],[222,49379,49380],{"xmlns":224},[226,49381,49382,49386],{},[229,49383,49384],{},[312,49385,314],{},[236,49387,314],{"encoding":238},[212,49389,49391],{"className":49390,"ariaHidden":243},[242],[212,49392,49394,49397],{"className":49393},[247],[212,49395],{"className":49396,"style":369},[251],[212,49398,314],{"className":49399},[256]," 时，散度由反向 KL（mode-seeking）连续过渡到正向 KL（mass-covering），中间在 ",[212,49402,49404,49421],{"className":49403,"translate":216},[215],[212,49405,49407],{"className":49406},[220],[222,49408,49409],{"xmlns":224},[226,49410,49411,49419],{},[229,49412,49413,49415,49417],{},[232,49414,44954],{},[307,49416,320],{},[312,49418,323],{},[236,49420,46687],{"encoding":238},[212,49422,49424,49442],{"className":49423,"ariaHidden":243},[242],[212,49425,49427,49430,49433,49436,49439],{"className":49426},[247],[212,49428],{"className":49429,"style":2543},[251],[212,49431,44954],{"className":49432,"style":44984},[256,257],[212,49434],{"className":49435,"style":355},[354],[212,49437,320],{"className":49438},[359],[212,49440],{"className":49441,"style":355},[354],[212,49443,49445,49448],{"className":49444},[247],[212,49446],{"className":49447,"style":369},[251],[212,49449,323],{"className":49450},[256]," 处恰好经过 Hellinger 这个对称点。在 Amari 的",[1194,49453,49454],{},"信息几何","里，α-族是唯一同时拥有 ",[212,49457,49459,49472],{"className":49458,"translate":216},[215],[212,49460,49462],{"className":49461},[220],[222,49463,49464],{"xmlns":224},[226,49465,49466,49470],{},[229,49467,49468],{},[232,49469,44954],{},[236,49471,49289],{"encoding":238},[212,49473,49475],{"className":49474,"ariaHidden":243},[242],[212,49476,49478,49481],{"className":49477},[247],[212,49479],{"className":49480,"style":2543},[251],[212,49482,44954],{"className":49483,"style":44984},[256,257],"-对偶平坦结构的单参数散度族：它诱导的度量是 Fisher 度量，诱导的仿射联络是 ",[212,49486,49488,49501],{"className":49487,"translate":216},[215],[212,49489,49491],{"className":49490},[220],[222,49492,49493],{"xmlns":224},[226,49494,49495,49499],{},[229,49496,49497],{},[232,49498,44954],{},[236,49500,49289],{"encoding":238},[212,49502,49504],{"className":49503,"ariaHidden":243},[242],[212,49505,49507,49510],{"className":49506},[247],[212,49508],{"className":49509,"style":2543},[251],[212,49511,44954],{"className":49512,"style":44984},[256,257],"-联络，这正是它被称为「散度范本」的原因。在机器学习中，",[212,49515,49517,49530],{"className":49516,"translate":216},[215],[212,49518,49520],{"className":49519},[220],[222,49521,49522],{"xmlns":224},[226,49523,49524,49528],{},[229,49525,49526],{},[232,49527,44954],{},[236,49529,49289],{"encoding":238},[212,49531,49533],{"className":49532,"ariaHidden":243},[242],[212,49534,49536,49539],{"className":49535},[247],[212,49537],{"className":49538,"style":2543},[251],[212,49540,44954],{"className":49541,"style":44984},[256,257],"-GAN 与 ",[212,49544,49546,49559],{"className":49545,"translate":216},[215],[212,49547,49549],{"className":49548},[220],[222,49550,49551],{"xmlns":224},[226,49552,49553,49557],{},[229,49554,49555],{},[232,49556,44954],{},[236,49558,49289],{"encoding":238},[212,49560,49562],{"className":49561,"ariaHidden":243},[242],[212,49563,49565,49568],{"className":49564},[247],[212,49566],{"className":49567,"style":2543},[251],[212,49569,44954],{"className":49570,"style":44984},[256,257],"-VI 用一个参数调节「对异常值的鲁棒性」与「模式覆盖」之间的取舍；在信号处理中它用于独立成分分析（ICA）与鲁棒估计。",[2509,49573,49575],{"id":49574},"_37-与-rényi-散度的关系","3.7 与 Rényi 散度的关系",[11,49577,49578],{},"Rényi 散度定义为",[212,49580,49582],{"className":49581,"translate":216},[377],[212,49583,49585,49713],{"className":49584,"translate":216},[215],[212,49586,49588],{"className":49587},[220],[222,49589,49590],{"xmlns":224,"display":386},[226,49591,49592,49710],{},[1441,49593,49594,49674],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,49595,49596,49620],{},[1450,49597,49598],{},[1453,49599,49600],{"scriptlevel":323,"displaystyle":243},[229,49601,49602,49610,49612,49614,49616,49618],{},[7751,49603,49604,49606,49608],{},[232,49605,396],{},[232,49607,44954],{},[232,49609,1231],{},[307,49611,310],{"stretchy":309},[232,49613,403],{},[232,49615,407],{"mathvariant":406},[232,49617,410],{},[307,49619,317],{"stretchy":309},[1450,49621,49622],{},[1453,49623,49624],{"scriptlevel":323,"displaystyle":243},[229,49625,49626,49628,49630,49642,49644,49646,49648,49654,49666,49668,49670,49672],{},[229,49627],{},[307,49629,320],{},[435,49631,49632,49634],{},[312,49633,314],{},[229,49635,49636,49638,49640],{},[232,49637,44954],{},[307,49639,5011],{},[312,49641,314],{},[232,49643,4298],{},[307,49645,4301],{},[307,49647,1485],{},[7012,49649,49650,49652],{},[232,49651,11],{},[232,49653,44954],{},[7012,49655,49656,49658],{},[232,49657,1141],{},[229,49659,49660,49662,49664],{},[312,49661,314],{},[307,49663,5011],{},[232,49665,44954],{},[1495,49667,1497],{},[232,49669,441],{},[232,49671,971],{},[307,49673,748],{"separator":243},[1447,49675,49676,49682],{},[1450,49677,49678],{},[1453,49679,49680],{"scriptlevel":323,"displaystyle":243},[229,49681],{},[1450,49683,49684],{},[1453,49685,49686],{"scriptlevel":323,"displaystyle":243},[229,49687,49688,49690,49692,49694,49696,49698,49700,49702,49704,49707],{},[229,49689],{},[354,49691],{"width":3460},[232,49693,44954],{},[307,49695,3101],{},[312,49697,323],{},[307,49699,748],{"separator":243},[1495,49701,4481],{},[232,49703,44954],{},[307,49705,49706],{"mathvariant":406},"≠",[312,49708,49709],{},"1.",[236,49711,49712],{"encoding":238},"\\begin{aligned}\nD^{R}_{\\alpha}(P\\|Q)\n&=\\frac{1}{\\alpha-1}\n\\log\\int p^{\\alpha}q^{1-\\alpha}\\,dx,\\\\[2pt]\n&\\qquad \\alpha>0,\\ \\alpha\\ne1 .\n\\end{aligned}",[212,49714,49716],{"className":49715,"ariaHidden":243},[242],[212,49717,49719,49723],{"className":49718},[247],[212,49720],{"className":49721,"style":49722},[251],"height:3.7223em;vertical-align:-1.6111em;",[212,49724,49726],{"className":49725},[256],[212,49727,49729,49846],{"className":49728},[1441],[212,49730,49732],{"className":49731},[1558],[212,49733,49735,49837],{"className":49734},[482,483],[212,49736,49738,49834],{"className":49737},[487],[212,49739,49742,49825],{"className":49740,"style":49741},[491],"height:2.1111em;",[212,49743,49745,49748],{"style":49744},"top:-4.1111em;",[212,49746],{"className":49747,"style":6471},[499],[212,49749,49751,49810,49813,49816,49819,49822],{"className":49750},[256],[212,49752,49754,49757],{"className":49753},[256],[212,49755,396],{"className":49756,"style":474},[256,257],[212,49758,49760],{"className":49759},[478],[212,49761,49763,49802],{"className":49762},[482,483],[212,49764,49766,49799],{"className":49765},[487],[212,49767,49769,49784],{"className":49768,"style":38712},[491],[212,49770,49772,49775],{"style":49771},"top:-2.453em;margin-left:-0.0278em;margin-right:0.05em;",[212,49773],{"className":49774,"style":500},[499],[212,49776,49778],{"className":49777},[504,505,506,507],[212,49779,49781],{"className":49780},[256,507],[212,49782,44954],{"className":49783,"style":44984},[256,257,507],[212,49785,49786,49789],{"style":8475},[212,49787],{"className":49788,"style":500},[499],[212,49790,49792],{"className":49791},[504,505,506,507],[212,49793,49795],{"className":49794},[256,507],[212,49796,1231],{"className":49797,"style":49798},[256,257,507],"margin-right:0.0077em;",[212,49800,515],{"className":49801},[514],[212,49803,49805],{"className":49804},[487],[212,49806,49808],{"className":49807,"style":8497},[491],[212,49809],{},[212,49811,310],{"className":49812},[343],[212,49814,403],{"className":49815,"style":531},[256,257],[212,49817,407],{"className":49818},[256],[212,49820,410],{"className":49821},[256,257],[212,49823,317],{"className":49824},[350],[212,49826,49828,49831],{"style":49827},"top:-2.1089em;",[212,49829],{"className":49830,"style":6471},[499],[212,49832],{"className":49833},[256],[212,49835,515],{"className":49836},[514],[212,49838,49840],{"className":49839},[487],[212,49841,49844],{"className":49842,"style":49843},[491],"height:1.6111em;",[212,49845],{},[212,49847,49849],{"className":49848},[1649],[212,49850,49852,50140],{"className":49851},[482,483],[212,49853,49855,50137],{"className":49854},[487],[212,49856,49858,50051],{"className":49857,"style":49741},[491],[212,49859,49860,49863],{"style":49744},[212,49861],{"className":49862,"style":6471},[499],[212,49864,49866,49869,49872,49875,49878,49952,49955,49960,49963,49966,49969,50001,50039,50042,50045,50048],{"className":49865},[256],[212,49867],{"className":49868},[256],[212,49870],{"className":49871,"style":355},[354],[212,49873,320],{"className":49874},[359],[212,49876],{"className":49877,"style":355},[354],[212,49879,49881,49884,49949],{"className":49880},[256],[212,49882],{"className":49883},[343,638],[212,49885,49887],{"className":49886},[435],[212,49888,49890,49941],{"className":49889},[482,483],[212,49891,49893,49938],{"className":49892},[487],[212,49894,49896,49919,49927],{"className":49895,"style":23089},[491],[212,49897,49898,49901],{"style":654},[212,49899],{"className":49900,"style":658},[499],[212,49902,49904,49907,49910,49913,49916],{"className":49903},[256],[212,49905,44954],{"className":49906,"style":44984},[256,257],[212,49908],{"className":49909,"style":2785},[354],[212,49911,5011],{"className":49912},[2789],[212,49914],{"className":49915,"style":2785},[354],[212,49917,314],{"className":49918},[256],[212,49920,49921,49924],{"style":670},[212,49922],{"className":49923,"style":658},[499],[212,49925],{"className":49926,"style":678},[677],[212,49928,49929,49932],{"style":681},[212,49930],{"className":49931,"style":658},[499],[212,49933,49935],{"className":49934},[256],[212,49936,314],{"className":49937},[256],[212,49939,515],{"className":49940},[514],[212,49942,49944],{"className":49943},[487],[212,49945,49947],{"className":49946,"style":17215},[491],[212,49948],{},[212,49950],{"className":49951},[350,638],[212,49953],{"className":49954,"style":603},[354],[212,49956,4352,49958],{"className":49957},[1682],[212,49959,4356],{"style":4355},[212,49961],{"className":49962,"style":603},[354],[212,49964,1485],{"className":49965,"style":1685},[1682,1683,1684],[212,49967],{"className":49968,"style":603},[354],[212,49970,49972,49975],{"className":49971},[256],[212,49973,11],{"className":49974},[256,257],[212,49976,49978],{"className":49977},[478],[212,49979,49981],{"className":49980},[482],[212,49982,49984],{"className":49983},[487],[212,49985,49987],{"className":49986,"style":46110},[491],[212,49988,49989,49992],{"style":8475},[212,49990],{"className":49991,"style":500},[499],[212,49993,49995],{"className":49994},[504,505,506,507],[212,49996,49998],{"className":49997},[256,507],[212,49999,44954],{"className":50000,"style":44984},[256,257,507],[212,50002,50004,50007],{"className":50003},[256],[212,50005,1141],{"className":50006,"style":1178},[256,257],[212,50008,50010],{"className":50009},[478],[212,50011,50013],{"className":50012},[482],[212,50014,50016],{"className":50015},[487],[212,50017,50019],{"className":50018,"style":19935},[491],[212,50020,50021,50024],{"style":8475},[212,50022],{"className":50023,"style":500},[499],[212,50025,50027],{"className":50026},[504,505,506,507],[212,50028,50030,50033,50036],{"className":50029},[256,507],[212,50031,314],{"className":50032},[256,507],[212,50034,5011],{"className":50035},[2789,507],[212,50037,44954],{"className":50038,"style":44984},[256,257,507],[212,50040],{"className":50041,"style":603},[354],[212,50043,441],{"className":50044},[256,257],[212,50046,971],{"className":50047},[256,257],[212,50049,748],{"className":50050},[770],[212,50052,50053,50056],{"style":49827},[212,50054],{"className":50055,"style":6471},[499],[212,50057,50059,50062,50065,50068,50071,50074,50077,50080,50083,50086,50089,50092,50095,50131,50134],{"className":50058},[256],[212,50060],{"className":50061},[256],[212,50063],{"className":50064,"style":3832},[354],[212,50066,44954],{"className":50067,"style":44984},[256,257],[212,50069],{"className":50070,"style":355},[354],[212,50072,3101],{"className":50073},[359],[212,50075],{"className":50076,"style":355},[354],[212,50078,323],{"className":50079},[256],[212,50081,748],{"className":50082},[770],[212,50084,4481],{"className":50085},[354],[212,50087],{"className":50088,"style":603},[354],[212,50090,44954],{"className":50091,"style":44984},[256,257],[212,50093],{"className":50094,"style":355},[354],[212,50096,50098,50125,50128],{"className":50097},[359],[212,50099,50101],{"className":50100},[359],[212,50102,50104],{"className":50103},[256,4598],[212,50105,50107],{"className":50106},[4602],[212,50108,50110,50113,50122],{"className":50109},[4606],[212,50111],{"className":50112,"style":252},[251],[212,50114,50116],{"className":50115},[4613],[212,50117,50119],{"className":50118},[256],[212,50120,4620],{"className":50121},[359],[212,50123],{"className":50124},[4624],[212,50126],{"className":50127},[354,4628],[212,50129,320],{"className":50130},[359],[212,50132],{"className":50133,"style":355},[354],[212,50135,49709],{"className":50136},[256],[212,50138,515],{"className":50139},[514],[212,50141,50143],{"className":50142},[487],[212,50144,50146],{"className":50145,"style":49843},[491],[212,50147],{},[11,50149,50150,50151,50183,50184,50235,50236,50412,50413,50614],{},"它不是（直接的）f-散度，因为 ",[212,50152,50154,50169],{"className":50153,"translate":216},[215],[212,50155,50157],{"className":50156},[220],[222,50158,50159],{"xmlns":224},[226,50160,50161,50167],{},[229,50162,50163,50165],{},[232,50164,4298],{},[307,50166,4301],{},[236,50168,21783],{"encoding":238},[212,50170,50172],{"className":50171,"ariaHidden":243},[242],[212,50173,50175,50178],{"className":50174},[247],[212,50176],{"className":50177,"style":252},[251],[212,50179,4352,50181],{"className":50180},[1682],[212,50182,4356],{"style":4355}," 包在积分外面（这正是它满足可乘可加性、但一般不满足数据处理不等式的根源：",[212,50185,50187,50205],{"className":50186,"translate":216},[215],[212,50188,50190],{"className":50189},[220],[222,50191,50192],{"xmlns":224},[226,50193,50194,50202],{},[229,50195,50196,50198,50200],{},[232,50197,44954],{},[307,50199,3101],{},[312,50201,314],{},[236,50203,50204],{"encoding":238},"\\alpha>1",[212,50206,50208,50226],{"className":50207,"ariaHidden":243},[242],[212,50209,50211,50214,50217,50220,50223],{"className":50210},[247],[212,50212],{"className":50213,"style":6122},[251],[212,50215,44954],{"className":50216,"style":44984},[256,257],[212,50218],{"className":50219,"style":355},[354],[212,50221,3101],{"className":50222},[359],[212,50224],{"className":50225,"style":355},[354],[212,50227,50229,50232],{"className":50228},[247],[212,50230],{"className":50231,"style":369},[251],[212,50233,314],{"className":50234},[256]," 的 Rényi 散度可以在随机变换下增大）。它与 α-散度是\"同一积分的两种包装\"：沿用 3.6 节的指数记号 ",[212,50237,50239,50278],{"className":50238,"translate":216},[215],[212,50240,50242],{"className":50241},[220],[222,50243,50244],{"xmlns":224},[226,50245,50246,50276],{},[229,50247,50248,50250,50252,50264,50266,50268,50270,50272,50274],{},[232,50249,15],{},[307,50251,320],{},[435,50253,50254,50262],{},[229,50255,50256,50258,50260],{},[312,50257,314],{},[307,50259,2668],{},[232,50261,44954],{},[312,50263,2661],{},[307,50265,6107],{},[307,50267,310],{"stretchy":309},[312,50269,323],{},[307,50271,748],{"separator":243},[312,50273,314],{},[307,50275,317],{"stretchy":309},[236,50277,45408],{"encoding":238},[212,50279,50281,50299,50388],{"className":50280,"ariaHidden":243},[242],[212,50282,50284,50287,50290,50293,50296],{"className":50283},[247],[212,50285],{"className":50286,"style":2543},[251],[212,50288,15],{"className":50289},[256,257],[212,50291],{"className":50292,"style":355},[354],[212,50294,320],{"className":50295},[359],[212,50297],{"className":50298,"style":355},[354],[212,50300,50302,50305,50379,50382,50385],{"className":50301},[247],[212,50303],{"className":50304,"style":2703},[251],[212,50306,50308,50311,50376],{"className":50307},[256],[212,50309],{"className":50310},[343,638],[212,50312,50314],{"className":50313},[435],[212,50315,50317,50368],{"className":50316},[482,483],[212,50318,50320,50365],{"className":50319},[487],[212,50321,50323,50337,50345],{"className":50322,"style":2722},[491],[212,50324,50325,50328],{"style":2725},[212,50326],{"className":50327,"style":658},[499],[212,50329,50331],{"className":50330},[504,505,506,507],[212,50332,50334],{"className":50333},[256,507],[212,50335,2661],{"className":50336},[256,507],[212,50338,50339,50342],{"style":670},[212,50340],{"className":50341,"style":658},[499],[212,50343],{"className":50344,"style":678},[677],[212,50346,50347,50350],{"style":2748},[212,50348],{"className":50349,"style":658},[499],[212,50351,50353],{"className":50352},[504,505,506,507],[212,50354,50356,50359,50362],{"className":50355},[256,507],[212,50357,314],{"className":50358},[256,507],[212,50360,2668],{"className":50361},[2789,507],[212,50363,44954],{"className":50364,"style":44984},[256,257,507],[212,50366,515],{"className":50367},[514],[212,50369,50371],{"className":50370},[487],[212,50372,50374],{"className":50373,"style":2770},[491],[212,50375],{},[212,50377],{"className":50378},[350,638],[212,50380],{"className":50381,"style":355},[354],[212,50383,6107],{"className":50384},[359],[212,50386],{"className":50387,"style":355},[354],[212,50389,50391,50394,50397,50400,50403,50406,50409],{"className":50390},[247],[212,50392],{"className":50393,"style":336},[251],[212,50395,310],{"className":50396},[343],[212,50398,323],{"className":50399},[256],[212,50401,748],{"className":50402},[770],[212,50404],{"className":50405,"style":603},[354],[212,50407,314],{"className":50408},[256],[212,50410,317],{"className":50411},[350],"， ",[212,50414,50416,50462],{"className":50415,"translate":216},[215],[212,50417,50419],{"className":50418},[220],[222,50420,50421],{"xmlns":224},[226,50422,50423,50459],{},[229,50424,50425,50431,50433,50435,50441,50453,50455,50457],{},[392,50426,50427,50429],{},[232,50428,33803],{},[232,50430,15],{},[307,50432,320],{},[307,50434,1485],{},[7012,50436,50437,50439],{},[232,50438,11],{},[232,50440,15],{},[7012,50442,50443,50445],{},[232,50444,1141],{},[229,50446,50447,50449,50451],{},[312,50448,314],{},[307,50450,5011],{},[232,50452,15],{},[1495,50454,1497],{},[232,50456,441],{},[232,50458,971],{},[236,50460,50461],{"encoding":238},"Z_a=\\int p^{a}q^{1-a}\\,dx",[212,50463,50465,50521],{"className":50464,"ariaHidden":243},[242],[212,50466,50468,50471,50512,50515,50518],{"className":50467},[247],[212,50469],{"className":50470,"style":16161},[251],[212,50472,50474,50477],{"className":50473},[256],[212,50475,33803],{"className":50476,"style":10982},[256,257],[212,50478,50480],{"className":50479},[478],[212,50481,50483,50504],{"className":50482},[482,483],[212,50484,50486,50501],{"className":50485},[487],[212,50487,50489],{"className":50488,"style":45129},[491],[212,50490,50492,50495],{"style":50491},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[212,50493],{"className":50494,"style":500},[499],[212,50496,50498],{"className":50497},[504,505,506,507],[212,50499,15],{"className":50500},[256,257,507],[212,50502,515],{"className":50503},[514],[212,50505,50507],{"className":50506},[487],[212,50508,50510],{"className":50509,"style":8166},[491],[212,50511],{},[212,50513],{"className":50514,"style":355},[354],[212,50516,320],{"className":50517},[359],[212,50519],{"className":50520,"style":355},[354],[212,50522,50524,50528,50531,50534,50567,50605,50608,50611],{"className":50523},[247],[212,50525],{"className":50526,"style":50527},[251],"height:1.1202em;vertical-align:-0.3061em;",[212,50529,1485],{"className":50530,"style":5815},[1682,1683,5814],[212,50532],{"className":50533,"style":603},[354],[212,50535,50537,50540],{"className":50536},[256],[212,50538,11],{"className":50539},[256,257],[212,50541,50543],{"className":50542},[478],[212,50544,50546],{"className":50545},[482],[212,50547,50549],{"className":50548},[487],[212,50550,50553],{"className":50551,"style":50552},[491],"height:0.6644em;",[212,50554,50555,50558],{"style":7063},[212,50556],{"className":50557,"style":500},[499],[212,50559,50561],{"className":50560},[504,505,506,507],[212,50562,50564],{"className":50563},[256,507],[212,50565,15],{"className":50566},[256,257,507],[212,50568,50570,50573],{"className":50569},[256],[212,50571,1141],{"className":50572,"style":1178},[256,257],[212,50574,50576],{"className":50575},[478],[212,50577,50579],{"className":50578},[482],[212,50580,50582],{"className":50581},[487],[212,50583,50585],{"className":50584,"style":20228},[491],[212,50586,50587,50590],{"style":7063},[212,50588],{"className":50589,"style":500},[499],[212,50591,50593],{"className":50592},[504,505,506,507],[212,50594,50596,50599,50602],{"className":50595},[256,507],[212,50597,314],{"className":50598},[256,507],[212,50600,5011],{"className":50601},[2789,507],[212,50603,15],{"className":50604},[256,257,507],[212,50606],{"className":50607,"style":603},[354],[212,50609,441],{"className":50610},[256,257],[212,50612,971],{"className":50613},[256,257],"，则 3.6 节给出",[212,50616,50618],{"className":50617,"translate":216},[377],[212,50619,50621,50667],{"className":50620,"translate":216},[215],[212,50622,50624],{"className":50623},[220],[222,50625,50626],{"xmlns":224,"display":386},[226,50627,50628,50664],{},[229,50629,50630,50636,50638,50640,50642,50644,50646,50648,50650,50652,50654,50656,50662],{},[392,50631,50632,50634],{},[232,50633,33803],{},[232,50635,15],{},[307,50637,320],{},[312,50639,314],{},[307,50641,5011],{},[232,50643,15],{},[307,50645,310],{"stretchy":309},[312,50647,314],{},[307,50649,5011],{},[232,50651,15],{},[307,50653,317],{"stretchy":309},[1495,50655,1497],{},[392,50657,50658,50660],{},[232,50659,396],{},[232,50661,44954],{},[307,50663,748],{"separator":243},[236,50665,50666],{"encoding":238},"Z_a=1-a(1-a)\\,D_\\alpha ,",[212,50668,50670,50725,50743,50767],{"className":50669,"ariaHidden":243},[242],[212,50671,50673,50676,50716,50719,50722],{"className":50672},[247],[212,50674],{"className":50675,"style":16161},[251],[212,50677,50679,50682],{"className":50678},[256],[212,50680,33803],{"className":50681,"style":10982},[256,257],[212,50683,50685],{"className":50684},[478],[212,50686,50688,50708],{"className":50687},[482,483],[212,50689,50691,50705],{"className":50690},[487],[212,50692,50694],{"className":50693,"style":45129},[491],[212,50695,50696,50699],{"style":50491},[212,50697],{"className":50698,"style":500},[499],[212,50700,50702],{"className":50701},[504,505,506,507],[212,50703,15],{"className":50704},[256,257,507],[212,50706,515],{"className":50707},[514],[212,50709,50711],{"className":50710},[487],[212,50712,50714],{"className":50713,"style":8166},[491],[212,50715],{},[212,50717],{"className":50718,"style":355},[354],[212,50720,320],{"className":50721},[359],[212,50723],{"className":50724,"style":355},[354],[212,50726,50728,50731,50734,50737,50740],{"className":50727},[247],[212,50729],{"className":50730,"style":12778},[251],[212,50732,314],{"className":50733},[256],[212,50735],{"className":50736,"style":2785},[354],[212,50738,5011],{"className":50739},[2789],[212,50741],{"className":50742,"style":2785},[354],[212,50744,50746,50749,50752,50755,50758,50761,50764],{"className":50745},[247],[212,50747],{"className":50748,"style":336},[251],[212,50750,15],{"className":50751},[256,257],[212,50753,310],{"className":50754},[343],[212,50756,314],{"className":50757},[256],[212,50759],{"className":50760,"style":2785},[354],[212,50762,5011],{"className":50763},[2789],[212,50765],{"className":50766,"style":2785},[354],[212,50768,50770,50773,50776,50779,50782,50822],{"className":50769},[247],[212,50771],{"className":50772,"style":336},[251],[212,50774,15],{"className":50775},[256,257],[212,50777,317],{"className":50778},[350],[212,50780],{"className":50781,"style":603},[354],[212,50783,50785,50788],{"className":50784},[256],[212,50786,396],{"className":50787,"style":474},[256,257],[212,50789,50791],{"className":50790},[478],[212,50792,50794,50814],{"className":50793},[482,483],[212,50795,50797,50811],{"className":50796},[487],[212,50798,50800],{"className":50799,"style":45129},[491],[212,50801,50802,50805],{"style":495},[212,50803],{"className":50804,"style":500},[499],[212,50806,50808],{"className":50807},[504,505,506,507],[212,50809,44954],{"className":50810,"style":44984},[256,257,507],[212,50812,515],{"className":50813},[514],[212,50815,50817],{"className":50816},[487],[212,50818,50820],{"className":50819,"style":8166},[491],[212,50821],{},[212,50823,748],{"className":50824},[770],[11,50826,50827,50828,50831,50832,50860,50861,50923,50924,50952],{},"而把 Rényi 的",[1194,50829,50830],{},"阶数","取为 ",[212,50833,50835,50848],{"className":50834,"translate":216},[215],[212,50836,50838],{"className":50837},[220],[222,50839,50840],{"xmlns":224},[226,50841,50842,50846],{},[229,50843,50844],{},[232,50845,15],{},[236,50847,15],{"encoding":238},[212,50849,50851],{"className":50850,"ariaHidden":243},[242],[212,50852,50854,50857],{"className":50853},[247],[212,50855],{"className":50856,"style":2543},[251],[212,50858,15],{"className":50859},[256,257],"（注意 order ",[212,50862,50864,50878],{"className":50863,"translate":216},[215],[212,50865,50867],{"className":50866},[220],[222,50868,50869],{"xmlns":224},[226,50870,50871,50875],{},[229,50872,50873],{},[307,50874,49706],{"mathvariant":406},[236,50876,50877],{"encoding":238},"\\neq",[212,50879,50881],{"className":50880,"ariaHidden":243},[242],[212,50882,50884,50887],{"className":50883},[247],[212,50885],{"className":50886,"style":252},[251],[212,50888,50890,50917,50920],{"className":50889},[359],[212,50891,50893],{"className":50892},[359],[212,50894,50896],{"className":50895},[256,4598],[212,50897,50899],{"className":50898},[4602],[212,50900,50902,50905,50914],{"className":50901},[4606],[212,50903],{"className":50904,"style":252},[251],[212,50906,50908],{"className":50907},[4613],[212,50909,50911],{"className":50910},[256],[212,50912,4620],{"className":50913},[359],[212,50915],{"className":50916},[4624],[212,50918],{"className":50919},[354,4628],[212,50921,320],{"className":50922},[359]," 3.6 的参数 ",[212,50925,50927,50940],{"className":50926,"translate":216},[215],[212,50928,50930],{"className":50929},[220],[222,50931,50932],{"xmlns":224},[226,50933,50934,50938],{},[229,50935,50936],{},[232,50937,44954],{},[236,50939,49289],{"encoding":238},[212,50941,50943],{"className":50942,"ariaHidden":243},[242],[212,50944,50946,50949],{"className":50945},[247],[212,50947],{"className":50948,"style":2543},[251],[212,50950,44954],{"className":50951,"style":44984},[256,257],"，只是经过线性换算）：",[212,50954,50956],{"className":50955,"translate":216},[377],[212,50957,50959,51063],{"className":50958,"translate":216},[215],[212,50960,50962],{"className":50961},[220],[222,50963,50964],{"xmlns":224,"display":386},[226,50965,50966,51060],{},[229,50967,50968,50976,50978,50980,50982,50984,50986,50988,51000,51002,51004,51010,51012,51014,51026,51028,51030,51032,51034,51036,51038,51040,51042,51044,51046,51048,51050,51056,51058],{},[7751,50969,50970,50972,50974],{},[232,50971,396],{},[232,50973,15],{},[232,50975,1231],{},[307,50977,310],{"stretchy":309},[232,50979,403],{},[232,50981,407],{"mathvariant":406},[232,50983,410],{},[307,50985,317],{"stretchy":309},[307,50987,320],{},[435,50989,50990,50992],{},[312,50991,314],{},[229,50993,50994,50996,50998],{},[232,50995,15],{},[307,50997,5011],{},[312,50999,314],{},[232,51001,4298],{},[307,51003,4301],{},[392,51005,51006,51008],{},[232,51007,33803],{},[232,51009,15],{},[307,51011,320],{},[307,51013,5011],{},[435,51015,51016,51018],{},[312,51017,314],{},[229,51019,51020,51022,51024],{},[312,51021,314],{},[307,51023,5011],{},[232,51025,15],{},[1495,51027,1497],{},[232,51029,4298],{},[307,51031,4301],{},[307,51033,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[312,51035,314],{},[307,51037,5011],{},[232,51039,15],{},[307,51041,310],{"stretchy":309},[312,51043,314],{},[307,51045,5011],{},[232,51047,15],{},[307,51049,317],{"stretchy":309},[392,51051,51052,51054],{},[232,51053,396],{},[232,51055,44954],{},[307,51057,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,51059,4573],{"mathvariant":406},[236,51061,51062],{"encoding":238},"D^{R}_{a}(P\\|Q)=\\frac{1}{a-1}\\log Z_a\n=-\\frac{1}{1-a}\\,\\log\\big(1-a(1-a)D_\\alpha\\big).",[212,51064,51066,51154,51294,51409,51433],{"className":51065,"ariaHidden":243},[242],[212,51067,51069,51073,51130,51133,51136,51139,51142,51145,51148,51151],{"className":51068},[247],[212,51070],{"className":51071,"style":51072},[251],"height:1.1413em;vertical-align:-0.25em;",[212,51074,51076,51079],{"className":51075},[256],[212,51077,396],{"className":51078,"style":474},[256,257],[212,51080,51082],{"className":51081},[478],[212,51083,51085,51122],{"className":51084},[482,483],[212,51086,51088,51119],{"className":51087},[487],[212,51089,51091,51105],{"className":51090,"style":38712},[491],[212,51092,51093,51096],{"style":49771},[212,51094],{"className":51095,"style":500},[499],[212,51097,51099],{"className":51098},[504,505,506,507],[212,51100,51102],{"className":51101},[256,507],[212,51103,15],{"className":51104},[256,257,507],[212,51106,51107,51110],{"style":8475},[212,51108],{"className":51109,"style":500},[499],[212,51111,51113],{"className":51112},[504,505,506,507],[212,51114,51116],{"className":51115},[256,507],[212,51117,1231],{"className":51118,"style":49798},[256,257,507],[212,51120,515],{"className":51121},[514],[212,51123,51125],{"className":51124},[487],[212,51126,51128],{"className":51127,"style":8497},[491],[212,51129],{},[212,51131,310],{"className":51132},[343],[212,51134,403],{"className":51135,"style":531},[256,257],[212,51137,407],{"className":51138},[256],[212,51140,410],{"className":51141},[256,257],[212,51143,317],{"className":51144},[350],[212,51146],{"className":51147,"style":355},[354],[212,51149,320],{"className":51150},[359],[212,51152],{"className":51153,"style":355},[354],[212,51155,51157,51160,51234,51237,51242,51245,51285,51288,51291],{"className":51156},[247],[212,51158],{"className":51159,"style":26816},[251],[212,51161,51163,51166,51231],{"className":51162},[256],[212,51164],{"className":51165},[343,638],[212,51167,51169],{"className":51168},[435],[212,51170,51172,51223],{"className":51171},[482,483],[212,51173,51175,51220],{"className":51174},[487],[212,51176,51178,51201,51209],{"className":51177,"style":23089},[491],[212,51179,51180,51183],{"style":654},[212,51181],{"className":51182,"style":658},[499],[212,51184,51186,51189,51192,51195,51198],{"className":51185},[256],[212,51187,15],{"className":51188},[256,257],[212,51190],{"className":51191,"style":2785},[354],[212,51193,5011],{"className":51194},[2789],[212,51196],{"className":51197,"style":2785},[354],[212,51199,314],{"className":51200},[256],[212,51202,51203,51206],{"style":670},[212,51204],{"className":51205,"style":658},[499],[212,51207],{"className":51208,"style":678},[677],[212,51210,51211,51214],{"style":681},[212,51212],{"className":51213,"style":658},[499],[212,51215,51217],{"className":51216},[256],[212,51218,314],{"className":51219},[256],[212,51221,515],{"className":51222},[514],[212,51224,51226],{"className":51225},[487],[212,51227,51229],{"className":51228,"style":17215},[491],[212,51230],{},[212,51232],{"className":51233},[350,638],[212,51235],{"className":51236,"style":603},[354],[212,51238,4352,51240],{"className":51239},[1682],[212,51241,4356],{"style":4355},[212,51243],{"className":51244,"style":603},[354],[212,51246,51248,51251],{"className":51247},[256],[212,51249,33803],{"className":51250,"style":10982},[256,257],[212,51252,51254],{"className":51253},[478],[212,51255,51257,51277],{"className":51256},[482,483],[212,51258,51260,51274],{"className":51259},[487],[212,51261,51263],{"className":51262,"style":45129},[491],[212,51264,51265,51268],{"style":50491},[212,51266],{"className":51267,"style":500},[499],[212,51269,51271],{"className":51270},[504,505,506,507],[212,51272,15],{"className":51273},[256,257,507],[212,51275,515],{"className":51276},[514],[212,51278,51280],{"className":51279},[487],[212,51281,51283],{"className":51282,"style":8166},[491],[212,51284],{},[212,51286],{"className":51287,"style":355},[354],[212,51289,320],{"className":51290},[359],[212,51292],{"className":51293,"style":355},[354],[212,51295,51297,51300,51303,51377,51380,51383,51388,51391,51397,51400,51403,51406],{"className":51296},[247],[212,51298],{"className":51299,"style":26816},[251],[212,51301,5011],{"className":51302},[256],[212,51304,51306,51309,51374],{"className":51305},[256],[212,51307],{"className":51308},[343,638],[212,51310,51312],{"className":51311},[435],[212,51313,51315,51366],{"className":51314},[482,483],[212,51316,51318,51363],{"className":51317},[487],[212,51319,51321,51344,51352],{"className":51320,"style":23089},[491],[212,51322,51323,51326],{"style":654},[212,51324],{"className":51325,"style":658},[499],[212,51327,51329,51332,51335,51338,51341],{"className":51328},[256],[212,51330,314],{"className":51331},[256],[212,51333],{"className":51334,"style":2785},[354],[212,51336,5011],{"className":51337},[2789],[212,51339],{"className":51340,"style":2785},[354],[212,51342,15],{"className":51343},[256,257],[212,51345,51346,51349],{"style":670},[212,51347],{"className":51348,"style":658},[499],[212,51350],{"className":51351,"style":678},[677],[212,51353,51354,51357],{"style":681},[212,51355],{"className":51356,"style":658},[499],[212,51358,51360],{"className":51359},[256],[212,51361,314],{"className":51362},[256],[212,51364,515],{"className":51365},[514],[212,51367,51369],{"className":51368},[487],[212,51370,51372],{"className":51371,"style":17215},[491],[212,51373],{},[212,51375],{"className":51376},[350,638],[212,51378],{"className":51379,"style":603},[354],[212,51381],{"className":51382,"style":603},[354],[212,51384,4352,51386],{"className":51385},[1682],[212,51387,4356],{"style":4355},[212,51389],{"className":51390,"style":603},[354],[212,51392,51394],{"className":51393},[256],[212,51395,310],{"className":51396},[616,9872],[212,51398,314],{"className":51399},[256],[212,51401],{"className":51402,"style":2785},[354],[212,51404,5011],{"className":51405},[2789],[212,51407],{"className":51408,"style":2785},[354],[212,51410,51412,51415,51418,51421,51424,51427,51430],{"className":51411},[247],[212,51413],{"className":51414,"style":336},[251],[212,51416,15],{"className":51417},[256,257],[212,51419,310],{"className":51420},[343],[212,51422,314],{"className":51423},[256],[212,51425],{"className":51426,"style":2785},[354],[212,51428,5011],{"className":51429},[2789],[212,51431],{"className":51432,"style":2785},[354],[212,51434,51436,51439,51442,51445,51485,51491],{"className":51435},[247],[212,51437],{"className":51438,"style":20763},[251],[212,51440,15],{"className":51441},[256,257],[212,51443,317],{"className":51444},[350],[212,51446,51448,51451],{"className":51447},[256],[212,51449,396],{"className":51450,"style":474},[256,257],[212,51452,51454],{"className":51453},[478],[212,51455,51457,51477],{"className":51456},[482,483],[212,51458,51460,51474],{"className":51459},[487],[212,51461,51463],{"className":51462,"style":45129},[491],[212,51464,51465,51468],{"style":495},[212,51466],{"className":51467,"style":500},[499],[212,51469,51471],{"className":51470},[504,505,506,507],[212,51472,44954],{"className":51473,"style":44984},[256,257,507],[212,51475,515],{"className":51476},[514],[212,51478,51480],{"className":51479},[487],[212,51481,51483],{"className":51482,"style":8166},[491],[212,51484],{},[212,51486,51488],{"className":51487},[256],[212,51489,317],{"className":51490},[616,9872],[212,51492,4573],{"className":51493},[256],[11,51495,51496,51497,51644,51645,51673,51674,51706],{},"这说明两者是一条\"幂—对数\"的两级包装链：f-散度是对似然比幂 ",[212,51498,51500,51526],{"className":51499,"translate":216},[215],[212,51501,51503],{"className":51502},[220],[222,51504,51505],{"xmlns":224},[226,51506,51507,51523],{},[229,51508,51509,51511,51517],{},[307,51510,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[435,51512,51513,51515],{},[232,51514,11],{},[232,51516,1141],{},[7012,51518,51519,51521],{},[307,51520,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,51522,15],{},[236,51524,51525],{"encoding":238},"\\big(\\frac pq\\big)^a",[212,51527,51529],{"className":51528,"ariaHidden":243},[242],[212,51530,51532,51536,51542,51610],{"className":51531},[247],[212,51533],{"className":51534,"style":51535},[251],"height:1.3854em;vertical-align:-0.4811em;",[212,51537,51539],{"className":51538},[256],[212,51540,310],{"className":51541},[616,9872],[212,51543,51545,51548,51607],{"className":51544},[256],[212,51546],{"className":51547},[343,638],[212,51549,51551],{"className":51550},[435],[212,51552,51554,51599],{"className":51553},[482,483],[212,51555,51557,51596],{"className":51556},[487],[212,51558,51560,51574,51582],{"className":51559,"style":3301},[491],[212,51561,51562,51565],{"style":2725},[212,51563],{"className":51564,"style":658},[499],[212,51566,51568],{"className":51567},[504,505,506,507],[212,51569,51571],{"className":51570},[256,507],[212,51572,1141],{"className":51573,"style":1178},[256,257,507],[212,51575,51576,51579],{"style":670},[212,51577],{"className":51578,"style":658},[499],[212,51580],{"className":51581,"style":678},[677],[212,51583,51584,51587],{"style":3051},[212,51585],{"className":51586,"style":658},[499],[212,51588,51590],{"className":51589},[504,505,506,507],[212,51591,51593],{"className":51592},[256,507],[212,51594,11],{"className":51595},[256,257,507],[212,51597,515],{"className":51598},[514],[212,51600,51602],{"className":51601},[487],[212,51603,51605],{"className":51604,"style":2937},[491],[212,51606],{},[212,51608],{"className":51609},[350,638],[212,51611,51613,51619],{"className":51612},[256],[212,51614,51616],{"className":51615},[256],[212,51617,317],{"className":51618},[616,9872],[212,51620,51622],{"className":51621},[478],[212,51623,51625],{"className":51624},[482],[212,51626,51628],{"className":51627},[487],[212,51629,51632],{"className":51630,"style":51631},[491],"height:0.9043em;",[212,51633,51635,51638],{"style":51634},"top:-3.3029em;margin-right:0.05em;",[212,51636],{"className":51637,"style":500},[499],[212,51639,51641],{"className":51640},[504,505,506,507],[212,51642,15],{"className":51643},[256,257,507]," 做 ",[212,51646,51648,51661],{"className":51647,"translate":216},[215],[212,51649,51651],{"className":51650},[220],[222,51652,51653],{"xmlns":224},[226,51654,51655,51659],{},[229,51656,51657],{},[232,51658,410],{},[236,51660,410],{"encoding":238},[212,51662,51664],{"className":51663,"ariaHidden":243},[242],[212,51665,51667,51670],{"className":51666},[247],[212,51668],{"className":51669,"style":763},[251],[212,51671,410],{"className":51672},[256,257]," 下的线性平均，Rényi 在外面再套一层对数。所以 f-散度族与 Rényi 族\"同源\"：后者是前者经 ",[212,51675,51677,51692],{"className":51676,"translate":216},[215],[212,51678,51680],{"className":51679},[220],[222,51681,51682],{"xmlns":224},[226,51683,51684,51690],{},[229,51685,51686,51688],{},[232,51687,4298],{},[307,51689,4301],{},[236,51691,21783],{"encoding":238},[212,51693,51695],{"className":51694,"ariaHidden":243},[242],[212,51696,51698,51701],{"className":51697},[247],[212,51699],{"className":51700,"style":252},[251],[212,51702,4352,51704],{"className":51703},[1682],[212,51705,4356],{"style":4355}," 变换后的\"信息量\"版本。",[11,51708,51709,51711,51712,51715],{},[1194,51710,24393],{}," Rényi 散度在",[1194,51713,51714],{},"假设检验","中直接就是误差指数：Chernoff 信息",[212,51717,51719],{"className":51718,"translate":216},[377],[212,51720,51722,51845],{"className":51721,"translate":216},[215],[212,51723,51725],{"className":51724},[220],[222,51726,51727],{"xmlns":224,"display":386},[226,51728,51729,51842],{},[229,51730,51731,51733,51735,51737,51739,51741,51743,51745,51765,51767,51769,51771,51773,51775,51783,51785,51787,51789,51791,51793,51795,51797,51799,51801,51822,51824,51830],{},[232,51732,39494],{},[307,51734,310],{"stretchy":309},[232,51736,403],{},[307,51738,748],{"separator":243},[232,51740,410],{},[307,51742,317],{"stretchy":309},[307,51744,320],{},[6214,51746,51747,51753],{},[229,51748,51749,51751],{},[232,51750,35632],{},[307,51752,4301],{},[229,51754,51755,51757,51759,51761,51763],{},[312,51756,323],{},[307,51758,7449],{},[232,51760,11539],{},[307,51762,7449],{},[312,51764,314],{},[307,51766,310],{"stretchy":309},[312,51768,314],{},[307,51770,5011],{},[232,51772,11539],{},[307,51774,317],{"stretchy":309},[7751,51776,51777,51779,51781],{},[232,51778,396],{},[232,51780,11539],{},[232,51782,1231],{},[307,51784,310],{"stretchy":309},[232,51786,403],{},[232,51788,407],{"mathvariant":406},[232,51790,410],{},[307,51792,317],{"stretchy":309},[307,51794,320],{},[307,51796,5011],{},[232,51798,4298],{},[307,51800,4301],{},[6214,51802,51803,51810],{},[229,51804,51805,51808],{},[232,51806,51807],{},"min",[307,51809,4301],{},[229,51811,51812,51814,51816,51818,51820],{},[312,51813,323],{},[307,51815,10150],{},[232,51817,11539],{},[307,51819,10150],{},[312,51821,314],{},[307,51823,1485],{},[7012,51825,51826,51828],{},[232,51827,11],{},[232,51829,11539],{},[7012,51831,51832,51834],{},[232,51833,1141],{},[229,51835,51836,51838,51840],{},[312,51837,314],{},[307,51839,5011],{},[232,51841,11539],{},[236,51843,51844],{"encoding":238},"C(P,Q)=\\sup_{0\u003C\\lambda\u003C1}\n(1-\\lambda)D^{R}_{\\lambda}(P\\|Q)\n=-\\log\\min_{0\\le\\lambda\\le1}\n\\int p^\\lambda q^{1-\\lambda}",[212,51846,51848,51884,51967,52060],{"className":51847,"ariaHidden":243},[242],[212,51849,51851,51854,51857,51860,51863,51866,51869,51872,51875,51878,51881],{"className":51850},[247],[212,51852],{"className":51853,"style":336},[251],[212,51855,39494],{"className":51856,"style":10982},[256,257],[212,51858,310],{"className":51859},[343],[212,51861,403],{"className":51862,"style":531},[256,257],[212,51864,748],{"className":51865},[770],[212,51867],{"className":51868,"style":603},[354],[212,51870,410],{"className":51871},[256,257],[212,51873,317],{"className":51874},[350],[212,51876],{"className":51877,"style":355},[354],[212,51879,320],{"className":51880},[359],[212,51882],{"className":51883,"style":355},[354],[212,51885,51887,51891,51952,51955,51958,51961,51964],{"className":51886},[247],[212,51888],{"className":51889,"style":51890},[251],"height:1.7239em;vertical-align:-0.9739em;",[212,51892,51894],{"className":51893},[1682,13916],[212,51895,51897,51943],{"className":51896},[482,483],[212,51898,51900,51940],{"className":51899},[487],[212,51901,51903,51930],{"className":51902,"style":2543},[491],[212,51904,51906,51909],{"style":51905},"top:-2.1535em;margin-left:0em;",[212,51907],{"className":51908,"style":658},[499],[212,51910,51912],{"className":51911},[504,505,506,507],[212,51913,51915,51918,51921,51924,51927],{"className":51914},[256,507],[212,51916,323],{"className":51917},[256,507],[212,51919,7449],{"className":51920},[359,507],[212,51922,11539],{"className":51923},[256,257,507],[212,51925,7449],{"className":51926},[359,507],[212,51928,314],{"className":51929},[256,507],[212,51931,51932,51935],{"style":12063},[212,51933],{"className":51934,"style":658},[499],[212,51936,51937],{},[212,51938,35632],{"className":51939},[1682],[212,51941,515],{"className":51942},[514],[212,51944,51946],{"className":51945},[487],[212,51947,51950],{"className":51948,"style":51949},[491],"height:0.9739em;",[212,51951],{},[212,51953,310],{"className":51954},[343],[212,51956,314],{"className":51957},[256],[212,51959],{"className":51960,"style":2785},[354],[212,51962,5011],{"className":51963},[2789],[212,51965],{"className":51966,"style":2785},[354],[212,51968,51970,51973,51976,51979,52036,52039,52042,52045,52048,52051,52054,52057],{"className":51969},[247],[212,51971],{"className":51972,"style":51072},[251],[212,51974,11539],{"className":51975},[256,257],[212,51977,317],{"className":51978},[350],[212,51980,51982,51985],{"className":51981},[256],[212,51983,396],{"className":51984,"style":474},[256,257],[212,51986,51988],{"className":51987},[478],[212,51989,51991,52028],{"className":51990},[482,483],[212,51992,51994,52025],{"className":51993},[487],[212,51995,51997,52011],{"className":51996,"style":38712},[491],[212,51998,51999,52002],{"style":49771},[212,52000],{"className":52001,"style":500},[499],[212,52003,52005],{"className":52004},[504,505,506,507],[212,52006,52008],{"className":52007},[256,507],[212,52009,11539],{"className":52010},[256,257,507],[212,52012,52013,52016],{"style":8475},[212,52014],{"className":52015,"style":500},[499],[212,52017,52019],{"className":52018},[504,505,506,507],[212,52020,52022],{"className":52021},[256,507],[212,52023,1231],{"className":52024,"style":49798},[256,257,507],[212,52026,515],{"className":52027},[514],[212,52029,52031],{"className":52030},[487],[212,52032,52034],{"className":52033,"style":8497},[491],[212,52035],{},[212,52037,310],{"className":52038},[343],[212,52040,403],{"className":52041,"style":531},[256,257],[212,52043,407],{"className":52044},[256],[212,52046,410],{"className":52047},[256,257],[212,52049,317],{"className":52050},[350],[212,52052],{"className":52053,"style":355},[354],[212,52055,320],{"className":52056},[359],[212,52058],{"className":52059,"style":355},[354],[212,52061,52063,52066,52069,52072,52077,52080,52142,52145,52148,52151,52180],{"className":52062},[247],[212,52064],{"className":52065,"style":5975},[251],[212,52067,5011],{"className":52068},[256],[212,52070],{"className":52071,"style":603},[354],[212,52073,4352,52075],{"className":52074},[1682],[212,52076,4356],{"style":4355},[212,52078],{"className":52079,"style":603},[354],[212,52081,52083],{"className":52082},[1682,13916],[212,52084,52086,52133],{"className":52085},[482,483],[212,52087,52089,52130],{"className":52088},[487],[212,52090,52093,52120],{"className":52091,"style":52092},[491],"height:0.6679em;",[212,52094,52096,52099],{"style":52095},"top:-2.3479em;margin-left:0em;",[212,52097],{"className":52098,"style":658},[499],[212,52100,52102],{"className":52101},[504,505,506,507],[212,52103,52105,52108,52111,52114,52117],{"className":52104},[256,507],[212,52106,323],{"className":52107},[256,507],[212,52109,10150],{"className":52110},[359,507],[212,52112,11539],{"className":52113},[256,257,507],[212,52115,10150],{"className":52116},[359,507],[212,52118,314],{"className":52119},[256,507],[212,52121,52122,52125],{"style":12063},[212,52123],{"className":52124,"style":658},[499],[212,52126,52127],{},[212,52128,51807],{"className":52129},[1682],[212,52131,515],{"className":52132},[514],[212,52134,52136],{"className":52135},[487],[212,52137,52140],{"className":52138,"style":52139},[491],"height:0.8473em;",[212,52141],{},[212,52143],{"className":52144,"style":603},[354],[212,52146,1485],{"className":52147,"style":1685},[1682,1683,1684],[212,52149],{"className":52150,"style":603},[354],[212,52152,52154,52157],{"className":52153},[256],[212,52155,11],{"className":52156},[256,257],[212,52158,52160],{"className":52159},[478],[212,52161,52163],{"className":52162},[482],[212,52164,52166],{"className":52165},[487],[212,52167,52169],{"className":52168,"style":48063},[491],[212,52170,52171,52174],{"style":8475},[212,52172],{"className":52173,"style":500},[499],[212,52175,52177],{"className":52176},[504,505,506,507],[212,52178,11539],{"className":52179},[256,257,507],[212,52181,52183,52186],{"className":52182},[256],[212,52184,1141],{"className":52185,"style":1178},[256,257],[212,52187,52189],{"className":52188},[478],[212,52190,52192],{"className":52191},[482],[212,52193,52195],{"className":52194},[487],[212,52196,52198],{"className":52197,"style":48063},[491],[212,52199,52200,52203],{"style":8475},[212,52201],{"className":52202,"style":500},[499],[212,52204,52206],{"className":52205},[504,505,506,507],[212,52207,52209,52212,52215],{"className":52208},[256,507],[212,52210,314],{"className":52211},[256,507],[212,52213,5011],{"className":52214},[2789,507],[212,52216,11539],{"className":52217},[256,257,507],[11,52219,52220,52221,52387,52388,4051,52459,52509,52510,52561,52562,52681,52682,52685],{},"决定对称检验错误概率的衰减速率，Stein 引理给出的单侧指数则是 ",[212,52222,52224,52256],{"className":52223,"translate":216},[215],[212,52225,52227],{"className":52226},[220],[222,52228,52229],{"xmlns":224},[226,52230,52231,52253],{},[229,52232,52233,52241,52243],{},[7751,52234,52235,52237,52239],{},[232,52236,396],{},[312,52238,314],{},[232,52240,1231],{},[307,52242,320],{},[392,52244,52245,52247],{},[232,52246,396],{},[229,52248,52249,52251],{},[232,52250,10894],{},[232,52252,22093],{},[236,52254,52255],{"encoding":238},"D^{R}_{1}=D_{KL}",[212,52257,52259,52335],{"className":52258,"ariaHidden":243},[242],[212,52260,52262,52266,52326,52329,52332],{"className":52261},[247],[212,52263],{"className":52264,"style":52265},[251],"height:1.0894em;vertical-align:-0.2481em;",[212,52267,52269,52272],{"className":52268},[256],[212,52270,396],{"className":52271,"style":474},[256,257],[212,52273,52275],{"className":52274},[478],[212,52276,52278,52317],{"className":52277},[482,483],[212,52279,52281,52314],{"className":52280},[487],[212,52282,52285,52300],{"className":52283,"style":52284},[491],"height:0.8413em;",[212,52286,52288,52291],{"style":52287},"top:-2.4519em;margin-left:-0.0278em;margin-right:0.05em;",[212,52289],{"className":52290,"style":500},[499],[212,52292,52294],{"className":52293},[504,505,506,507],[212,52295,52297],{"className":52296},[256,507],[212,52298,314],{"className":52299},[256,507],[212,52301,52302,52305],{"style":7063},[212,52303],{"className":52304,"style":500},[499],[212,52306,52308],{"className":52307},[504,505,506,507],[212,52309,52311],{"className":52310},[256,507],[212,52312,1231],{"className":52313,"style":49798},[256,257,507],[212,52315,515],{"className":52316},[514],[212,52318,52320],{"className":52319},[487],[212,52321,52324],{"className":52322,"style":52323},[491],"height:0.2481em;",[212,52325],{},[212,52327],{"className":52328,"style":355},[354],[212,52330,320],{"className":52331},[359],[212,52333],{"className":52334,"style":355},[354],[212,52336,52338,52341],{"className":52337},[247],[212,52339],{"className":52340,"style":16161},[251],[212,52342,52344,52347],{"className":52343},[256],[212,52345,396],{"className":52346,"style":474},[256,257],[212,52348,52350],{"className":52349},[478],[212,52351,52353,52379],{"className":52352},[482,483],[212,52354,52356,52376],{"className":52355},[487],[212,52357,52359],{"className":52358,"style":576},[491],[212,52360,52361,52364],{"style":495},[212,52362],{"className":52363,"style":500},[499],[212,52365,52367],{"className":52366},[504,505,506,507],[212,52368,52370,52373],{"className":52369},[256,507],[212,52371,10894],{"className":52372,"style":10982},[256,257,507],[212,52374,22093],{"className":52375},[256,257,507],[212,52377,515],{"className":52378},[514],[212,52380,52382],{"className":52381},[487],[212,52383,52385],{"className":52384,"style":8166},[491],[212,52386],{},"。对应的 Rényi 熵 ",[212,52389,52391,52409],{"className":52390,"translate":216},[215],[212,52392,52394],{"className":52393},[220],[222,52395,52396],{"xmlns":224},[226,52397,52398,52406],{},[229,52399,52400],{},[392,52401,52402,52404],{},[232,52403,34084],{},[232,52405,44954],{},[236,52407,52408],{"encoding":238},"H_\\alpha",[212,52410,52412],{"className":52411,"ariaHidden":243},[242],[212,52413,52415,52418],{"className":52414},[247],[212,52416],{"className":52417,"style":16161},[251],[212,52419,52421,52424],{"className":52420},[256],[212,52422,34084],{"className":52423,"style":34238},[256,257],[212,52425,52427],{"className":52426},[478],[212,52428,52430,52451],{"className":52429},[482,483],[212,52431,52433,52448],{"className":52432},[487],[212,52434,52436],{"className":52435,"style":45129},[491],[212,52437,52439,52442],{"style":52438},"top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;",[212,52440],{"className":52441,"style":500},[499],[212,52443,52445],{"className":52444},[504,505,506,507],[212,52446,44954],{"className":52447,"style":44984},[256,257,507],[212,52449,515],{"className":52450},[514],[212,52452,52454],{"className":52453},[487],[212,52455,52457],{"className":52456,"style":8166},[491],[212,52458],{},[212,52460,52462,52479],{"className":52461,"translate":216},[215],[212,52463,52465],{"className":52464},[220],[222,52466,52467],{"xmlns":224},[226,52468,52469,52477],{},[229,52470,52471,52473,52475],{},[232,52472,44954],{},[307,52474,1228],{},[312,52476,314],{},[236,52478,47414],{"encoding":238},[212,52480,52482,52500],{"className":52481,"ariaHidden":243},[242],[212,52483,52485,52488,52491,52494,52497],{"className":52484},[247],[212,52486],{"className":52487,"style":2543},[251],[212,52489,44954],{"className":52490,"style":44984},[256,257],[212,52492],{"className":52493,"style":355},[354],[212,52495,1228],{"className":52496},[359],[212,52498],{"className":52499,"style":355},[354],[212,52501,52503,52506],{"className":52502},[247],[212,52504],{"className":52505,"style":369},[251],[212,52507,314],{"className":52508},[256]," 时退化为 Shannon 熵、在 ",[212,52511,52513,52531],{"className":52512,"translate":216},[215],[212,52514,52516],{"className":52515},[220],[222,52517,52518],{"xmlns":224},[226,52519,52520,52528],{},[229,52521,52522,52524,52526],{},[232,52523,44954],{},[307,52525,1228],{},[232,52527,1223],{"mathvariant":406},[236,52529,52530],{"encoding":238},"\\alpha\\to\\infty",[212,52532,52534,52552],{"className":52533,"ariaHidden":243},[242],[212,52535,52537,52540,52543,52546,52549],{"className":52536},[247],[212,52538],{"className":52539,"style":2543},[251],[212,52541,44954],{"className":52542,"style":44984},[256,257],[212,52544],{"className":52545,"style":355},[354],[212,52547,1228],{"className":52548},[359],[212,52550],{"className":52551,"style":355},[354],[212,52553,52555,52558],{"className":52554},[247],[212,52556],{"className":52557,"style":2543},[251],[212,52559,1223],{"className":52560},[256]," 时退化为 min-entropy ",[212,52563,52565,52602],{"className":52564,"translate":216},[215],[212,52566,52568],{"className":52567},[220],[222,52569,52570],{"xmlns":224},[226,52571,52572,52599],{},[229,52573,52574,52576,52578,52580,52591,52593,52595,52597],{},[307,52575,5011],{},[232,52577,4298],{},[307,52579,4301],{},[392,52581,52582,52589],{},[229,52583,52584,52587],{},[232,52585,52586],{},"max",[307,52588,4301],{},[232,52590,971],{},[232,52592,11],{},[307,52594,310],{"stretchy":309},[232,52596,971],{},[307,52598,317],{"stretchy":309},[236,52600,52601],{"encoding":238},"-\\log\\max_x p(x)",[212,52603,52605],{"className":52604,"ariaHidden":243},[242],[212,52606,52608,52611,52614,52617,52622,52625,52666,52669,52672,52675,52678],{"className":52607},[247],[212,52609],{"className":52610,"style":336},[251],[212,52612,5011],{"className":52613},[256],[212,52615],{"className":52616,"style":603},[354],[212,52618,4352,52620],{"className":52619},[1682],[212,52621,4356],{"style":4355},[212,52623],{"className":52624,"style":603},[354],[212,52626,52628,52631],{"className":52627},[1682],[212,52629,52586],{"className":52630},[1682],[212,52632,52634],{"className":52633},[478],[212,52635,52637,52658],{"className":52636},[482,483],[212,52638,52640,52655],{"className":52639},[487],[212,52641,52643],{"className":52642,"style":45129},[491],[212,52644,52646,52649],{"style":52645},"top:-2.55em;margin-right:0.05em;",[212,52647],{"className":52648,"style":500},[499],[212,52650,52652],{"className":52651},[504,505,506,507],[212,52653,971],{"className":52654},[256,257,507],[212,52656,515],{"className":52657},[514],[212,52659,52661],{"className":52660},[487],[212,52662,52664],{"className":52663,"style":8166},[491],[212,52665],{},[212,52667],{"className":52668,"style":603},[354],[212,52670,11],{"className":52671},[256,257],[212,52673,310],{"className":52674},[343],[212,52676,971],{"className":52677},[256,257],[212,52679,317],{"className":52680},[350],"，因此在密码学、随机性提取与 ",[1194,52683,52684],{},"Rényi 差分隐私（RDP）"," 中被用来对隐私预算做更紧致的记账。它与 f-散度族的\"同源\"关系也给出一条实用经验：讨论可加性、信息几何与变分表示时用 f-散度更顺手，讨论误差指数与熵时用它的对数版本更自然。",[2509,52687,52689],{"id":52688},"_38-汇总表","3.8 汇总表",[52691,52692,52693,52788],"table",{},[52694,52695,52696],"thead",{},[52697,52698,52699,52703,52749,52751,52754],"tr",{},[52700,52701,52702],"th",{},"散度",[52700,52704,52705],{},[212,52706,52708,52728],{"className":52707,"translate":216},[215],[212,52709,52711],{"className":52710},[220],[222,52712,52713],{"xmlns":224},[226,52714,52715,52725],{},[229,52716,52717,52719,52721,52723],{},[232,52718,234],{},[307,52720,310],{"stretchy":309},[232,52722,966],{},[307,52724,317],{"stretchy":309},[236,52726,52727],{"encoding":238},"f(t)",[212,52729,52731],{"className":52730,"ariaHidden":243},[242],[212,52732,52734,52737,52740,52743,52746],{"className":52733},[247],[212,52735],{"className":52736,"style":336},[251],[212,52738,234],{"className":52739,"style":258},[256,257],[212,52741,310],{"className":52742},[343],[212,52744,966],{"className":52745},[256,257],[212,52747,317],{"className":52748},[350],[52700,52750,29886],{},[52700,52752,52753],{},"有界",[52700,52755,52756,52787],{},[212,52757,52759,52775],{"className":52758,"translate":216},[215],[212,52760,52762],{"className":52761},[220],[222,52763,52764],{"xmlns":224},[226,52765,52766,52772],{},[229,52767,52768,52770],{},[232,52769,46872],{},[307,52771,4301],{},[236,52773,52774],{"encoding":238},"\\lim",[212,52776,52778],{"className":52777,"ariaHidden":243},[242],[212,52779,52781,52784],{"className":52780},[247],[212,52782],{"className":52783,"style":12797},[251],[212,52785,46872],{"className":52786},[1682]," 行为（不重叠支撑）",[52789,52790,52791,52992,53191,53319,53717,53936,54131,54411,54687],"tbody",{},[52697,52792,52793,52901,52952,52955,52957],{},[52794,52795,52796,52797],"td",{},"KL ",[212,52798,52800,52831],{"className":52799,"translate":216},[215],[212,52801,52803],{"className":52802},[220],[222,52804,52805],{"xmlns":224},[226,52806,52807,52829],{},[229,52808,52809,52819,52821,52823,52825,52827],{},[392,52810,52811,52813],{},[232,52812,396],{},[229,52814,52815,52817],{},[232,52816,10894],{},[232,52818,22093],{},[307,52820,310],{"stretchy":309},[232,52822,403],{},[232,52824,407],{"mathvariant":406},[232,52826,410],{},[307,52828,317],{"stretchy":309},[236,52830,24553],{"encoding":238},[212,52832,52834],{"className":52833,"ariaHidden":243},[242],[212,52835,52837,52840,52886,52889,52892,52895,52898],{"className":52836},[247],[212,52838],{"className":52839,"style":336},[251],[212,52841,52843,52846],{"className":52842},[256],[212,52844,396],{"className":52845,"style":474},[256,257],[212,52847,52849],{"className":52848},[478],[212,52850,52852,52878],{"className":52851},[482,483],[212,52853,52855,52875],{"className":52854},[487],[212,52856,52858],{"className":52857,"style":576},[491],[212,52859,52860,52863],{"style":495},[212,52861],{"className":52862,"style":500},[499],[212,52864,52866],{"className":52865},[504,505,506,507],[212,52867,52869,52872],{"className":52868},[256,507],[212,52870,10894],{"className":52871,"style":10982},[256,257,507],[212,52873,22093],{"className":52874},[256,257,507],[212,52876,515],{"className":52877},[514],[212,52879,52881],{"className":52880},[487],[212,52882,52884],{"className":52883,"style":8166},[491],[212,52885],{},[212,52887,310],{"className":52888},[343],[212,52890,403],{"className":52891,"style":531},[256,257],[212,52893,407],{"className":52894},[256],[212,52896,410],{"className":52897},[256,257],[212,52899,317],{"className":52900},[350],[52794,52902,52903],{},[212,52904,52906,52926],{"className":52905,"translate":216},[215],[212,52907,52909],{"className":52908},[220],[222,52910,52911],{"xmlns":224},[226,52912,52913,52923],{},[229,52914,52915,52917,52919,52921],{},[232,52916,966],{},[232,52918,4298],{},[307,52920,4301],{},[232,52922,966],{},[236,52924,52925],{"encoding":238},"t\\log 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KL 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",[212,54693,54695,54722],{"className":54694,"translate":216},[215],[212,54696,54698],{"className":54697},[220],[222,54699,54700],{"xmlns":224},[226,54701,54702,54720],{},[229,54703,54704,54706,54708,54710,54712,54714,54716,54718],{},[232,54705,44954],{},[307,54707,6107],{},[307,54709,310],{"stretchy":309},[307,54711,5011],{},[312,54713,314],{},[307,54715,748],{"separator":243},[312,54717,314],{},[307,54719,317],{"stretchy":309},[236,54721,44971],{"encoding":238},[212,54723,54725,54743],{"className":54724,"ariaHidden":243},[242],[212,54726,54728,54731,54734,54737,54740],{"className":54727},[247],[212,54729],{"className":54730,"style":6122},[251],[212,54732,44954],{"className":54733,"style":44984},[256,257],[212,54735],{"className":54736,"style":355},[354],[212,54738,6107],{"className":54739},[359],[212,54741],{"className":54742,"style":355},[354],[212,54744,54746,54749,54752,54755,54758,54761,54764,54767],{"className":54745},[247],[212,54747],{"className":54748,"style":336},[251],[212,54750,310],{"className":54751},[343],[212,54753,5011],{"className":54754},[256],[212,54756,314],{"className":54757},[256],[212,54759,748],{"className":54760},[770],[212,54762],{"className":54763,"style":603},[354],[212,54765,314],{"className":54766},[256],[212,54768,317],{"className":54769},[350],[52794,54771,54772],{},[212,54773,54775,54831],{"className":54774,"translate":216},[215],[212,54776,54778],{"className":54777},[220],[222,54779,54780],{"xmlns":224},[226,54781,54782,54828],{},[229,54783,54784,54800,54802,54804,54806,54826],{},[435,54785,54786,54788],{},[312,54787,39189],{},[229,54789,54790,54792,54794],{},[312,54791,314],{},[307,54793,5011],{},[7012,54795,54796,54798],{},[232,54797,44954],{},[312,54799,2661],{},[307,54801,310],{"stretchy":309},[312,54803,314],{},[307,54805,5011],{},[7012,54807,54808,54810],{},[232,54809,966],{},[229,54811,54812,54814,54816,54818,54820,54822,54824],{},[307,54813,310],{"stretchy":309},[312,54815,314],{},[307,54817,2668],{},[232,54819,44954],{},[307,54821,317],{"stretchy":309},[232,54823,1138],{"mathvariant":406},[312,54825,2661],{},[307,54827,317],{"stretchy":309},[236,54829,54830],{"encoding":238},"\\frac{4}{1-\\alpha^2}(1-t^{(1+\\alpha)\u002F2})",[212,54832,54834,54955],{"className":54833,"ariaHidden":243},[242],[212,54835,54837,54840,54940,54943,54946,54949,54952],{"className":54836},[247],[212,54838],{"className":54839,"style":45604},[251],[212,54841,54843,54846,54937],{"className":54842},[256],[212,54844],{"className":54845},[343,638],[212,54847,54849],{"className":54848},[435],[212,54850,54852,54929],{"className":54851},[482,483],[212,54853,54855,54926],{"className":54854},[487],[212,54856,54858,54904,54912],{"className":54857,"style":2722},[491],[212,54859,54860,54863],{"style":2725},[212,54861],{"className":54862,"style":658},[499],[212,54864,54866],{"className":54865},[504,505,506,507],[212,54867,54869,54872,54875],{"className":54868},[256,507],[212,54870,314],{"className":54871},[256,507],[212,54873,5011],{"className":54874},[2789,507],[212,54876,54878,54881],{"className":54877},[256,507],[212,54879,44954],{"className":54880,"style":44984},[256,257,507],[212,54882,54884],{"className":54883},[478],[212,54885,54887],{"className":54886},[482],[212,54888,54890],{"className":54889},[487],[212,54891,54893],{"className":54892,"style":45658},[491],[212,54894,54895,54898],{"style":45661},[212,54896],{"className":54897,"style":30406},[499],[212,54899,54901],{"className":54900},[504,30410,9872,507],[212,54902,2661],{"className":54903},[256,507],[212,54905,54906,54909],{"style":670},[212,54907],{"className":54908,"style":658},[499],[212,54910],{"className":54911,"style":678},[677],[212,54913,54914,54917],{"style":2748},[212,54915],{"className":54916,"style":658},[499],[212,54918,54920],{"className":54919},[504,505,506,507],[212,54921,54923],{"className":54922},[256,507],[212,54924,39189],{"className":54925},[256,507],[212,54927,515],{"className":54928},[514],[212,54930,54932],{"className":54931},[487],[212,54933,54935],{"className":54934,"style":16629},[491],[212,54936],{},[212,54938],{"className":54939},[350,638],[212,54941,310],{"className":54942},[343],[212,54944,314],{"className":54945},[256],[212,54947],{"className":54948,"style":2785},[354],[212,54950,5011],{"className":54951},[2789],[212,54953],{"className":54954,"style":2785},[354],[212,54956,54958,54962,55010],{"className":54957},[247],[212,54959],{"className":54960,"style":54961},[251],"height:1.138em;vertical-align:-0.25em;",[212,54963,54965,54968],{"className":54964},[256],[212,54966,966],{"className":54967},[256,257],[212,54969,54971],{"className":54970},[478],[212,54972,54974],{"className":54973},[482],[212,54975,54977],{"className":54976},[487],[212,54978,54981],{"className":54979,"style":54980},[491],"height:0.888em;",[212,54982,54983,54986],{"style":7063},[212,54984],{"className":54985,"style":500},[499],[212,54987,54989],{"className":54988},[504,505,506,507],[212,54990,54992,54995,54998,55001,55004,55007],{"className":54991},[256,507],[212,54993,310],{"className":54994},[343,507],[212,54996,314],{"className":54997},[256,507],[212,54999,2668],{"className":55000},[2789,507],[212,55002,44954],{"className":55003,"style":44984},[256,257,507],[212,55005,317],{"className":55006},[350,507],[212,55008,45350],{"className":55009},[256,507],[212,55011,317],{"className":55012},[350],[52794,55014,52954],{},[52794,55016,52954],{},[52794,55018,55019,55020,53674],{},"有限（",[212,55021,55023,55043],{"className":55022,"translate":216},[215],[212,55024,55026],{"className":55025},[220],[222,55027,55028],{"xmlns":224},[226,55029,55030,55040],{},[229,55031,55032,55034,55036,55038],{},[232,55033,44954],{},[307,55035,49706],{"mathvariant":406},[307,55037,46807],{},[312,55039,314],{},[236,55041,55042],{"encoding":238},"\\alpha\\ne\\pm1",[212,55044,55046,55097],{"className":55045,"ariaHidden":243},[242],[212,55047,55049,55052,55055,55058,55094],{"className":55048},[247],[212,55050],{"className":55051,"style":252},[251],[212,55053,44954],{"className":55054,"style":44984},[256,257],[212,55056],{"className":55057,"style":355},[354],[212,55059,55061,55088,55091],{"className":55060},[359],[212,55062,55064],{"className":55063},[359],[212,55065,55067],{"className":55066},[256,4598],[212,55068,55070],{"className":55069},[4602],[212,55071,55073,55076,55085],{"className":55072},[4606],[212,55074],{"className":55075,"style":252},[251],[212,55077,55079],{"className":55078},[4613],[212,55080,55082],{"className":55081},[256],[212,55083,4620],{"className":55084},[359],[212,55086],{"className":55087},[4624],[212,55089],{"className":55090},[354,4628],[212,55092,320],{"className":55093},[359],[212,55095],{"className":55096,"style":355},[354],[212,55098,55100,55103,55106],{"className":55099},[247],[212,55101],{"className":55102,"style":12778},[251],[212,55104,46807],{"className":55105},[256],[212,55107,314],{"className":55108},[256],[725,55110,55112],{"id":55111},"_4-基本性质","4. 基本性质",[11,55114,55115,55116,15995,55180,55337,55338,10378],{},"下列性质逐个给出推导。约定 ",[212,55117,55119,55141],{"className":55118,"translate":216},[215],[212,55120,55122],{"className":55121},[220],[222,55123,55124],{"xmlns":224},[226,55125,55126,55138],{},[229,55127,55128,55130,55132,55134,55136],{},[232,55129,403],{},[307,55131,748],{"separator":243},[232,55133,410],{},[307,55135,911],{},[232,55137,2562],{},[236,55139,55140],{"encoding":238},"P,Q\\ll\\mu",[212,55142,55144,55171],{"className":55143,"ariaHidden":243},[242],[212,55145,55147,55150,55153,55156,55159,55162,55165,55168],{"className":55146},[247],[212,55148],{"className":55149,"style":763},[251],[212,55151,403],{"className":55152,"style":531},[256,257],[212,55154,748],{"className":55155},[770],[212,55157],{"className":55158,"style":603},[354],[212,55160,410],{"className":55161},[256,257],[212,55163],{"className":55164,"style":355},[354],[212,55166,911],{"className":55167},[359],[212,55169],{"className":55170,"style":355},[354],[212,55172,55174,55177],{"className":55173},[247],[212,55175],{"className":55176,"style":2474},[251],[212,55178,2562],{"className":55179},[256,257],[212,55181,55183,55215],{"className":55182,"translate":216},[215],[212,55184,55186],{"className":55185},[220],[222,55187,55188],{"xmlns":224},[226,55189,55190,55212],{},[229,55191,55192,55194,55196,55202,55204,55206,55208,55210],{},[232,55193,2562],{},[307,55195,320],{},[435,55197,55198,55200],{},[312,55199,314],{},[312,55201,2661],{},[307,55203,310],{"stretchy":309},[232,55205,403],{},[307,55207,2668],{},[232,55209,410],{},[307,55211,317],{"stretchy":309},[236,55213,55214],{"encoding":238},"\\mu=\\frac12(P+Q)",[212,55216,55218,55236,55325],{"className":55217,"ariaHidden":243},[242],[212,55219,55221,55224,55227,55230,55233],{"className":55220},[247],[212,55222],{"className":55223,"style":2474},[251],[212,55225,2562],{"className":55226},[256,257],[212,55228],{"className":55229,"style":355},[354],[212,55231,320],{"className":55232},[359],[212,55234],{"className":55235,"style":355},[354],[212,55237,55239,55242,55310,55313,55316,55319,55322],{"className":55238},[247],[212,55240],{"className":55241,"style":2703},[251],[212,55243,55245,55248,55307],{"className":55244},[256],[212,55246],{"className":55247},[343,638],[212,55249,55251],{"className":55250},[435],[212,55252,55254,55299],{"className":55253},[482,483],[212,55255,55257,55296],{"className":55256},[487],[212,55258,55260,55274,55282],{"className":55259,"style":2722},[491],[212,55261,55262,55265],{"style":2725},[212,55263],{"className":55264,"style":658},[499],[212,55266,55268],{"className":55267},[504,505,506,507],[212,55269,55271],{"className":55270},[256,507],[212,55272,2661],{"className":55273},[256,507],[212,55275,55276,55279],{"style":670},[212,55277],{"className":55278,"style":658},[499],[212,55280],{"className":55281,"style":678},[677],[212,55283,55284,55287],{"style":2748},[212,55285],{"className":55286,"style":658},[499],[212,55288,55290],{"className":55289},[504,505,506,507],[212,55291,55293],{"className":55292},[256,507],[212,55294,314],{"className":55295},[256,507],[212,55297,515],{"className":55298},[514],[212,55300,55302],{"className":55301},[487],[212,55303,55305],{"className":55304,"style":2770},[491],[212,55306],{},[212,55308],{"className":55309},[350,638],[212,55311,310],{"className":55312},[343],[212,55314,403],{"className":55315,"style":531},[256,257],[212,55317],{"className":55318,"style":2785},[354],[212,55320,2668],{"className":55321},[2789],[212,55323],{"className":55324,"style":2785},[354],[212,55326,55328,55331,55334],{"className":55327},[247],[212,55329],{"className":55330,"style":336},[251],[212,55332,410],{"className":55333},[256,257],[212,55335,317],{"className":55336},[350]," 或任一控制测度），",[212,55339,55341,55366],{"className":55340,"translate":216},[215],[212,55342,55344],{"className":55343},[220],[222,55345,55346],{"xmlns":224},[226,55347,55348,55364],{},[229,55349,55350,55352,55354,55356,55358,55360,55362],{},[232,55351,966],{},[307,55353,320],{},[232,55355,441],{},[232,55357,403],{},[232,55359,1138],{"mathvariant":406},[232,55361,441],{},[232,55363,410],{},[236,55365,5531],{"encoding":238},[212,55367,55369,55387],{"className":55368,"ariaHidden":243},[242],[212,55370,55372,55375,55378,55381,55384],{"className":55371},[247],[212,55373],{"className":55374,"style":5541},[251],[212,55376,966],{"className":55377},[256,257],[212,55379],{"className":55380,"style":355},[354],[212,55382,320],{"className":55383},[359],[212,55385],{"className":55386,"style":355},[354],[212,55388,55390,55393,55396,55399,55402,55405],{"className":55389},[247],[212,55391],{"className":55392,"style":336},[251],[212,55394,441],{"className":55395},[256,257],[212,55397,403],{"className":55398,"style":531},[256,257],[212,55400,1138],{"className":55401},[256],[212,55403,441],{"className":55404},[256,257],[212,55406,410],{"className":55407},[256,257],[2509,55409,55411],{"id":55410},"_41-非负性","4.1 非负性",[24,55413,55414,55461,55586],{},[11,55415,55416,55419,55420,2943],{},[1194,55417,55418],{},"命题 4.1（非负性）"," 对一切概率分布 ",[212,55421,55423,55440],{"className":55422,"translate":216},[215],[212,55424,55426],{"className":55425},[220],[222,55427,55428],{"xmlns":224},[226,55429,55430,55438],{},[229,55431,55432,55434,55436],{},[232,55433,403],{},[307,55435,748],{"separator":243},[232,55437,410],{},[236,55439,753],{"encoding":238},[212,55441,55443],{"className":55442,"ariaHidden":243},[242],[212,55444,55446,55449,55452,55455,55458],{"className":55445},[247],[212,55447],{"className":55448,"style":763},[251],[212,55450,403],{"className":55451,"style":531},[256,257],[212,55453,748],{"className":55454},[770],[212,55456],{"className":55457,"style":603},[354],[212,55459,410],{"className":55460},[256,257],[212,55462,55464],{"className":55463,"translate":216},[377],[212,55465,55467,55501],{"className":55466,"translate":216},[215],[212,55468,55470],{"className":55469},[220],[222,55471,55472],{"xmlns":224,"display":386},[226,55473,55474,55498],{},[229,55475,55476,55482,55484,55486,55488,55490,55492,55494,55496],{},[392,55477,55478,55480],{},[232,55479,396],{},[232,55481,234],{},[307,55483,310],{"stretchy":309},[232,55485,403],{},[232,55487,407],{"mathvariant":406},[232,55489,410],{},[307,55491,317],{"stretchy":309},[307,55493,7126],{},[312,55495,323],{},[307,55497,748],{"separator":243},[236,55499,55500],{"encoding":238},"D_f(P\\|Q)\\ge 0,",[212,55502,55504,55574],{"className":55503,"ariaHidden":243},[242],[212,55505,55507,55510,55550,55553,55556,55559,55562,55565,55568,55571],{"className":55506},[247],[212,55508],{"className":55509,"style":467},[251],[212,55511,55513,55516],{"className":55512},[256],[212,55514,396],{"className":55515,"style":474},[256,257],[212,55517,55519],{"className":55518},[478],[212,55520,55522,55542],{"className":55521},[482,483],[212,55523,55525,55539],{"className":55524},[487],[212,55526,55528],{"className":55527,"style":492},[491],[212,55529,55530,55533],{"style":495},[212,55531],{"className":55532,"style":500},[499],[212,55534,55536],{"className":55535},[504,505,506,507],[212,55537,234],{"className":55538,"style":258},[256,257,507],[212,55540,515],{"className":55541},[514],[212,55543,55545],{"className":55544},[487],[212,55546,55548],{"className":55547,"style":522},[491],[212,55549],{},[212,55551,310],{"className":55552},[343],[212,55554,403],{"className":55555,"style":531},[256,257],[212,55557,407],{"className":55558},[256],[212,55560,410],{"className":55561},[256,257],[212,55563,317],{"className":55564},[350],[212,55566],{"className":55567,"style":355},[354],[212,55569,7126],{"className":55570},[359],[212,55572],{"className":55573,"style":355},[354],[212,55575,55577,55580,55583],{"className":55576},[247],[212,55578],{"className":55579,"style":9556},[251],[212,55581,323],{"className":55582},[256],[212,55584,748],{"className":55585},[770],[11,55587,55588,55589,55617,55618,10378],{},"且当 ",[212,55590,55592,55605],{"className":55591,"translate":216},[215],[212,55593,55595],{"className":55594},[220],[222,55596,55597],{"xmlns":224},[226,55598,55599,55603],{},[229,55600,55601],{},[232,55602,234],{},[236,55604,234],{"encoding":238},[212,55606,55608],{"className":55607,"ariaHidden":243},[242],[212,55609,55611,55614],{"className":55610},[247],[212,55612],{"className":55613,"style":252},[251],[212,55615,234],{"className":55616,"style":258},[256,257]," 严格凸时，等号成立当且仅当 ",[212,55619,55621,55638],{"className":55620,"translate":216},[215],[212,55622,55624],{"className":55623},[220],[222,55625,55626],{"xmlns":224},[226,55627,55628,55636],{},[229,55629,55630,55632,55634],{},[232,55631,403],{},[307,55633,320],{},[232,55635,410],{},[236,55637,10469],{"encoding":238},[212,55639,55641,55659],{"className":55640,"ariaHidden":243},[242],[212,55642,55644,55647,55650,55653,55656],{"className":55643},[247],[212,55645],{"className":55646,"style":861},[251],[212,55648,403],{"className":55649,"style":531},[256,257],[212,55651],{"className":55652,"style":355},[354],[212,55654,320],{"className":55655},[359],[212,55657],{"className":55658,"style":355},[354],[212,55660,55662,55665],{"className":55661},[247],[212,55663],{"className":55664,"style":763},[251],[212,55666,410],{"className":55667},[256,257],[11,55669,55670,55673,55674,55703,55704,55732,55733,4051,55862,55890,55891,55941,55942,55970,55971,56139,56140,56232,56233,56283,56284,56334],{},[1194,55671,55672],{},"证明。"," Jensen 已给出 ",[212,55675,55677,55691],{"className":55676,"translate":216},[215],[212,55678,55680],{"className":55679},[220],[222,55681,55682],{"xmlns":224},[226,55683,55684,55688],{},[229,55685,55686],{},[307,55687,7126],{},[236,55689,55690],{"encoding":238},"\\ge",[212,55692,55694],{"className":55693,"ariaHidden":243},[242],[212,55695,55697,55700],{"className":55696},[247],[212,55698],{"className":55699,"style":43388},[251],[212,55701,7126],{"className":55702},[359],"（见 2.1）。等号条件：若 ",[212,55705,55707,55720],{"className":55706,"translate":216},[215],[212,55708,55710],{"className":55709},[220],[222,55711,55712],{"xmlns":224},[226,55713,55714,55718],{},[229,55715,55716],{},[232,55717,234],{},[236,55719,234],{"encoding":238},[212,55721,55723],{"className":55722,"ariaHidden":243},[242],[212,55724,55726,55729],{"className":55725},[247],[212,55727],{"className":55728,"style":252},[251],[212,55730,234],{"className":55731,"style":258},[256,257]," 严格凸，Jensen 取等号当且仅当 ",[212,55734,55736,55768],{"className":55735,"translate":216},[215],[212,55737,55739],{"className":55738},[220],[222,55740,55741],{"xmlns":224},[226,55742,55743,55765],{},[229,55744,55745,55747,55749,55755,55757,55759,55761,55763],{},[232,55746,966],{},[307,55748,320],{},[392,55750,55751,55753],{},[232,55752,420],{"mathvariant":419},[232,55754,410],{},[307,55756,427],{"stretchy":309},[232,55758,966],{},[307,55760,454],{"stretchy":309},[307,55762,320],{},[312,55764,314],{},[236,55766,55767],{"encoding":238},"t=\\mathbb E_Q[t]=1",[212,55769,55771,55789,55853],{"className":55770,"ariaHidden":243},[242],[212,55772,55774,55777,55780,55783,55786],{"className":55773},[247],[212,55775],{"className":55776,"style":5541},[251],[212,55778,966],{"className":55779},[256,257],[212,55781],{"className":55782,"style":355},[354],[212,55784,320],{"className":55785},[359],[212,55787],{"className":55788,"style":355},[354],[212,55790,55792,55795,55835,55838,55841,55844,55847,55850],{"className":55791},[247],[212,55793],{"className":55794,"style":467},[251],[212,55796,55798,55801],{"className":55797},[256],[212,55799,420],{"className":55800},[256,563],[212,55802,55804],{"className":55803},[478],[212,55805,55807,55827],{"className":55806},[482,483],[212,55808,55810,55824],{"className":55809},[487],[212,55811,55813],{"className":55812,"style":576},[491],[212,55814,55815,55818],{"style":579},[212,55816],{"className":55817,"style":500},[499],[212,55819,55821],{"className":55820},[504,505,506,507],[212,55822,410],{"className":55823},[256,257,507],[212,55825,515],{"className":55826},[514],[212,55828,55830],{"className":55829},[487],[212,55831,55833],{"className":55832,"style":522},[491],[212,55834],{},[212,55836,427],{"className":55837},[343],[212,55839,966],{"className":55840},[256,257],[212,55842,454],{"className":55843},[350],[212,55845],{"className":55846,"style":355},[354],[212,55848,320],{"className":55849},[359],[212,55851],{"className":55852,"style":355},[354],[212,55854,55856,55859],{"className":55855},[247],[212,55857],{"className":55858,"style":369},[251],[212,55860,314],{"className":55861},[256],[212,55863,55865,55878],{"className":55864,"translate":216},[215],[212,55866,55868],{"className":55867},[220],[222,55869,55870],{"xmlns":224},[226,55871,55872,55876],{},[229,55873,55874],{},[232,55875,410],{},[236,55877,410],{"encoding":238},[212,55879,55881],{"className":55880,"ariaHidden":243},[242],[212,55882,55884,55887],{"className":55883},[247],[212,55885],{"className":55886,"style":763},[251],[212,55888,410],{"className":55889},[256,257]," 下几乎必然成立，即 ",[212,55892,55894,55911],{"className":55893,"translate":216},[215],[212,55895,55897],{"className":55896},[220],[222,55898,55899],{"xmlns":224},[226,55900,55901,55909],{},[229,55902,55903,55905,55907],{},[232,55904,403],{},[307,55906,320],{},[232,55908,410],{},[236,55910,10469],{"encoding":238},[212,55912,55914,55932],{"className":55913,"ariaHidden":243},[242],[212,55915,55917,55920,55923,55926,55929],{"className":55916},[247],[212,55918],{"className":55919,"style":861},[251],[212,55921,403],{"className":55922,"style":531},[256,257],[212,55924],{"className":55925,"style":355},[354],[212,55927,320],{"className":55928},[359],[212,55930],{"className":55931,"style":355},[354],[212,55933,55935,55938],{"className":55934},[247],[212,55936],{"className":55937,"style":763},[251],[212,55939,410],{"className":55940},[256,257],"。若 ",[212,55943,55945,55958],{"className":55944,"translate":216},[215],[212,55946,55948],{"className":55947},[220],[222,55949,55950],{"xmlns":224},[226,55951,55952,55956],{},[229,55953,55954],{},[232,55955,234],{},[236,55957,234],{"encoding":238},[212,55959,55961],{"className":55960,"ariaHidden":243},[242],[212,55962,55964,55967],{"className":55963},[247],[212,55965],{"className":55966,"style":252},[251],[212,55968,234],{"className":55969,"style":258},[256,257]," 只是凸而非严格凸（如 ",[212,55972,55974,56011],{"className":55973,"translate":216},[215],[212,55975,55977],{"className":55976},[220],[222,55978,55979],{"xmlns":224},[226,55980,55981,56009],{},[229,55982,55983,55985,55987,55989,55991,55993,55999,56001,56003,56005,56007],{},[232,55984,234],{},[307,55986,310],{"stretchy":309},[232,55988,966],{},[307,55990,317],{"stretchy":309},[307,55992,320],{},[435,55994,55995,55997],{},[312,55996,314],{},[312,55998,2661],{},[232,56000,5006],{"mathvariant":406},[232,56002,966],{},[307,56004,5011],{},[312,56006,314],{},[232,56008,5006],{"mathvariant":406},[236,56010,34756],{"encoding":238},[212,56012,56014,56041,56130],{"className":56013,"ariaHidden":243},[242],[212,56015,56017,56020,56023,56026,56029,56032,56035,56038],{"className":56016},[247],[212,56018],{"className":56019,"style":336},[251],[212,56021,234],{"className":56022,"style":258},[256,257],[212,56024,310],{"className":56025},[343],[212,56027,966],{"className":56028},[256,257],[212,56030,317],{"className":56031},[350],[212,56033],{"className":56034,"style":355},[354],[212,56036,320],{"className":56037},[359],[212,56039],{"className":56040,"style":355},[354],[212,56042,56044,56047,56115,56118,56121,56124,56127],{"className":56043},[247],[212,56045],{"className":56046,"style":2703},[251],[212,56048,56050,56053,56112],{"className":56049},[256],[212,56051],{"className":56052},[343,638],[212,56054,56056],{"className":56055},[435],[212,56057,56059,56104],{"className":56058},[482,483],[212,56060,56062,56101],{"className":56061},[487],[212,56063,56065,56079,56087],{"className":56064,"style":2722},[491],[212,56066,56067,56070],{"style":2725},[212,56068],{"className":56069,"style":658},[499],[212,56071,56073],{"className":56072},[504,505,506,507],[212,56074,56076],{"className":56075},[256,507],[212,56077,2661],{"className":56078},[256,507],[212,56080,56081,56084],{"style":670},[212,56082],{"className":56083,"style":658},[499],[212,56085],{"className":56086,"style":678},[677],[212,56088,56089,56092],{"style":2748},[212,56090],{"className":56091,"style":658},[499],[212,56093,56095],{"className":56094},[504,505,506,507],[212,56096,56098],{"className":56097},[256,507],[212,56099,314],{"className":56100},[256,507],[212,56102,515],{"className":56103},[514],[212,56105,56107],{"className":56106},[487],[212,56108,56110],{"className":56109,"style":2770},[491],[212,56111],{},[212,56113],{"className":56114},[350,638],[212,56116,5006],{"className":56117},[256],[212,56119,966],{"className":56120},[256,257],[212,56122],{"className":56123,"style":2785},[354],[212,56125,5011],{"className":56126},[2789],[212,56128],{"className":56129,"style":2785},[354],[212,56131,56133,56136],{"className":56132},[247],[212,56134],{"className":56135,"style":336},[251],[212,56137,34879],{"className":56138},[256],"），则只能保证 ",[212,56141,56143,56165],{"className":56142,"translate":216},[215],[212,56144,56146],{"className":56145},[220],[222,56147,56148],{"xmlns":224},[226,56149,56150,56162],{},[229,56151,56152,56158,56160],{},[392,56153,56154,56156],{},[232,56155,396],{},[232,56157,234],{},[307,56159,320],{},[312,56161,323],{},[236,56163,56164],{"encoding":238},"D_f=0",[212,56166,56168,56223],{"className":56167,"ariaHidden":243},[242],[212,56169,56171,56174,56214,56217,56220],{"className":56170},[247],[212,56172],{"className":56173,"style":4230},[251],[212,56175,56177,56180],{"className":56176},[256],[212,56178,396],{"className":56179,"style":474},[256,257],[212,56181,56183],{"className":56182},[478],[212,56184,56186,56206],{"className":56185},[482,483],[212,56187,56189,56203],{"className":56188},[487],[212,56190,56192],{"className":56191,"style":492},[491],[212,56193,56194,56197],{"style":495},[212,56195],{"className":56196,"style":500},[499],[212,56198,56200],{"className":56199},[504,505,506,507],[212,56201,234],{"className":56202,"style":258},[256,257,507],[212,56204,515],{"className":56205},[514],[212,56207,56209],{"className":56208},[487],[212,56210,56212],{"className":56211,"style":522},[491],[212,56213],{},[212,56215],{"className":56216,"style":355},[354],[212,56218,320],{"className":56219},[359],[212,56221],{"className":56222,"style":355},[354],[212,56224,56226,56229],{"className":56225},[247],[212,56227],{"className":56228,"style":369},[251],[212,56230,323],{"className":56231},[256]," 时不必然 ",[212,56234,56236,56253],{"className":56235,"translate":216},[215],[212,56237,56239],{"className":56238},[220],[222,56240,56241],{"xmlns":224},[226,56242,56243,56251],{},[229,56244,56245,56247,56249],{},[232,56246,403],{},[307,56248,320],{},[232,56250,410],{},[236,56252,10469],{"encoding":238},[212,56254,56256,56274],{"className":56255,"ariaHidden":243},[242],[212,56257,56259,56262,56265,56268,56271],{"className":56258},[247],[212,56260],{"className":56261,"style":861},[251],[212,56263,403],{"className":56264,"style":531},[256,257],[212,56266],{"className":56267,"style":355},[354],[212,56269,320],{"className":56270},[359],[212,56272],{"className":56273,"style":355},[354],[212,56275,56277,56280],{"className":56276},[247],[212,56278],{"className":56279,"style":763},[251],[212,56281,410],{"className":56282},[256,257],"：TV 是反例，",[212,56285,56287,56304],{"className":56286,"translate":216},[215],[212,56288,56290],{"className":56289},[220],[222,56291,56292],{"xmlns":224},[226,56293,56294,56302],{},[229,56295,56296,56298,56300],{},[232,56297,403],{},[307,56299,320],{},[232,56301,410],{},[236,56303,10469],{"encoding":238},[212,56305,56307,56325],{"className":56306,"ariaHidden":243},[242],[212,56308,56310,56313,56316,56319,56322],{"className":56309},[247],[212,56311],{"className":56312,"style":861},[251],[212,56314,403],{"className":56315,"style":531},[256,257],[212,56317],{"className":56318,"style":355},[354],[212,56320,320],{"className":56321},[359],[212,56323],{"className":56324,"style":355},[354],[212,56326,56328,56331],{"className":56327},[247],[212,56329],{"className":56330,"style":763},[251],[212,56332,410],{"className":56333},[256,257]," 时才是唯一使 TV 为 0 的一对（TV 也对）。",[2509,56336,56338],{"id":56337},"_42-联合凸性","4.2 联合凸性",[24,56340,56341,56813],{},[11,56342,56343,56346,56347,2943,56543,2943,56739,41838],{},[1194,56344,56345],{},"命题 4.2（联合凸性）"," 若 ",[212,56348,56350,56391],{"className":56349,"translate":216},[215],[212,56351,56353],{"className":56352},[220],[222,56354,56355],{"xmlns":224},[226,56356,56357,56389],{},[229,56358,56359,56361,56363,56365,56371,56373,56375,56377,56379,56381,56383],{},[232,56360,403],{},[307,56362,320],{},[232,56364,11539],{},[392,56366,56367,56369],{},[232,56368,403],{},[312,56370,314],{},[307,56372,2668],{},[307,56374,310],{"stretchy":309},[312,56376,314],{},[307,56378,5011],{},[232,56380,11539],{},[307,56382,317],{"stretchy":309},[392,56384,56385,56387],{},[232,56386,403],{},[312,56388,2661],{},[236,56390,11646],{"encoding":238},[212,56392,56394,56412,56470,56491],{"className":56393,"ariaHidden":243},[242],[212,56395,56397,56400,56403,56406,56409],{"className":56396},[247],[212,56398],{"className":56399,"style":861},[251],[212,56401,403],{"className":56402,"style":531},[256,257],[212,56404],{"className":56405,"style":355},[354],[212,56407,320],{"className":56408},[359],[212,56410],{"className":56411,"style":355},[354],[212,56413,56415,56418,56421,56461,56464,56467],{"className":56414},[247],[212,56416],{"className":56417,"style":11674},[251],[212,56419,11539],{"className":56420},[256,257],[212,56422,56424,56427],{"className":56423},[256],[212,56425,403],{"className":56426,"style":531},[256,257],[212,56428,56430],{"className":56429},[478],[212,56431,56433,56453],{"className":56432},[482,483],[212,56434,56436,56450],{"className":56435},[487],[212,56437,56439],{"className":56438,"style":11333},[491],[212,56440,56441,56444],{"style":11336},[212,56442],{"className":56443,"style":500},[499],[212,56445,56447],{"className":56446},[504,505,506,507],[212,56448,314],{"className":56449},[256,507],[212,56451,515],{"className":56452},[514],[212,56454,56456],{"className":56455},[487],[212,56457,56459],{"className":56458,"style":8166},[491],[212,56460],{},[212,56462],{"className":56463,"style":2785},[354],[212,56465,2668],{"className":56466},[2789],[212,56468],{"className":56469,"style":2785},[354],[212,56471,56473,56476,56479,56482,56485,56488],{"className":56472},[247],[212,56474],{"className":56475,"style":336},[251],[212,56477,310],{"className":56478},[343],[212,56480,314],{"className":56481},[256],[212,56483],{"className":56484,"style":2785},[354],[212,56486,5011],{"className":56487},[2789],[212,56489],{"className":56490,"style":2785},[354],[212,56492,56494,56497,56500,56503],{"className":56493},[247],[212,56495],{"className":56496,"style":336},[251],[212,56498,11539],{"className":56499},[256,257],[212,56501,317],{"className":56502},[350],[212,56504,56506,56509],{"className":56505},[256],[212,56507,403],{"className":56508,"style":531},[256,257],[212,56510,56512],{"className":56511},[478],[212,56513,56515,56535],{"className":56514},[482,483],[212,56516,56518,56532],{"className":56517},[487],[212,56519,56521],{"className":56520,"style":11333},[491],[212,56522,56523,56526],{"style":11336},[212,56524],{"className":56525,"style":500},[499],[212,56527,56529],{"className":56528},[504,505,506,507],[212,56530,2661],{"className":56531},[256,507],[212,56533,515],{"className":56534},[514],[212,56536,56538],{"className":56537},[487],[212,56539,56541],{"className":56540,"style":8166},[491],[212,56542],{},[212,56544,56546,56587],{"className":56545,"translate":216},[215],[212,56547,56549],{"className":56548},[220],[222,56550,56551],{"xmlns":224},[226,56552,56553,56585],{},[229,56554,56555,56557,56559,56561,56567,56569,56571,56573,56575,56577,56579],{},[232,56556,410],{},[307,56558,320],{},[232,56560,11539],{},[392,56562,56563,56565],{},[232,56564,410],{},[312,56566,314],{},[307,56568,2668],{},[307,56570,310],{"stretchy":309},[312,56572,314],{},[307,56574,5011],{},[232,56576,11539],{},[307,56578,317],{"stretchy":309},[392,56580,56581,56583],{},[232,56582,410],{},[312,56584,2661],{},[236,56586,11844],{"encoding":238},[212,56588,56590,56608,56666,56687],{"className":56589,"ariaHidden":243},[242],[212,56591,56593,56596,56599,56602,56605],{"className":56592},[247],[212,56594],{"className":56595,"style":763},[251],[212,56597,410],{"className":56598},[256,257],[212,56600],{"className":56601,"style":355},[354],[212,56603,320],{"className":56604},[359],[212,56606],{"className":56607,"style":355},[354],[212,56609,56611,56614,56617,56657,56660,56663],{"className":56610},[247],[212,56612],{"className":56613,"style":252},[251],[212,56615,11539],{"className":56616},[256,257],[212,56618,56620,56623],{"className":56619},[256],[212,56621,410],{"className":56622},[256,257],[212,56624,56626],{"className":56625},[478],[212,56627,56629,56649],{"className":56628},[482,483],[212,56630,56632,56646],{"className":56631},[487],[212,56633,56635],{"className":56634,"style":11333},[491],[212,56636,56637,56640],{"style":579},[212,56638],{"className":56639,"style":500},[499],[212,56641,56643],{"className":56642},[504,505,506,507],[212,56644,314],{"className":56645},[256,507],[212,56647,515],{"className":56648},[514],[212,56650,56652],{"className":56651},[487],[212,56653,56655],{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这是 ",[212,57304,57306,57319],{"className":57305,"translate":216},[215],[212,57307,57309],{"className":57308},[220],[222,57310,57311],{"xmlns":224},[226,57312,57313,57317],{},[229,57314,57315],{},[232,57316,234],{},[236,57318,234],{"encoding":238},[212,57320,57322],{"className":57321,"ariaHidden":243},[242],[212,57323,57325,57328],{"className":57324},[247],[212,57326],{"className":57327,"style":252},[251],[212,57329,234],{"className":57330,"style":258},[256,257]," 凸性加上「",[212,57333,57335,57351],{"className":57334,"translate":216},[215],[212,57336,57338],{"className":57337},[220],[222,57339,57340],{"xmlns":224},[226,57341,57342,57348],{},[229,57343,57344,57346],{},[232,57345,35632],{},[307,57347,4301],{},[236,57349,57350],{"encoding":238},"\\sup",[212,57352,57354],{"className":57353,"ariaHidden":243},[242],[212,57355,57357,57360],{"className":57356},[247],[212,57358],{"className":57359,"style":2474},[251],[212,57361,35632],{"className":57362},[1682]," 与线性运算」的标准结果，也可用 f-散度的变分表示（4.4 节）直接看：",[212,57365,57367,57447],{"className":57366,"translate":216},[215],[212,57368,57370],{"className":57369},[220],[222,57371,57372],{"xmlns":224},[226,57373,57374,57444],{},[229,57375,57376,57382,57384,57386,57388,57390,57392,57394,57404,57406,57412,57414,57416,57418,57420,57426,57428,57434,57436,57438,57440,57442],{},[392,57377,57378,57380],{},[232,57379,396],{},[232,57381,234],{},[307,57383,310],{"stretchy":309},[232,57385,403],{},[232,57387,407],{"mathvariant":406},[232,57389,410],{},[307,57391,317],{"stretchy":309},[307,57393,320],{},[392,57395,57396,57402],{},[229,57397,57398,57400],{},[232,57399,35632],{},[307,57401,4301],{},[232,57403,4356],{},[307,57405,3096],{"stretchy":309},[392,57407,57408,57410],{},[232,57409,420],{"mathvariant":419},[232,57411,403],{},[307,57413,427],{"stretchy":309},[232,57415,4356],{},[307,57417,454],{"stretchy":309},[307,57419,5011],{},[392,57421,57422,57424],{},[232,57423,420],{"mathvariant":419},[232,57425,410],{},[307,57427,427],{"stretchy":309},[7012,57429,57430,57432],{},[232,57431,234],{},[307,57433,7771],{},[307,57435,310],{"stretchy":309},[232,57437,4356],{},[307,57439,317],{"stretchy":309},[307,57441,454],{"stretchy":309},[307,57443,3106],{"stretchy":309},[236,57445,57446],{"encoding":238},"D_f(P\\|Q)=\\sup_g\\{\\mathbb E_P[g]-\\mathbb E_Q[f^*(g)]\\}",[212,57448,57450,57520,57629],{"className":57449,"ariaHidden":243},[242],[212,57451,57453,57456,57496,57499,57502,57505,57508,57511,57514,57517],{"className":57452},[247],[212,57454],{"className":57455,"style":467},[251],[212,57457,57459,57462],{"className":57458},[256],[212,57460,396],{"className":57461,"style":474},[256,257],[212,57463,57465],{"className":57464},[478],[212,57466,57468,57488],{"className":57467},[482,483],[212,57469,57471,57485],{"className":57470},[487],[212,57472,57474],{"className":57473,"style":492},[491],[212,57475,57476,57479],{"style":495},[212,57477],{"className":57478,"style":500},[499],[212,57480,57482],{"className":57481},[504,505,506,507],[212,57483,234],{"className":57484,"style":258},[256,257,507],[212,57486,515],{"className":57487},[514],[212,57489,57491],{"className":57490},[487],[212,57492,57494],{"className":57493,"style":522},[491],[212,57495],{},[212,57497,310],{"className":57498},[343],[212,57500,403],{"className":57501,"style":531},[256,257],[212,57503,407],{"className":57504},[256],[212,57506,410],{"className":57507},[256,257],[212,57509,317],{"className":57510},[350],[212,57512],{"className":57513,"style":355},[354],[212,57515,320],{"className":57516},[359],[212,57518],{"className":57519,"style":355},[354],[212,57521,57523,57527,57568,57571,57611,57614,57617,57620,57623,57626],{"className":57522},[247],[212,57524],{"className":57525,"style":57526},[251],"height:1.1302em;vertical-align:-0.3802em;",[212,57528,57530,57533],{"className":57529},[1682],[212,57531,35632],{"className":57532},[1682],[212,57534,57536],{"className":57535},[478],[212,57537,57539,57559],{"className":57538},[482,483],[212,57540,57542,57556],{"className":57541},[487],[212,57543,57545],{"className":57544,"style":37199},[491],[212,57546,57547,57550],{"style":35778},[212,57548],{"className":57549,"style":500},[499],[212,57551,57553],{"className":57552},[504,505,506,507],[212,57554,4356],{"className":57555,"style":1178},[256,257,507],[212,57557,515],{"className":57558},[514],[212,57560,57562],{"className":57561},[487],[212,57563,57566],{"className":57564,"style":57565},[491],"height:0.3802em;",[212,57567],{},[212,57569,3096],{"className":57570},[343],[212,57572,57574,57577],{"className":57573},[256],[212,57575,420],{"className":57576},[256,563],[212,57578,57580],{"className":57579},[478],[212,57581,57583,57603],{"className":57582},[482,483],[212,57584,57586,57600],{"className":57585},[487],[212,57587,57589],{"className":57588,"style":576},[491],[212,57590,57591,57594],{"style":579},[212,57592],{"className":57593,"style":500},[499],[212,57595,57597],{"className":57596},[504,505,506,507],[212,57598,403],{"className":57599,"style":531},[256,257,507],[212,57601,515],{"className":57602},[514],[212,57604,57606],{"className":57605},[487],[212,57607,57609],{"className":57608,"style":8166},[491],[212,57610],{},[212,57612,427],{"className":57613},[343],[212,57615,4356],{"className":57616,"style":1178},[256,257],[212,57618,454],{"className":57619},[350],[212,57621],{"className":57622,"style":2785},[354],[212,57624,5011],{"className":57625},[2789],[212,57627],{"className":57628,"style":2785},[354],[212,57630,57632,57635,57675,57678,57707,57710,57713],{"className":57631},[247],[212,57633],{"className":57634,"style":467},[251],[212,57636,57638,57641],{"className":57637},[256],[212,57639,420],{"className":57640},[256,563],[212,57642,57644],{"className":57643},[478],[212,57645,57647,57667],{"className":57646},[482,483],[212,57648,57650,57664],{"className":57649},[487],[212,57651,57653],{"className":57652,"style":576},[491],[212,57654,57655,57658],{"style":579},[212,57656],{"className":57657,"style":500},[499],[212,57659,57661],{"className":57660},[504,505,506,507],[212,57662,410],{"className":57663},[256,257,507],[212,57665,515],{"className":57666},[514],[212,57668,57670],{"className":57669},[487],[212,57671,57673],{"className":57672,"style":522},[491],[212,57674],{},[212,57676,427],{"className":57677},[343],[212,57679,57681,57684],{"className":57680},[256],[212,57682,234],{"className":57683,"style":258},[256,257],[212,57685,57687],{"className":57686},[478],[212,57688,57690],{"className":57689},[482],[212,57691,57693],{"className":57692},[487],[212,57694,57696],{"className":57695,"style":8697},[491],[212,57697,57698,57701],{"style":7063},[212,57699],{"className":57700,"style":500},[499],[212,57702,57704],{"className":57703},[504,505,506,507],[212,57705,7771],{"className":57706},[2789,507],[212,57708,310],{"className":57709},[343],[212,57711,4356],{"className":57712,"style":1178},[256,257],[212,57714,57716],{"className":57715},[350],")]}","，右端关于 ",[212,57719,57721,57742],{"className":57720,"translate":216},[215],[212,57722,57724],{"className":57723},[220],[222,57725,57726],{"xmlns":224},[226,57727,57728,57740],{},[229,57729,57730,57732,57734,57736,57738],{},[307,57731,310],{"stretchy":309},[232,57733,403],{},[307,57735,748],{"separator":243},[232,57737,410],{},[307,57739,317],{"stretchy":309},[236,57741,11231],{"encoding":238},[212,57743,57745],{"className":57744,"ariaHidden":243},[242],[212,57746,57748,57751,57754,57757,57760,57763,57766],{"className":57747},[247],[212,57749],{"className":57750,"style":336},[251],[212,57752,310],{"className":57753},[343],[212,57755,403],{"className":57756,"style":531},[256,257],[212,57758,748],{"className":57759},[770],[212,57761],{"className":57762,"style":603},[354],[212,57764,410],{"className":57765},[256,257],[212,57767,317],{"className":57768},[350]," 是凸的（",[212,57771,57773,57797],{"className":57772,"translate":216},[215],[212,57774,57776],{"className":57775},[220],[222,57777,57778],{"xmlns":224},[226,57779,57780,57794],{},[229,57781,57782,57788,57790,57792],{},[392,57783,57784,57786],{},[232,57785,420],{"mathvariant":419},[232,57787,403],{},[307,57789,427],{"stretchy":309},[232,57791,4356],{},[307,57793,454],{"stretchy":309},[236,57795,57796],{"encoding":238},"\\mathbb E_P[g]",[212,57798,57800],{"className":57799,"ariaHidden":243},[242],[212,57801,57803,57806,57846,57849,57852],{"className":57802},[247],[212,57804],{"className":57805,"style":336},[251],[212,57807,57809,57812],{"className":57808},[256],[212,57810,420],{"className":57811},[256,563],[212,57813,57815],{"className":57814},[478],[212,57816,57818,57838],{"className":57817},[482,483],[212,57819,57821,57835],{"className":57820},[487],[212,57822,57824],{"className":57823,"style":576},[491],[212,57825,57826,57829],{"style":579},[212,57827],{"className":57828,"style":500},[499],[212,57830,57832],{"className":57831},[504,505,506,507],[212,57833,403],{"className":57834,"style":531},[256,257,507],[212,57836,515],{"className":57837},[514],[212,57839,57841],{"className":57840},[487],[212,57842,57844],{"className":57843,"style":8166},[491],[212,57845],{},[212,57847,427],{"className":57848},[343],[212,57850,4356],{"className":57851,"style":1178},[256,257],[212,57853,454],{"className":57854},[350]," 线性、",[212,57857,57859,57895],{"className":57858,"translate":216},[215],[212,57860,57862],{"className":57861},[220],[222,57863,57864],{"xmlns":224},[226,57865,57866,57892],{},[229,57867,57868,57870,57876,57878,57884,57886,57888,57890],{},[307,57869,5011],{},[392,57871,57872,57874],{},[232,57873,420],{"mathvariant":419},[232,57875,410],{},[307,57877,427],{"stretchy":309},[7012,57879,57880,57882],{},[232,57881,234],{},[307,57883,7771],{},[307,57885,310],{"stretchy":309},[232,57887,4356],{},[307,57889,317],{"stretchy":309},[307,57891,454],{"stretchy":309},[236,57893,57894],{"encoding":238},"-\\mathbb E_Q[f^*(g)]",[212,57896,57898],{"className":57897,"ariaHidden":243},[242],[212,57899,57901,57904,57907,57947,57950,57979,57982,57985],{"className":57900},[247],[212,57902],{"className":57903,"style":467},[251],[212,57905,5011],{"className":57906},[256],[212,57908,57910,57913],{"className":57909},[256],[212,57911,420],{"className":57912},[256,563],[212,57914,57916],{"className":57915},[478],[212,57917,57919,57939],{"className":57918},[482,483],[212,57920,57922,57936],{"className":57921},[487],[212,57923,57925],{"className":57924,"style":576},[491],[212,57926,57927,57930],{"style":579},[212,57928],{"className":57929,"style":500},[499],[212,57931,57933],{"className":57932},[504,505,506,507],[212,57934,410],{"className":57935},[256,257,507],[212,57937,515],{"className":57938},[514],[212,57940,57942],{"className":57941},[487],[212,57943,57945],{"className":57944,"style":522},[491],[212,57946],{},[212,57948,427],{"className":57949},[343],[212,57951,57953,57956],{"className":57952},[256],[212,57954,234],{"className":57955,"style":258},[256,257],[212,57957,57959],{"className":57958},[478],[212,57960,57962],{"className":57961},[482],[212,57963,57965],{"className":57964},[487],[212,57966,57968],{"className":57967,"style":8697},[491],[212,57969,57970,57973],{"style":7063},[212,57971],{"className":57972,"style":500},[499],[212,57974,57976],{"className":57975},[504,505,506,507],[212,57977,7771],{"className":57978},[2789,507],[212,57980,310],{"className":57981},[343],[212,57983,4356],{"className":57984,"style":1178},[256,257],[212,57986,20590],{"className":57987},[350]," 线性），取上确界后仍凸。",[11,57990,57991,57992,2943,58020,58138,58139,2943,58167,11165,58284,9598,58287,58403,58404,58432,58433,58461,58462,58490],{},"等价地，固定 ",[212,57993,57995,58008],{"className":57994,"translate":216},[215],[212,57996,57998],{"className":57997},[220],[222,57999,58000],{"xmlns":224},[226,58001,58002,58006],{},[229,58003,58004],{},[232,58005,410],{},[236,58007,410],{"encoding":238},[212,58009,58011],{"className":58010,"ariaHidden":243},[242],[212,58012,58014,58017],{"className":58013},[247],[212,58015],{"className":58016,"style":763},[251],[212,58018,410],{"className":58019},[256,257],[212,58021,58023,58055],{"className":58022,"translate":216},[215],[212,58024,58026],{"className":58025},[220],[222,58027,58028],{"xmlns":224},[226,58029,58030,58052],{},[229,58031,58032,58034,58036,58042,58044,58046,58048,58050],{},[232,58033,403],{},[307,58035,8882],{},[392,58037,58038,58040],{},[232,58039,396],{},[232,58041,234],{},[307,58043,310],{"stretchy":309},[232,58045,403],{},[232,58047,407],{"mathvariant":406},[232,58049,410],{},[307,58051,317],{"stretchy":309},[236,58053,58054],{"encoding":238},"P\\mapsto D_f(P\\|Q)",[212,58056,58058,58077],{"className":58057,"ariaHidden":243},[242],[212,58059,58061,58065,58068,58071,58074],{"className":58060},[247],[212,58062],{"className":58063,"style":58064},[251],"height:0.6943em;vertical-align:-0.011em;",[212,58066,403],{"className":58067,"style":531},[256,257],[212,58069],{"className":58070,"style":355},[354],[212,58072,8882],{"className":58073},[359],[212,58075],{"className":58076,"style":355},[354],[212,58078,58080,58083,58123,58126,58129,58132,58135],{"className":58079},[247],[212,58081],{"className":58082,"style":467},[251],[212,58084,58086,58089],{"className":58085},[256],[212,58087,396],{"className":58088,"style":474},[256,257],[212,58090,58092],{"className":58091},[478],[212,58093,58095,58115],{"className":58094},[482,483],[212,58096,58098,58112],{"className":58097},[487],[212,58099,58101],{"className":58100,"style":492},[491],[212,58102,58103,58106],{"style":495},[212,58104],{"className":58105,"style":500},[499],[212,58107,58109],{"className":58108},[504,505,506,507],[212,58110,234],{"className":58111,"style":258},[256,257,507],[212,58113,515],{"className":58114},[514],[212,58116,58118],{"className":58117},[487],[212,58119,58121],{"className":58120,"style":522},[491],[212,58122],{},[212,58124,310],{"className":58125},[343],[212,58127,403],{"className":58128,"style":531},[256,257],[212,58130,407],{"className":58131},[256],[212,58133,410],{"className":58134},[256,257],[212,58136,317],{"className":58137},[350]," 凸；固定 ",[212,58140,58142,58155],{"className":58141,"translate":216},[215],[212,58143,58145],{"className":58144},[220],[222,58146,58147],{"xmlns":224},[226,58148,58149,58153],{},[229,58150,58151],{},[232,58152,403],{},[236,58154,403],{"encoding":238},[212,58156,58158],{"className":58157,"ariaHidden":243},[242],[212,58159,58161,58164],{"className":58160},[247],[212,58162],{"className":58163,"style":861},[251],[212,58165,403],{"className":58166,"style":531},[256,257],[212,58168,58170,58202],{"className":58169,"translate":216},[215],[212,58171,58173],{"className":58172},[220],[222,58174,58175],{"xmlns":224},[226,58176,58177,58199],{},[229,58178,58179,58181,58183,58189,58191,58193,58195,58197],{},[232,58180,410],{},[307,58182,8882],{},[392,58184,58185,58187],{},[232,58186,396],{},[232,58188,234],{},[307,58190,310],{"stretchy":309},[232,58192,403],{},[232,58194,407],{"mathvariant":406},[232,58196,410],{},[307,58198,317],{"stretchy":309},[236,58200,58201],{"encoding":238},"Q\\mapsto D_f(P\\|Q)",[212,58203,58205,58223],{"className":58204,"ariaHidden":243},[242],[212,58206,58208,58211,58214,58217,58220],{"className":58207},[247],[212,58209],{"className":58210,"style":763},[251],[212,58212,410],{"className":58213},[256,257],[212,58215],{"className":58216,"style":355},[354],[212,58218,8882],{"className":58219},[359],[212,58221],{"className":58222,"style":355},[354],[212,58224,58226,58229,58269,58272,58275,58278,58281],{"className":58225},[247],[212,58227],{"className":58228,"style":467},[251],[212,58230,58232,58235],{"className":58231},[256],[212,58233,396],{"className":58234,"style":474},[256,257],[212,58236,58238],{"className":58237},[478],[212,58239,58241,58261],{"className":58240},[482,483],[212,58242,58244,58258],{"className":58243},[487],[212,58245,58247],{"className":58246,"style":492},[491],[212,58248,58249,58252],{"style":495},[212,58250],{"className":58251,"style":500},[499],[212,58253,58255],{"className":58254},[504,505,506,507],[212,58256,234],{"className":58257,"style":258},[256,257,507],[212,58259,515],{"className":58260},[514],[212,58262,58264],{"className":58263},[487],[212,58265,58267],{"className":58266,"style":522},[491],[212,58268],{},[212,58270,310],{"className":58271},[343],[212,58273,403],{"className":58274,"style":531},[256,257],[212,58276,407],{"className":58277},[256],[212,58279,410],{"className":58280},[256,257],[212,58282,317],{"className":58283},[350],[1194,58285,58286],{},"注意",[212,58288,58290,58321],{"className":58289,"translate":216},[215],[212,58291,58293],{"className":58292},[220],[222,58294,58295],{"xmlns":224},[226,58296,58297,58319],{},[229,58298,58299,58301,58303,58309,58311,58313,58315,58317],{},[232,58300,410],{},[307,58302,8882],{},[392,58304,58305,58307],{},[232,58306,396],{},[232,58308,234],{},[307,58310,310],{"stretchy":309},[232,58312,403],{},[232,58314,407],{"mathvariant":406},[232,58316,410],{},[307,58318,317],{"stretchy":309},[236,58320,58201],{"encoding":238},[212,58322,58324,58342],{"className":58323,"ariaHidden":243},[242],[212,58325,58327,58330,58333,58336,58339],{"className":58326},[247],[212,58328],{"className":58329,"style":763},[251],[212,58331,410],{"className":58332},[256,257],[212,58334],{"className":58335,"style":355},[354],[212,58337,8882],{"className":58338},[359],[212,58340],{"className":58341,"style":355},[354],[212,58343,58345,58348,58388,58391,58394,58397,58400],{"className":58344},[247],[212,58346],{"className":58347,"style":467},[251],[212,58349,58351,58354],{"className":58350},[256],[212,58352,396],{"className":58353,"style":474},[256,257],[212,58355,58357],{"className":58356},[478],[212,58358,58360,58380],{"className":58359},[482,483],[212,58361,58363,58377],{"className":58362},[487],[212,58364,58366],{"className":58365,"style":492},[491],[212,58367,58368,58371],{"style":495},[212,58369],{"className":58370,"style":500},[499],[212,58372,58374],{"className":58373},[504,505,506,507],[212,58375,234],{"className":58376,"style":258},[256,257,507],[212,58378,515],{"className":58379},[514],[212,58381,58383],{"className":58382},[487],[212,58384,58386],{"className":58385,"style":522},[491],[212,58387],{},[212,58389,310],{"className":58390},[343],[212,58392,403],{"className":58393,"style":531},[256,257],[212,58395,407],{"className":58396},[256],[212,58398,410],{"className":58399},[256,257],[212,58401,317],{"className":58402},[350]," 凸是「以 ",[212,58405,58407,58420],{"className":58406,"translate":216},[215],[212,58408,58410],{"className":58409},[220],[222,58411,58412],{"xmlns":224},[226,58413,58414,58418],{},[229,58415,58416],{},[232,58417,410],{},[236,58419,410],{"encoding":238},[212,58421,58423],{"className":58422,"ariaHidden":243},[242],[212,58424,58426,58429],{"className":58425},[247],[212,58427],{"className":58428,"style":763},[251],[212,58430,410],{"className":58431},[256,257]," 为参照」的凸性，它与「",[212,58434,58436,58449],{"className":58435,"translate":216},[215],[212,58437,58439],{"className":58438},[220],[222,58440,58441],{"xmlns":224},[226,58442,58443,58447],{},[229,58444,58445],{},[232,58446,410],{},[236,58448,410],{"encoding":238},[212,58450,58452],{"className":58451,"ariaHidden":243},[242],[212,58453,58455,58458],{"className":58454},[247],[212,58456],{"className":58457,"style":763},[251],[212,58459,410],{"className":58460},[256,257]," 出现在分母上」的直觉相反，这个凸性正是变分推断里「对 ",[212,58463,58465,58478],{"className":58464,"translate":216},[215],[212,58466,58468],{"className":58467},[220],[222,58469,58470],{"xmlns":224},[226,58471,58472,58476],{},[229,58473,58474],{},[232,58475,1141],{},[236,58477,1141],{"encoding":238},[212,58479,58481],{"className":58480,"ariaHidden":243},[242],[212,58482,58484,58487],{"className":58483},[247],[212,58485],{"className":58486,"style":2474},[251],[212,58488,1141],{"className":58489,"style":1178},[256,257]," 做平均场优化收敛到全局最优」的根据之一。",[2509,58492,58494],{"id":58493},"_43-斜对称关系","4.3 斜对称关系",[24,58496,58497,58599,58817],{},[11,58498,58499,58502,58503,58598],{},[1194,58500,58501],{},"定义 4.1（斜共轭）"," 对 ",[212,58504,58506,58535],{"className":58505,"translate":216},[215],[212,58507,58509],{"className":58508},[220],[222,58510,58511],{"xmlns":224},[226,58512,58513,58533],{},[229,58514,58515,58517,58519,58521,58523,58525,58527,58529,58531],{},[232,58516,234],{},[307,58518,1214],{},[307,58520,427],{"stretchy":309},[312,58522,323],{},[307,58524,748],{"separator":243},[232,58526,1223],{"mathvariant":406},[307,58528,317],{"stretchy":309},[307,58530,1228],{},[232,58532,1231],{"mathvariant":419},[236,58534,1234],{"encoding":238},[212,58536,58538,58556,58589],{"className":58537,"ariaHidden":243},[242],[212,58539,58541,58544,58547,58550,58553],{"className":58540},[247],[212,58542],{"className":58543,"style":252},[251],[212,58545,234],{"className":58546,"style":258},[256,257],[212,58548],{"className":58549,"style":355},[354],[212,58551,1214],{"className":58552},[359],[212,58554],{"className":58555,"style":355},[354],[212,58557,58559,58562,58565,58568,58571,58574,58577,58580,58583,58586],{"className":58558},[247],[212,58560],{"className":58561,"style":336},[251],[212,58563,427],{"className":58564},[343],[212,58566,323],{"className":58567},[256],[212,58569,748],{"className":58570},[770],[212,58572],{"className":58573,"style":603},[354],[212,58575,1223],{"className":58576},[256],[212,58578,317],{"className":58579},[350],[212,58581],{"className":58582,"style":355},[354],[212,58584,1228],{"className":58585},[359],[212,58587],{"className":58588,"style":355},[354],[212,58590,58592,58595],{"className":58591},[247],[212,58593],{"className":58594,"style":1295},[251],[212,58596,1231],{"className":58597},[256,563],"，称",[212,58600,58602],{"className":58601,"translate":216},[377],[212,58603,58605,58667],{"className":58604,"translate":216},[215],[212,58606,58608],{"className":58607},[220],[222,58609,58610],{"xmlns":224,"display":386},[226,58611,58612,58664],{},[229,58613,58614,58630,58632,58634,58636,58638,58640,58642,58644,58646,58648,58650,58652,58654,58656,58658,58660,58662],{},[7751,58615,58616,58618,58628],{},[232,58617,234],{},[229,58619,58620,58622,58624,58626],{},[232,58621,7759],{},[232,58623,7762],{},[232,58625,7765],{},[232,58627,7768],{},[307,58629,7771],{"lspace":1445,"rspace":1445},[307,58631,310],{"stretchy":309},[232,58633,966],{},[307,58635,317],{"stretchy":309},[307,58637,320],{},[232,58639,966],{},[1495,58641,1497],{},[232,58643,234],{},[307,58645,310],{"stretchy":309},[312,58647,314],{},[232,58649,1138],{"mathvariant":406},[232,58651,966],{},[307,58653,317],{"stretchy":309},[307,58655,748],{"separator":243},[354,58657],{"width":3460},[232,58659,966],{},[307,58661,3101],{},[312,58663,323],{},[236,58665,58666],{"encoding":238},"f^{*}_{skew}(t)=t\\,f(1\u002Ft),\\qquad t>0",[212,58668,58670,58760,58808],{"className":58669,"ariaHidden":243},[242],[212,58671,58673,58676,58742,58745,58748,58751,58754,58757],{"className":58672},[247],[212,58674],{"className":58675,"style":336},[251],[212,58677,58679,58682],{"className":58678},[256],[212,58680,234],{"className":58681,"style":258},[256,257],[212,58683,58685],{"className":58684},[478],[212,58686,58688,58734],{"className":58687},[482,483],[212,58689,58691,58731],{"className":58690},[487],[212,58692,58694,58717],{"className":58693,"style":8446},[491],[212,58695,58696,58699],{"style":8449},[212,58697],{"className":58698,"style":500},[499],[212,58700,58702],{"className":58701},[504,505,506,507],[212,58703,58705,58708,58711,58714],{"className":58704},[256,507],[212,58706,7759],{"className":58707},[256,257,507],[212,58709,7762],{"className":58710,"style":8465},[256,257,507],[212,58712,7765],{"className":58713},[256,257,507],[212,58715,7768],{"className":58716,"style":8472},[256,257,507],[212,58718,58719,58722],{"style":8475},[212,58720],{"className":58721,"style":500},[499],[212,58723,58725],{"className":58724},[504,505,506,507],[212,58726,58728],{"className":58727},[256,507],[212,58729,7771],{"className":58730},[256,507],[212,58732,515],{"className":58733},[514],[212,58735,58737],{"className":58736},[487],[212,58738,58740],{"className":58739,"style":8497},[491],[212,58741],{},[212,58743,310],{"className":58744},[343],[212,58746,966],{"className":58747},[256,257],[212,58749,317],{"className":58750},[350],[212,58752],{"className":58753,"style":355},[354],[212,58755,320],{"className":58756},[359],[212,58758],{"className":58759,"style":355},[354],[212,58761,58763,58766,58769,58772,58775,58778,58781,58784,58787,58790,58793,58796,58799,58802,58805],{"className":58762},[247],[212,58764],{"className":58765,"style":336},[251],[212,58767,966],{"className":58768},[256,257],[212,58770],{"className":58771,"style":603},[354],[212,58773,234],{"className":58774,"style":258},[256,257],[212,58776,310],{"className":58777},[343],[212,58779,8787],{"className":58780},[256],[212,58782,966],{"className":58783},[256,257],[212,58785,317],{"className":58786},[350],[212,58788,748],{"className":58789},[770],[212,58791],{"className":58792,"style":3832},[354],[212,58794],{"className":58795,"style":603},[354],[212,58797,966],{"className":58798},[256,257],[212,58800],{"className":58801,"style":355},[354],[212,58803,3101],{"className":58804},[359],[212,58806],{"className":58807,"style":355},[354],[212,58809,58811,58814],{"className":58810},[247],[212,58812],{"className":58813,"style":369},[251],[212,58815,323],{"className":58816},[256],[11,58818,58819,58820,34025,58848,10378],{},"为 ",[212,58821,58823,58836],{"className":58822,"translate":216},[215],[212,58824,58826],{"className":58825},[220],[222,58827,58828],{"xmlns":224},[226,58829,58830,58834],{},[229,58831,58832],{},[232,58833,234],{},[236,58835,234],{"encoding":238},[212,58837,58839],{"className":58838,"ariaHidden":243},[242],[212,58840,58842,58845],{"className":58841},[247],[212,58843],{"className":58844,"style":252},[251],[212,58846,234],{"className":58847,"style":258},[256,257],[1194,58849,35988],{},[24,58851,58852,58899],{},[11,58853,58854,58857,58858,2943],{},[1194,58855,58856],{},"命题 4.3（斜对称）"," 对任意概率分布 ",[212,58859,58861,58878],{"className":58860,"translate":216},[215],[212,58862,58864],{"className":58863},[220],[222,58865,58866],{"xmlns":224},[226,58867,58868,58876],{},[229,58869,58870,58872,58874],{},[232,58871,403],{},[307,58873,748],{"separator":243},[232,58875,410],{},[236,58877,753],{"encoding":238},[212,58879,58881],{"className":58880,"ariaHidden":243},[242],[212,58882,58884,58887,58890,58893,58896],{"className":58883},[247],[212,58885],{"className":58886,"style":763},[251],[212,58888,403],{"className":58889,"style":531},[256,257],[212,58891,748],{"className":58892},[770],[212,58894],{"className":58895,"style":603},[354],[212,58897,410],{"className":58898},[256,257],[212,58900,58902],{"className":58901,"translate":216},[377],[212,58903,58905,58967],{"className":58904,"translate":216},[215],[212,58906,58908],{"className":58907},[220],[222,58909,58910],{"xmlns":224,"display":386},[226,58911,58912,58964],{},[229,58913,58914,58920,58922,58924,58926,58928,58930,58932,58952,58954,58956,58958,58960,58962],{},[392,58915,58916,58918],{},[232,58917,396],{},[232,58919,234],{},[307,58921,310],{"stretchy":309},[232,58923,403],{},[232,58925,407],{"mathvariant":406},[232,58927,410],{},[307,58929,317],{"stretchy":309},[307,58931,320],{},[392,58933,58934,58936],{},[232,58935,396],{},[7751,58937,58938,58940,58950],{},[232,58939,234],{},[229,58941,58942,58944,58946,58948],{},[232,58943,7759],{},[232,58945,7762],{},[232,58947,7765],{},[232,58949,7768],{},[307,58951,7771],{"lspace":1445,"rspace":1445},[307,58953,310],{"stretchy":309},[232,58955,410],{},[232,58957,407],{"mathvariant":406},[232,58959,403],{},[307,58961,317],{"stretchy":309},[232,58963,4573],{"mathvariant":406},[236,58965,58966],{"encoding":238},"D_f(P\\|Q)=D_{f^{*}_{skew}}(Q\\|P).",[212,58968,58970,59040],{"className":58969,"ariaHidden":243},[242],[212,58971,58973,58976,59016,59019,59022,59025,59028,59031,59034,59037],{"className":58972},[247],[212,58974],{"className":58975,"style":467},[251],[212,58977,58979,58982],{"className":58978},[256],[212,58980,396],{"className":58981,"style":474},[256,257],[212,58983,58985],{"className":58984},[478],[212,58986,58988,59008],{"className":58987},[482,483],[212,58989,58991,59005],{"className":58990},[487],[212,58992,58994],{"className":58993,"style":492},[491],[212,58995,58996,58999],{"style":495},[212,58997],{"className":58998,"style":500},[499],[212,59000,59002],{"className":59001},[504,505,506,507],[212,59003,234],{"className":59004,"style":258},[256,257,507],[212,59006,515],{"className":59007},[514],[212,59009,59011],{"className":59010},[487],[212,59012,59014],{"className":59013,"style":522},[491],[212,59015],{},[212,59017,310],{"className":59018},[343],[212,59020,403],{"className":59021,"style":531},[256,257],[212,59023,407],{"className":59024},[256],[212,59026,410],{"className":59027},[256,257],[212,59029,317],{"className":59030},[350],[212,59032],{"className":59033,"style":355},[354],[212,59035,320],{"className":59036},[359],[212,59038],{"className":59039,"style":355},[354],[212,59041,59043,59047,59158,59161,59164,59167,59170,59173],{"className":59042},[247],[212,59044],{"className":59045,"style":59046},[251],"height:1.1431em;vertical-align:-0.3931em;",[212,59048,59050,59053],{"className":59049},[256],[212,59051,396],{"className":59052,"style":474},[256,257],[212,59054,59056],{"className":59055},[478],[212,59057,59059,59149],{"className":59058},[482,483],[212,59060,59062,59146],{"className":59061},[487],[212,59063,59065],{"className":59064,"style":492},[491],[212,59066,59067,59070],{"style":495},[212,59068],{"className":59069,"style":500},[499],[212,59071,59073],{"className":59072},[504,505,506,507],[212,59074,59076],{"className":59075},[256,507],[212,59077,59079,59082],{"className":59078},[256,507],[212,59080,234],{"className":59081,"style":258},[256,257,507],[212,59083,59085],{"className":59084},[478],[212,59086,59088,59137],{"className":59087},[482,483],[212,59089,59091,59134],{"className":59090},[487],[212,59092,59095,59119],{"className":59093,"style":59094},[491],"height:0.6771em;",[212,59096,59098,59101],{"style":59097},"top:-2.1528em;margin-left:-0.1076em;margin-right:0.0714em;",[212,59099],{"className":59100,"style":30406},[499],[212,59102,59104],{"className":59103},[504,30410,9872,507],[212,59105,59107,59110,59113,59116],{"className":59106},[256,507],[212,59108,7759],{"className":59109},[256,257,507],[212,59111,7762],{"className":59112,"style":8465},[256,257,507],[212,59114,7765],{"className":59115},[256,257,507],[212,59117,7768],{"className":59118,"style":8472},[256,257,507],[212,59120,59122,59125],{"style":59121},"top:-2.8448em;margin-right:0.0714em;",[212,59123],{"className":59124,"style":30406},[499],[212,59126,59128],{"className":59127},[504,30410,9872,507],[212,59129,59131],{"className":59130},[256,507],[212,59132,7771],{"className":59133},[256,507],[212,59135,515],{"className":59136},[514],[212,59138,59140],{"className":59139},[487],[212,59141,59144],{"className":59142,"style":59143},[491],"he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f(t)\\,dQ\n=\\int f\\!\\left(\\frac1s\\right) s\\,dP\\\\\n&=\\int 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对称（",[212,60090,60092,60138],{"className":60091,"translate":216},[215],[212,60093,60095],{"className":60094},[220],[222,60096,60097],{"xmlns":224},[226,60098,60099,60135],{},[229,60100,60101,60107,60109,60111,60113,60115,60117,60119,60125,60127,60129,60131,60133],{},[392,60102,60103,60105],{},[232,60104,396],{},[232,60106,234],{},[307,60108,310],{"stretchy":309},[232,60110,403],{},[232,60112,407],{"mathvariant":406},[232,60114,410],{},[307,60116,317],{"stretchy":309},[307,60118,320],{},[392,60120,60121,60123],{},[232,60122,396],{},[232,60124,234],{},[307,60126,310],{"stretchy":309},[232,60128,410],{},[232,60130,407],{"mathvariant":406},[232,60132,403],{},[307,60134,317],{"stretchy":309},[236,60136,60137],{"encoding":238},"D_f(P\\|Q)=D_f(Q\\|P)",[212,60139,60141,60211],{"className":60140,"ariaHidden":243},[242],[212,60142,60144,60147,60187,60190,60193,60196,60199,60202,60205,60208],{"className":60143},[247],[212,60145],{"className":60146,"style":467},[251],[212,60148,60150,60153],{"className":60149},[256],[212,60151,396],{"className":60152,"style":474},[256,257],[212,60154,60156],{"className":60155},[478],[212,60157,60159,60179],{"className":60158},[482,483],[212,60160,60162,60176],{"className":60161},[487],[212,60163,60165],{"className":60164,"style":492},[491],[212,60166,60167,60170],{"style":495},[212,60168],{"className":60169,"style":500},[499],[212,60171,60173],{"className":60172},[504,505,506,507],[212,60174,234],{"className":60175,"style":258},[256,257,507],[212,60177,515],{"className":60178},[514],[212,60180,60182],{"className":60181},[487],[212,60183,60185],{"className":60184,"style":522},[491],[212,60186],{},[212,60188,310],{"className":60189},[343],[212,60191,403],{"className":60192,"style":531},[256,257],[212,60194,407],{"className":60195},[256],[212,60197,410],{"className":60198},[256,257],[212,60200,317],{"className":60201},[350],[212,60203],{"className":60204,"style":355},[354],[212,60206,320],{"className":60207},[359],[212,60209],{"className":60210,"style":355},[354],[212,60212,60214,60217,60257,60260,60263,60266,60269],{"className":60213},[247],[212,60215],{"className":60216,"style":467},[251],[212,60218,60220,60223],{"className":60219},[256],[212,60221,396],{"className":60222,"style":474},[256,257],[212,60224,60226],{"className":60225},[478],[212,60227,60229,60249],{"className":60228},[482,483],[212,60230,60232,60246],{"className":60231},[487],[212,60233,60235],{"className":60234,"style":492},[491],[212,60236,60237,60240],{"style":495},[212,60238],{"className":60239,"style":500},[499],[212,60241,60243],{"className":60242},[504,505,506,507],[212,60244,234],{"className":60245,"style":258},[256,257,507],[212,60247,515],{"className":60248},[514],[212,60250,60252],{"className":60251},[487],[212,60253,60255],{"className":60254,"style":522},[491],[212,60256],{},[212,60258,310],{"className":60259},[343],[212,60261,410],{"className":60262},[256,257],[212,60264,407],{"className":60265},[256],[212,60267,403],{"className":60268,"style":531},[256,257],[212,60270,317],{"className":60271},[350]," 对所有 ",[212,60274,60276,60293],{"className":60275,"translate":216},[215],[212,60277,60279],{"className":60278},[220],[222,60280,60281],{"xmlns":224},[226,60282,60283,60291],{},[229,60284,60285,60287,60289],{},[232,60286,403],{},[307,60288,748],{"separator":243},[232,60290,410],{},[236,60292,753],{"encoding":238},[212,60294,60296],{"className":60295,"ariaHidden":243},[242],[212,60297,60299,60302,60305,60308,60311],{"className":60298},[247],[212,60300],{"className":60301,"style":763},[251],[212,60303,403],{"className":60304,"style":531},[256,257],[212,60306,748],{"className":60307},[770],[212,60309],{"className":60310,"style":603},[354],[212,60312,410],{"className":60313},[256,257],"）当且仅当 ",[212,60316,60318,60349],{"className":60317,"translate":216},[215],[212,60319,60321],{"className":60320},[220],[222,60322,60323],{"xmlns":224},[226,60324,60325,60347],{},[229,60326,60327,60343,60345],{},[7751,60328,60329,60331,60341],{},[232,60330,234],{},[229,60332,60333,60335,60337,60339],{},[232,60334,7759],{},[232,60336,7762],{},[232,60338,7765],{},[232,60340,7768],{},[307,60342,7771],{"lspace":1445,"rspace":1445},[307,60344,320],{},[232,60346,234],{},[236,60348,44353],{"encoding":238},[212,60350,60352,60433],{"className":60351,"ariaHidden":243},[242],[212,60353,60355,60358,60424,60427,60430],{"className":60354},[247],[212,60356],{"className":60357,"style":44363},[251],[212,60359,60361,60364],{"className":60360},[256],[212,60362,234],{"className":60363,"style":258},[256,257],[212,60365,60367],{"className":60366},[478],[212,60368,60370,60416],{"className":60369},[482,483],[212,60371,60373,60413],{"className":60372},[487],[212,60374,60376,60399],{"className":60375,"style":8697},[491],[212,60377,60378,60381],{"style":8700},[212,60379],{"className":60380,"style":500},[499],[212,60382,60384],{"className":60383},[504,505,506,507],[212,60385,60387,60390,60393,60396],{"className":60386},[256,507],[212,60388,7759],{"className":60389},[256,257,507],[212,60391,7762],{"className":60392,"style":8465},[256,257,507],[212,60394,7765],{"className":60395},[256,257,507],[212,60397,7768],{"className":60398,"style":8472},[256,257,507],[212,60400,60401,60404],{"style":7063},[212,60402],{"className":60403,"style":500},[499],[212,60405,60407],{"className":60406},[504,505,506,507],[212,60408,60410],{"className":60409},[256,507],[212,60411,7771],{"className":60412},[256,507],[212,60414,515],{"className":60415},[514],[212,60417,60419],{"className":60418},[487],[212,60420,60422],{"className":60421,"style":8745},[491],[212,60423],{},[212,60425],{"className":60426,"style":355},[354],[212,60428,320],{"className":60429},[359],[212,60431],{"className":60432,"style":355},[354],[212,60434,60436,60439],{"className":60435},[247],[212,60437],{"className":60438,"style":252},[251],[212,60440,234],{"className":60441,"style":258},[256,257],"（模去 ",[212,60444,60446,60469],{"className":60445,"translate":216},[215],[212,60447,60449],{"className":60448},[220],[222,60450,60451],{"xmlns":224},[226,60452,60453,60467],{},[229,60454,60455,60457,60459,60461,60463,60465],{},[232,60456,6104],{},[307,60458,310],{"stretchy":309},[232,60460,966],{},[307,60462,5011],{},[312,60464,314],{},[307,60466,317],{"stretchy":309},[236,60468,6818],{"encoding":238},[212,60470,60472,60496],{"className":60471,"ariaHidden":243},[242],[212,60473,60475,60478,60481,60484,60487,60490,60493],{"className":60474},[247],[212,60476],{"className":60477,"style":336},[251],[212,60479,6104],{"className":60480},[256,257],[212,60482,310],{"className":60483},[343],[212,60485,966],{"className":60486},[256,257],[212,60488],{"className":60489,"style":2785},[354],[212,60491,5011],{"className":60492},[2789],[212,60494],{"className":60495,"style":2785},[354],[212,60497,60499,60502,60505],{"className":60498},[247],[212,60500],{"className":60501,"style":336},[251],[212,60503,314],{"className":60504},[256],[212,60506,317],{"className":60507},[350],"）。验证 TV：",[212,60510,60512,60566],{"className":60511,"translate":216},[215],[212,60513,60515],{"className":60514},[220],[222,60516,60517],{"xmlns":224},[226,60518,60519,60563],{},[229,60520,60521,60523,60525,60531,60533,60535,60537,60539,60541,60543,60545,60547,60553,60555,60557,60559,60561],{},[232,60522,966],{},[307,60524,3497],{},[435,60526,60527,60529],{},[312,60528,314],{},[312,60530,2661],{},[232,60532,5006],{"mathvariant":406},[312,60534,314],{},[232,60536,1138],{"mathvariant":406},[232,60538,966],{},[307,60540,5011],{},[312,60542,314],{},[232,60544,5006],{"mathvariant":406},[307,60546,320],{},[435,60548,60549,60551],{},[312,60550,314],{},[312,60552,2661],{},[232,60554,5006],{"mathvariant":406},[232,60556,966],{},[307,60558,5011],{},[312,60560,314],{},[232,60562,5006],{"mathvariant":406},[236,60564,60565],{"encoding":238},"t\\cdot\\frac12|1\u002Ft-1|=\\frac12|t-1|",[212,60567,60569,60587,60677,60695,60784],{"className":60568,"ariaHidden":243},[242],[212,60570,60572,60575,60578,60581,60584],{"className":60571},[247],[212,60573],{"className":60574,"style":5541},[251],[212,60576,966],{"className":60577},[256,257],[212,60579],{"className":60580,"style":2785},[354],[212,60582,3497],{"className":60583},[2789],[212,60585],{"className":60586,"style":2785},[354],[212,60588,60590,60593,60661,60665,60668,60671,60674],{"className":60589},[247],[212,60591],{"className":60592,"style":2703},[251],[212,60594,60596,60599,60658],{"className":60595},[256],[212,60597],{"className":60598},[343,638],[212,60600,60602],{"className":60601},[435],[212,60603,60605,60650],{"className":60604},[482,483],[212,60606,60608,60647],{"className":60607},[487],[212,60609,60611,60625,60633],{"className":60610,"style":2722},[491],[212,60612,60613,60616],{"style":2725},[212,60614],{"className":60615,"style":658},[499],[212,60617,60619],{"className":60618},[504,505,506,507],[212,60620,60622],{"className":60621},[256,507],[212,60623,2661],{"className":60624},[256,507],[212,60626,60627,60630],{"style":670},[212,60628],{"className":60629,"style":658},[499],[212,60631],{"className":60632,"style":678},[677],[212,60634,60635,60638],{"style":2748},[212,60636],{"className":60637,"style":658},[499],[212,60639,60641],{"className":60640},[504,505,506,507],[212,60642,60644],{"className":60643},[256,507],[212,60645,314],{"className":60646},[256,507],[212,60648,515],{"className":60649},[514],[212,60651,60653],{"className":60652},[487],[212,60654,60656],{"className":60655,"style":2770},[491],[212,60657],{},[212,60659],{"className":60660},[350,638],[212,60662,60664],{"className":60663},[256],"∣1\u002F",[212,60666,966],{"className":60667},[256,257],[212,60669],{"className":60670,"style":2785},[354],[212,60672,5011],{"className":60673},[2789],[212,60675],{"className":60676,"style":2785},[354],[212,60678,60680,60683,60686,60689,60692],{"className":60679},[247],[212,60681],{"className":60682,"style":336},[251],[212,60684,34879],{"className":60685},[256],[212,60687],{"className":60688,"style":355},[354],[212,60690,320],{"className":60691},[359],[212,60693],{"className":60694,"style":355},[354],[212,60696,60698,60701,60769,60772,60775,60778,60781],{"className":60697},[247],[212,60699],{"className":60700,"style":2703},[251],[212,60702,60704,60707,60766],{"className":60703},[256],[212,60705],{"className":60706},[343,638],[212,60708,60710],{"className":60709},[435],[212,60711,60713,60758],{"className":60712},[482,483],[212,60714,60716,60755],{"className":60715},[487],[212,60717,60719,60733,60741],{"className":60718,"style":2722},[491],[212,60720,60721,60724],{"style":2725},[212,60722],{"className":60723,"style":658},[499],[212,60725,60727],{"className":60726},[504,505,506,507],[212,60728,60730],{"className":60729},[256,507],[212,60731,2661],{"className":60732},[256,507],[212,60734,60735,60738],{"style":670},[212,60736],{"className":60737,"style":658},[499],[212,60739],{"className":60740,"style":678},[677],[212,60742,60743,60746],{"style":2748},[212,60744],{"className":60745,"style":658},[499],[212,60747,60749],{"className":60748},[504,505,506,507],[212,60750,60752],{"className":60751},[256,507],[212,60753,314],{"className":60754},[256,507],[212,60756,515],{"className":60757},[514],[212,60759,60761],{"className":60760},[487],[212,60762,60764],{"className":60763,"style":2770},[491],[212,60765],{},[212,60767],{"className":60768},[350,638],[212,60770,5006],{"className":60771},[256],[212,60773,966],{"className":60774},[256,257],[212,60776],{"className":60777,"style":2785},[354],[212,60779,5011],{"className":60780},[2789],[212,60782],{"className":60783,"style":2785},[354],[212,60785,60787,60790],{"className":60786},[247],[212,60788],{"className":60789,"style":336},[251],[212,60791,34879],{"className":60792},[256],"；JS 的 ",[212,60795,60797,60832],{"className":60796,"translate":216},[215],[212,60798,60800],{"className":60799},[220],[222,60801,60802],{"xmlns":224},[226,60803,60804,60830],{},[229,60805,60806,60808,60810,60812,60814,60816,60818,60820,60822,60824,60826,60828],{},[232,60807,966],{},[232,60809,234],{},[307,60811,310],{"stretchy":309},[312,60813,314],{},[232,60815,1138],{"mathvariant":406},[232,60817,966],{},[307,60819,317],{"stretchy":309},[307,60821,320],{},[232,60823,234],{},[307,60825,310],{"stretchy":309},[232,60827,966],{},[307,60829,317],{"stretchy":309},[236,60831,23769],{"encoding":238},[212,60833,60835,60868],{"className":60834,"ariaHidden":243},[242],[212,60836,60838,60841,60844,60847,60850,60853,60856,60859,60862,60865],{"className":60837},[247],[212,60839],{"className":60840,"style":336},[251],[212,60842,966],{"className":60843},[256,257],[212,60845,234],{"className":60846,"style":258},[256,257],[212,60848,310],{"className":60849},[343],[212,60851,8787],{"className":60852},[256],[212,60854,966],{"className":60855},[256,257],[212,60857,317],{"className":60858},[350],[212,60860],{"className":60861,"style":355},[354],[212,60863,320],{"className":60864},[359],[212,60866],{"className":60867,"style":355},[354],[212,60869,60871,60874,60877,60880,60883],{"className":60870},[247],[212,60872],{"className":60873,"style":336},[251],[212,60875,234],{"className":60876,"style":258},[256,257],[212,60878,310],{"className":60879},[343],[212,60881,966],{"className":60882},[256,257],[212,60884,317],{"className":60885},[350]," 也已验算；KL 显然不满足，故不对称。",[2509,60888,60890],{"id":60889},"_44-变分表示","4.4 变分表示",[24,60892,60893,60987,61213,61216,61592],{},[11,60894,60895,11260,60898,60957,60958,60986],{},[1194,60896,60897],{},"定理 4.1（变分表示 \u002F Fenchel 对偶）",[212,60899,60901,60919],{"className":60900,"translate":216},[215],[212,60902,60904],{"className":60903},[220],[222,60905,60906],{"xmlns":224},[226,60907,60908,60916],{},[229,60909,60910],{},[7012,60911,60912,60914],{},[232,60913,234],{},[307,60915,7771],{},[236,60917,60918],{"encoding":238},"f^*",[212,60920,60922],{"className":60921,"ariaHidden":243},[242],[212,60923,60925,60928],{"className":60924},[247],[212,60926],{"className":60927,"style":252},[251],[212,60929,60931,60934],{"className":60930},[256],[212,60932,234],{"className":60933,"style":258},[256,257],[212,60935,60937],{"className":60936},[478],[212,60938,60940],{"className":60939},[482],[212,60941,60943],{"className":60942},[487],[212,60944,60946],{"className":60945,"style":8697},[491],[212,60947,60948,60951],{"style":7063},[212,60949],{"className":60950,"style":500},[499],[212,60952,60954],{"className":60953},[504,505,506,507],[212,60955,7771],{"className":60956},[2789,507]," 为 ",[212,60959,60961,60974],{"className":60960,"translate":216},[215],[212,60962,60964],{"className":60963},[220],[222,60965,60966],{"xmlns":224},[226,60967,60968,60972],{},[229,60969,60970],{},[232,60971,234],{},[236,60973,234],{"encoding":238},[212,60975,60977],{"className":60976,"ariaHidden":243},[242],[212,60978,60980,60983],{"className":60979},[247],[212,60981],{"className":60982,"style":252},[251],[212,60984,234],{"className":60985,"style":258},[256,257]," 的凸共轭（Fenchel 共轭）",[212,60988,60990],{"className":60989,"translate":216},[377],[212,60991,60993,61055],{"className":60992,"translate":216},[215],[212,60994,60996],{"className":60995},[220],[222,60997,60998],{"xmlns":224,"display":386},[226,60999,61000,61052],{},[229,61001,61002,61008,61010,61012,61014,61016,61032,61034,61036,61038,61040,61042,61044,61046,61048,61050],{},[7012,61003,61004,61006],{},[232,61005,234],{},[307,61007,7771],{},[307,61009,310],{"stretchy":309},[232,61011,40437],{},[307,61013,317],{"stretchy":309},[307,61015,320],{},[6214,61017,61018,61024],{},[229,61019,61020,61022],{},[232,61021,35632],{},[307,61023,4301],{},[229,61025,61026,61028,61030],{},[232,61027,966],{},[307,61029,7126],{},[312,61031,323],{},[307,61033,3096],{"stretchy":309},[232,61035,40437],{},[232,61037,966],{},[307,61039,5011],{},[232,61041,234],{},[307,61043,310],{"stretchy":309},[232,61045,966],{},[307,61047,317],{"stretchy":309},[307,61049,3106],{"stretchy":309},[307,61051,748],{"separator":243},[236,61053,61054],{"encoding":238},"f^*(y)=\\sup_{t\\ge0}\\{yt-f(t)\\},",[212,61056,61058,61111,61191],{"className":61057,"ariaHidden":243},[242],[212,61059,61061,61064,61093,61096,61099,61102,61105,61108],{"className":61060},[247],[212,61062],{"className":61063,"style":336},[251],[212,61065,61067,61070],{"className":61066},[256],[212,61068,234],{"className":61069,"style":258},[256,257],[212,61071,61073],{"className":61072},[478],[212,61074,61076],{"className":61075},[482],[212,61077,61079],{"className":61078},[487],[212,61080,61082],{"className":61081,"style":8446},[491],[212,61083,61084,61087],{"style":8475},[212,61085],{"className":61086,"style":500},[499],[212,61088,61090],{"className":61089},[504,505,506,507],[212,61091,7771],{"className":61092},[2789,507],[212,61094,310],{"className":61095},[343],[212,61097,40437],{"className":61098,"style":1178},[256,257],[212,61100,317],{"className":61101},[350],[212,61103],{"className":61104,"style":355},[354],[212,61106,320],{"className":61107},[359],[212,61109],{"className":61110,"style":355},[354],[212,61112,61114,61118,61173,61176,61179,61182,61185,61188],{"className":61113},[247],[212,61115],{"className":61116,"style":61117},[251],"height:1.7567em;vertical-align:-1.0067em;",[212,61119,61121],{"className":61120},[1682,13916],[212,61122,61124,61164],{"className":61123},[482,483],[212,61125,61127,61161],{"className":61126},[487],[212,61128,61130,61151],{"className":61129,"style":2543},[491],[212,61131,61133,61136],{"style":61132},"top:-2.1885em;margin-left:0em;",[212,61134],{"className":61135,"style":658},[499],[212,61137,61139],{"className":61138},[504,505,506,507],[212,61140,61142,61145,61148],{"className":61141},[256,507],[212,61143,966],{"className":61144},[256,257,507],[212,61146,7126],{"className":61147},[359,507],[212,61149,323],{"className":61150},[256,507],[212,61152,61153,61156],{"style":12063},[212,61154],{"className":61155,"style":658},[499],[212,61157,61158],{},[212,61159,35632],{"className":61160},[1682],[212,61162,515],{"className":61163},[514],[212,61165,61167],{"className":61166},[487],[212,61168,61171],{"className":61169,"style":61170},[491],"height:1.0067em;",[212,61172],{},[212,61174,3096],{"className":61175},[343],[212,61177,40437],{"className":61178,"style":1178},[256,257],[212,61180,966],{"className":61181},[256,257],[212,61183],{"className":61184,"style":2785},[354],[212,61186,5011],{"className":61187},[2789],[212,61189],{"className":61190,"style":2785},[354],[212,61192,61194,61197,61200,61203,61206,61210],{"className":61193},[247],[212,61195],{"className":61196,"style":336},[251],[212,61198,234],{"className":61199,"style":258},[256,257],[212,61201,310],{"className":61202},[343],[212,61204,966],{"className":61205},[256,257],[212,61207,61209],{"className":61208},[350],")}",[212,61211,748],{"className":61212},[770],[11,61214,61215],{},"则",[212,61217,61219],{"className":61218,"translate":216},[377],[212,61220,61222,61306],{"className":61221,"translate":216},[215],[212,61223,61225],{"className":61224},[220],[222,61226,61227],{"xmlns":224,"display":386},[226,61228,61229,61303],{},[229,61230,61231,61237,61239,61241,61243,61245,61247,61249,61259,61301],{},[392,61232,61233,61235],{},[232,61234,396],{},[232,61236,234],{},[307,61238,310],{"stretchy":309},[232,61240,403],{},[232,61242,407],{"mathvariant":406},[232,61244,410],{},[307,61246,317],{"stretchy":309},[307,61248,320],{},[6214,61250,61251,61257],{},[229,61252,61253,61255],{},[232,61254,35632],{},[307,61256,4301],{},[232,61258,4356],{},[229,61260,61261,61263,61269,61271,61273,61275,61277,61283,61285,61291,61293,61295,61297,61299],{},[307,61262,3096],{"fence":243},[392,61264,61265,61267],{},[232,61266,420],{"mathvariant":419},[232,61268,403],{},[307,61270,427],{"stretchy":309},[232,61272,4356],{},[307,61274,454],{"stretchy":309},[307,61276,5011],{},[392,61278,61279,61281],{},[232,61280,420],{"mathvariant":419},[232,61282,410],{},[307,61284,427],{"stretchy":309},[7012,61286,61287,61289],{},[232,61288,234],{},[307,61290,7771],{},[307,61292,310],{"stretchy":309},[232,61294,4356],{},[307,61296,317],{"stretchy":309},[307,61298,454],{"stretchy":309},[307,61300,3106],{"fence":243},[307,61302,748],{"separator":243},[236,61304,61305],{"encoding":238},"D_f(P\\|Q)=\\sup_{g}\n\\left\\{\\mathbb E_P[g]\n-\\mathbb E_Q[f^*(g)]\\right\\},",[212,61307,61309,61379],{"className":61308,"ariaHidden":243},[242],[212,61310,61312,61315,61355,61358,61361,61364,61367,61370,61373,61376],{"className":61311},[247],[212,61313],{"className":61314,"style":467},[251],[212,61316,61318,61321],{"className":61317},[256],[212,61319,396],{"className":61320,"style":474},[256,257],[212,61322,61324],{"className":61323},[478],[212,61325,61327,61347],{"className":61326},[482,483],[212,61328,61330,61344],{"className":61329},[487],[212,61331,61333],{"className":61332,"style":492},[491],[212,61334,61335,61338],{"style":495},[212,61336],{"className":61337,"style":500},[499],[212,61339,61341],{"className":61340},[504,505,506,507],[212,61342,234],{"className":61343,"style":258},[256,257,507],[212,61345,515],{"className":61346},[514],[212,61348,61350],{"className":61349},[487],[212,61351,61353],{"className":61352,"style":522},[491],[212,61354],{},[212,61356,310],{"className":61357},[343],[212,61359,403],{"className":61360,"style":531},[256,257],[212,61362,407],{"className":61363},[256],[212,61365,410],{"className":61366},[256,257],[212,61368,317],{"className":61369},[350],[212,61371],{"className":61372,"style":355},[354],[212,61374,320],{"className":61375},[359],[212,61377],{"className":61378,"style":355},[354],[212,61380,61382,61386,61435,61438,61586,61589],{"className":61381},[247],[212,61383],{"className":61384,"style":61385},[251],"height:1.7805em;vertical-align:-1.0305em;",[212,61387,61389],{"className":61388},[1682,13916],[212,61390,61392,61426],{"className":61391},[482,483],[212,61393,61395,61423],{"className":61394},[487],[212,61396,61398,61413],{"className":61397,"style":2543},[491],[212,61399,61401,61404],{"style":61400},"top:-2.2056em;margin-left:0em;",[212,61402],{"className":61403,"style":658},[499],[212,61405,61407],{"className":61406},[504,505,506,507],[212,61408,61410],{"className":61409},[256,507],[212,61411,4356],{"className":61412,"style":1178},[256,257,507],[212,61414,61415,61418],{"style":12063},[212,61416],{"className":61417,"style":658},[499],[212,61419,61420],{},[212,61421,35632],{"className":61422},[1682],[212,61424,515],{"className":61425},[514],[212,61427,61429],{"className":61428},[487],[212,61430,61433],{"className":61431,"style":61432},[491],"height:1.0305em;",[212,61434],{},[212,61436],{"className":61437,"style":603},[354],[212,61439,61441,61444,61484,61487,61490,61493,61496,61499,61502,61542,61545,61574,61577,61580,61583],{"className":61440},[607],[212,61442,3096],{"className":61443,"style":612},[343,611],[212,61445,61447,61450],{"className":61446},[256],[212,61448,420],{"className":61449},[256,563],[212,61451,61453],{"className":61452},[478],[212,61454,61456,61476],{"className":61455},[482,483],[212,61457,61459,61473],{"className":61458},[487],[212,61460,61462],{"className":61461,"style":576},[491],[212,61463,61464,61467],{"style":579},[212,61465],{"className":61466,"style":500},[499],[212,61468,61470],{"className":61469},[504,505,506,507],[212,61471,403],{"className":61472,"style":531},[256,257,507],[212,61474,515],{"className":61475},[514],[212,61477,61479],{"className":61478},[487],[212,61480,61482],{"className":61481,"style":8166},[491],[212,61483],{},[212,61485,427],{"className":61486},[343],[212,61488,4356],{"className":61489,"style":1178},[256,257],[212,61491,454],{"className":61492},[350],[212,61494],{"className":61495,"style":2785},[354],[212,61497,5011],{"className":61498},[2789],[212,61500],{"className":61501,"style":2785},[354],[212,61503,61505,61508],{"className":61504},[256],[212,61506,420],{"className":61507},[256,563],[212,61509,61511],{"className":61510},[478],[212,61512,61514,61534],{"className":61513},[482,483],[212,61515,61517,61531],{"className":61516},[487],[212,61518,61520],{"className":61519,"style":576},[491],[212,61521,61522,61525],{"style":579},[212,61523],{"className":61524,"style":500},[499],[212,61526,61528],{"className":61527},[504,505,506,507],[212,61529,410],{"className":61530},[256,257,507],[212,61532,515],{"className":61533},[514],[212,61535,61537],{"className":61536},[487],[212,61538,61540],{"className":61539,"style":522},[491],[212,61541],{},[212,61543,427],{"className":61544},[343],[212,61546,61548,61551],{"className":61547},[256],[212,61549,234],{"className":61550,"style":258},[256,257],[212,61552,61554],{"className":61553},[478],[212,61555,61557],{"className":61556},[482],[212,61558,61560],{"className":61559},[487],[212,61561,61563],{"className":61562,"style":8446},[491],[212,61564,61565,61568],{"style":8475},[212,61566],{"className":61567,"style":500},[499],[212,61569,61571],{"className":61570},[504,505,506,507],[212,61572,7771],{"className":61573},[2789,507],[212,61575,310],{"className":61576},[343],[212,61578,4356],{"className":61579,"style":1178},[256,257],[212,61581,20590],{"className":61582},[350],[212,61584,3106],{"className":61585,"style":612},[350,611],[212,61587],{"className":61588,"style":603},[354],[212,61590,748],{"className":61591},[770],[11,61593,61594,61595,10378],{},"其中上确界取遍所有使两个期望都有定义的可测函数 ",[212,61596,61598,61629],{"className":61597,"translate":216},[215],[212,61599,61601],{"className":61600},[220],[222,61602,61603],{"xmlns":224},[226,61604,61605,61626],{},[229,61606,61607,61609,61611,61613,61615,61618,61620],{},[232,61608,4356],{},[307,61610,1214],{},[232,61612,795],{"mathvariant":794},[307,61614,1228],{},[232,61616,61617],{"mathvariant":406},"dom",[307,61619,4301],{},[7012,61621,61622,61624],{},[232,61623,234],{},[307,61625,7771],{},[236,61627,61628],{"encoding":238},"g:\\mathcal X\\to\\operatorname{dom} f^*",[212,61630,61632,61650,61668],{"className":61631,"ariaHidden":243},[242],[212,61633,61635,61638,61641,61644,61647],{"className":61634},[247],[212,61636],{"className":61637,"style":2474},[251],[212,61639,4356],{"className":61640,"style":1178},[256,257],[212,61642],{"className":61643,"style":355},[354],[212,61645,1214],{"className":61646},[359],[212,61648],{"className":61649,"style":355},[354],[212,61651,61653,61656,61659,61662,61665],{"className":61652},[247],[212,61654],{"className":61655,"style":861},[251],[212,61657,795],{"className":61658,"style":822},[256,821],[212,61660],{"className":61661,"style":355},[354],[212,61663,1228],{"className":61664},[359],[212,61666],{"className":61667,"style":355},[354],[212,61669,61671,61674,61680,61683],{"className":61670},[247],[212,61672],{"className":61673,"style":252},[251],[212,61675,61677],{"className":61676},[1682],[212,61678,61617],{"className":61679},[256,32862],[212,61681],{"className":61682,"style":603},[354],[212,61684,61686,61689],{"className":61685},[256],[212,61687,234],{"className":61688,"style":258},[256,257],[212,61690,61692],{"className":61691},[478],[212,61693,61695],{"className":61694},[482],[212,61696,61698],{"className":61697},[487],[212,61699,61701],{"className":61700,"style":8697},[491],[212,61702,61703,61706],{"style":7063},[212,61704],{"className":61705,"style":500},[499],[212,61707,61709],{"className":61708},[504,505,506,507],[212,61710,7771],{"className":61711},[2789,507],[11,61713,61714,61717,61718,61746],{},[1194,61715,61716],{},"证明（Fenchel 对偶）。"," 由共轭函数的性质（Fenchel–Moreau，",[212,61719,61721,61734],{"className":61720,"translate":216},[215],[212,61722,61724],{"className":61723},[220],[222,61725,61726],{"xmlns":224},[226,61727,61728,61732],{},[229,61729,61730],{},[232,61731,234],{},[236,61733,234],{"encoding":238},[212,61735,61737],{"className":61736,"ariaHidden":243},[242],[212,61738,61740,61743],{"className":61739},[247],[212,61741],{"className":61742,"style":252},[251],[212,61744,234],{"className":61745,"style":258},[256,257]," 凸闭），",[212,61748,61750],{"className":61749,"translate":216},[377],[212,61751,61753,61820],{"className":61752,"translate":216},[215],[212,61754,61756],{"className":61755},[220],[222,61757,61758],{"xmlns":224,"display":386},[226,61759,61760,61817],{},[229,61761,61762,61764,61766,61768,61770,61772,61782,61784,61786,61788,61790,61796,61798,61800,61802,61804,61806,61808,61811,61813,61815],{},[232,61763,234],{},[307,61765,310],{"stretchy":309},[232,61767,966],{},[307,61769,317],{"stretchy":309},[307,61771,320],{},[6214,61773,61774,61780],{},[229,61775,61776,61778],{},[232,61777,35632],{},[307,61779,4301],{},[232,61781,40437],{},[307,61783,3096],{"stretchy":309},[232,61785,40437],{},[232,61787,966],{},[307,61789,5011],{},[7012,61791,61792,61794],{},[232,61793,234],{},[307,61795,7771],{},[307,61797,310],{"stretchy":309},[232,61799,40437],{},[307,61801,317],{"stretchy":309},[307,61803,3106],{"stretchy":309},[307,61805,748],{"separator":243},[354,61807],{"width":3460},[232,61809,61810],{"mathvariant":406},"∀",[232,61812,966],{},[307,61814,7126],{},[312,61816,5962],{},[236,61818,61819],{"encoding":238},"f(t)=\\sup_{y}\\{yt-f^*(y)\\},\n\\qquad \\forall t\\ge0 .",[212,61821,61823,61850,61921,61989],{"className":61822,"ariaHidden":243},[242],[212,61824,61826,61829,61832,61835,61838,61841,61844,61847],{"className":61825},[247],[212,61827],{"className":61828,"style":336},[251],[212,61830,234],{"className":61831,"style":258},[256,257],[212,61833,310],{"className":61834},[343],[212,61836,966],{"className":61837},[256,257],[212,61839,317],{"className":61840},[350],[212,61842],{"className":61843,"style":355},[354],[212,61845,320],{"className":61846},[359],[212,61848],{"className":61849,"style":355},[354],[212,61851,61853,61856,61903,61906,61909,61912,61915,61918],{"className":61852},[247],[212,61854],{"className":61855,"style":61385},[251],[212,61857,61859],{"className":61858},[1682,13916],[212,61860,61862,61895],{"className":61861},[482,483],[212,61863,61865,61892],{"className":61864},[487],[212,61866,61868,61882],{"className":61867,"style":2543},[491],[212,61869,61870,61873],{"style":61400},[212,61871],{"className":61872,"style":658},[499],[212,61874,61876],{"className":61875},[504,505,506,507],[212,61877,61879],{"className":61878},[256,507],[212,61880,40437],{"className":61881,"style":1178},[256,257,507],[212,61883,61884,61887],{"style":12063},[212,61885],{"className":61886,"style":658},[499],[212,61888,61889],{},[212,61890,35632],{"className":61891},[1682],[212,61893,515],{"className":61894},[514],[212,61896,61898],{"className":61897},[487],[212,61899,61901],{"className":61900,"style":61432},[491],[212,61902],{},[212,61904,3096],{"className":61905},[343],[212,61907,40437],{"className":61908,"style":1178},[256,257],[212,61910,966],{"className":61911},[256,257],[212,61913],{"className":61914,"style":2785},[354],[212,61916,5011],{"className":61917},[2789],[212,61919],{"className":61920,"style":2785},[354],[212,61922,61924,61927,61956,61959,61962,61965,61968,61971,61974,61977,61980,61983,61986],{"className":61923},[247],[212,61925],{"className":61926,"style":336},[251],[212,61928,61930,61933],{"className":61929},[256],[212,61931,234],{"className":61932,"style":258},[256,257],[212,61934,61936],{"className":61935},[478],[212,61937,61939],{"className":61938},[482],[212,61940,61942],{"className":61941},[487],[212,61943,61945],{"className":61944,"style":8446},[491],[212,61946,61947,61950],{"style":8475},[212,61948],{"className":61949,"style":500},[499],[212,61951,61953],{"className":61952},[504,505,506,507],[212,61954,7771],{"className":61955},[2789,507],[212,61957,310],{"className":61958},[343],[212,61960,40437],{"className":61961,"style":1178},[256,257],[212,61963,61209],{"className":61964},[350],[212,61966,748],{"className":61967},[770],[212,61969],{"className":61970,"style":3832},[354],[212,61972],{"className":61973,"style":603},[354],[212,61975,61810],{"className":61976},[256],[212,61978,966],{"className":61979},[256,257],[212,61981],{"className":61982,"style":355},[354],[212,61984,7126],{"className":61985},[359],[212,61987],{"className":61988,"style":355},[354],[212,61990,61992,61995],{"className":61991},[247],[212,61993],{"className":61994,"style":369},[251],[212,61996,5962],{"className":61997},[256],[11,61999,17246,62000,62134,62135,62163],{},[212,62001,62003,62033],{"className":62002,"translate":216},[215],[212,62004,62006],{"className":62005},[220],[222,62007,62008],{"xmlns":224},[226,62009,62010,62030],{},[229,62011,62012,62014,62016],{},[232,62013,966],{},[307,62015,320],{},[435,62017,62018,62024],{},[229,62019,62020,62022],{},[232,62021,441],{},[232,62023,403],{},[229,62025,62026,62028],{},[232,62027,441],{},[232,62029,410],{},[236,62031,62032],{"encoding":238},"t=\\frac{dP}{dQ}",[212,62034,62036,62054],{"className":62035,"ariaHidden":243},[242],[212,62037,62039,62042,62045,62048,62051],{"className":62038},[247],[212,62040],{"className":62041,"style":5541},[251],[212,62043,966],{"className":62044},[256,257],[212,62046],{"className":62047,"style":355},[354],[212,62049,320],{"className":62050},[359],[212,62052],{"className":62053,"style":355},[354],[212,62055,62057,62060],{"className":62056},[247],[212,62058],{"className":62059,"style":2866},[251],[212,62061,62063,62066,62131],{"className":62062},[256],[212,62064],{"className":62065},[343,638],[212,62067,62069],{"className":62068},[435],[212,62070,62072,62123],{"className":62071},[482,483],[212,62073,62075,62120],{"className":62074},[487],[212,62076,62078,62095,62103],{"className":62077,"style":2885},[491],[212,62079,62080,62083],{"style":2725},[212,62081],{"className":62082,"style":658},[499],[212,62084,62086],{"className":62085},[504,505,506,507],[212,62087,62089,62092],{"className":62088},[256,507],[212,62090,441],{"className":62091},[256,257,507],[212,62093,410],{"className":62094},[256,257,507],[212,62096,62097,62100],{"style":670},[212,62098],{"className":62099,"style":658},[499],[212,62101],{"className":62102,"style":678},[677],[212,62104,62105,62108],{"style":2748},[212,62106],{"className":62107,"style":658},[499],[212,62109,62111],{"className":62110},[504,505,506,507],[212,62112,62114,62117],{"className":62113},[256,507],[212,62115,441],{"className":62116},[256,257,507],[212,62118,403],{"className":62119,"style":531},[256,257,507],[212,62121,515],{"className":62122},[514],[212,62124,62126],{"className":62125},[487],[212,62127,62129],{"className":62128,"style":2937},[491],[212,62130],{},[212,62132],{"className":62133},[350,638]," 代入并对 ",[212,62136,62138,62151],{"className":62137,"translate":216},[215],[212,62139,62141],{"className":62140},[220],[222,62142,62143],{"xmlns":224},[226,62144,62145,62149],{},[229,62146,62147],{},[232,62148,410],{},[236,62150,410],{"encoding":238},[212,62152,62154],{"className":62153,"ariaHidden":243},[242],[212,62155,62157,62160],{"className":62156},[247],[212,62158],{"className":62159,"style":763},[251],[212,62161,410],{"className":62162},[256,257]," 积分：",[212,62165,62167],{"className":62166,"translate":216},[377],[212,62168,62170,62412],{"className":62169,"translate":216},[215],[212,62171,62173],{"className":62172},[220],[222,62174,62175],{"xmlns":224,"display":386},[226,62176,62177,62409],{},[1441,62178,62179,62265,62339],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,62180,62181,62203],{},[1450,62182,62183],{},[1453,62184,62185],{"scriptlevel":323,"displaystyle":243},[229,62186,62187,62193,62195,62197,62199,62201],{},[392,62188,62189,62191],{},[232,62190,396],{},[232,62192,234],{},[307,62194,310],{"stretchy":309},[232,62196,403],{},[232,62198,407],{"mathvariant":406},[232,62200,410],{},[307,62202,317],{"stretchy":309},[1450,62204,62205],{},[1453,62206,62207],{"scriptlevel":323,"displaystyle":243},[229,62208,62209,62211,62213,62215,62225,62227,62229,62231,62245,62247,62253,62255,62257,62259,62261,62263],{},[229,62210],{},[307,62212,320],{},[307,62214,1485],{},[6214,62216,62217,62223],{},[229,62218,62219,62221],{},[232,62220,35632],{},[307,62222,4301],{},[232,62224,40437],{},[307,62226,3096],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[232,62228,40437],{},[1495,62230,1497],{},[435,62232,62233,62239],{},[229,62234,62235,62237],{},[232,62236,441],{},[232,62238,403],{},[229,62240,62241,62243],{},[232,62242,441],{},[232,62244,410],{},[307,62246,5011],{},[7012,62248,62249,62251],{},[232,62250,234],{},[307,62252,7771],{},[307,62254,310],{"stretchy":309},[232,62256,40437],{},[307,62258,317],{"stretchy":309},[307,62260,3106],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[232,62262,441],{},[232,62264,410],{},[1447,62266,62267,62273],{},[1450,62268,62269],{},[1453,62270,62271],{"scriptlevel":323,"displaystyle":243},[229,62272],{},[1450,62274,62275],{},[1453,62276,62277],{"scriptlevel":323,"displaystyle":243},[229,62278,62279,62281,62283,62285,62287,62297,62299,62301,62303,62305,62319,62321,62327,62329,62331,62333,62335,62337],{},[229,62280],{},[1495,62282,4481],{},[307,62284,7126],{},[1495,62286,4481],{},[6214,62288,62289,62295],{},[229,62290,62291,62293],{},[232,62292,35632],{},[307,62294,4301],{},[232,62296,40437],{},[307,62298,1485],{},[307,62300,3096],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[232,62302,40437],{},[1495,62304,1497],{},[435,62306,62307,62313],{},[229,62308,62309,62311],{},[232,62310,441],{},[232,62312,403],{},[229,62314,62315,62317],{},[232,62316,441],{},[232,62318,410],{},[307,62320,5011],{},[7012,62322,62323,62325],{},[232,62324,234],{},[307,62326,7771],{},[307,62328,310],{"stretchy":309},[232,62330,40437],{},[307,62332,317],{"stretchy":309},[307,62334,3106],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[232,62336,441],{},[232,62338,410],{},[1447,62340,62341,62347],{},[1450,62342,62343],{},[1453,62344,62345],{"scriptlevel":323,"displaystyle":243},[229,62346],{},[1450,62348,62349],{},[1453,62350,62351],{"scriptlevel":323,"displaystyle":243},[229,62352,62353,62355,62357,62367,62369,62375,62377,62379,62381,62383,62389,62391,62397,62399,62401,62403,62405,62407],{},[229,62354],{},[307,62356,320],{},[6214,62358,62359,62365],{},[229,62360,62361,62363],{},[232,62362,35632],{},[307,62364,4301],{},[232,62366,40437],{},[307,62368,3096],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[392,62370,62371,62373],{},[232,62372,420],{"mathvariant":419},[232,62374,403],{},[307,62376,427],{"stretchy":309},[232,62378,40437],{},[307,62380,454],{"stretchy":309},[307,62382,5011],{},[392,62384,62385,62387],{},[232,62386,420],{"mathvariant":419},[232,62388,410],{},[307,62390,427],{"stretchy":309},[7012,62392,62393,62395],{},[232,62394,234],{},[307,62396,7771],{},[307,62398,310],{"stretchy":309},[232,62400,40437],{},[307,62402,317],{"stretchy":309},[307,62404,454],{"stretchy":309},[307,62406,3106],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,62408,4573],{"mathvariant":406},[236,62410,62411],{"encoding":238},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\int \\sup_y\\Big\\{y\\,\\frac{dP}{dQ}\n-f^*(y)\\Big\\}dQ\\\\\n&\\ \\ge\\ \\sup_y\\int\\Big\\{y\\,\\frac{dP}{dQ}\n-f^*(y)\\Big\\}dQ\\\\\n&=\\sup_y\\big\\{\\mathbb E_P[y]\n-\\mathbb E_Q[f^*(y)]\\big\\}.\n\\end{aligned}",[212,62413,62415],{"className":62414,"ariaHidden":243},[242],[212,62416,62418,62422],{"className":62417},[247],[212,62419],{"className":62420,"style":62421},[251],"height:7.2845em;vertical-align:-3.3923em;",[212,62423,62425],{"className":62424},[256],[212,62426,62428,62536],{"className":62427},[1441],[212,62429,62431],{"className":62430},[1558],[212,62432,62434,62527],{"className":62433},[482,483],[212,62435,62437,62524],{"className":62436},[487],[212,62438,62441,62506,62515],{"className":62439,"style":62440},[491],"height:3.8923em;",[212,62442,62444,62448],{"style":62443},"top:-5.8923em;",[212,62445],{"className":62446,"style":62447},[499],"height:3.3714em;",[212,62449,62451,62491,62494,62497,62500,62503],{"className":62450},[256],[212,62452,62454,62457],{"className":62453},[256],[212,62455,396],{"className":62456,"style":474},[256,257],[212,62458,62460],{"className":62459},[478],[212,62461,62463,62483],{"className":62462},[482,483],[212,62464,62466,62480],{"className":62465},[487],[212,62467,62469],{"className":62468,"style":492},[491],[212,62470,62471,62474],{"style":495},[212,62472],{"className":62473,"style":500},[499],[212,62475,62477],{"className":62476},[504,505,506,507],[212,62478,234],{"className":62479,"style":258},[256,257,507],[212,62481,515],{"className":62482},[514],[212,62484,62486],{"className":62485},[487],[212,62487,62489],{"className":62488,"style":522},[491],[212,62490],{},[212,62492,310],{"className":62493},[343],[212,62495,403],{"className":62496,"style":531},[256,257],[212,62498,407],{"className":62499},[256],[212,62501,410],{"className":62502},[256,257],[212,62504,317],{"className":62505},[350],[212,62507,62509,62512],{"style":62508},"top:-3.1903em;",[212,62510],{"className":62511,"style":62447},[499],[212,62513],{"className":62514},[256],[212,62516,62518,62521],{"style":62517},"top:-1.0097em;",[212,62519],{"className":62520,"style":62447},[499],[212,62522],{"className":62523},[256],[212,62525,515],{"className":62526},[514],[212,62528,62530],{"className":62529},[487],[212,62531,62534],{"className":62532,"style":62533},[491],"height:3.3923em;",[212,62535],{},[212,62537,62539],{"className":62538},[1649],[212,62540,62542,63202],{"className":62541},[482,483],[212,62543,62545,63199],{"className":62544},[487],[212,62546,62548,62760,62978],{"className":62547,"style":62440},[491],[212,62549,62550,62553],{"style":62443},[212,62551],{"className":62552,"style":62447},[499],[212,62554,62556,62559,62562,62565,62568,62571,62574,62618,62621,62627,62630,62633,62701,62704,62707,62710,62739,62742,62745,62748,62754,62757],{"className":62555},[256],[212,62557],{"className":62558},[256],[212,62560],{"className":62561,"style":355},[354],[212,62563,320],{"className":62564},[359],[212,62566],{"className":62567,"style":355},[354],[212,62569,1485],{"className":62570,"style":1685},[1682,1683,1684],[212,62572],{"className":62573,"style":603},[354],[212,62575,62577],{"className":62576},[1682,13916],[212,62578,62580,62610],{"className":62579},[482,483],[212,62581,62583,62607],{"className":62582},[487],[212,62584,62586,62597],{"className":62585,"style":2543},[491],[212,62587,62588,62591],{"style":61400},[212,62589],{"className":62590,"style":658},[499],[212,62592,62594],{"className":62593},[504,505,506,507],[212,62595,40437],{"className":62596,"style":1178},[256,257,507],[212,62598,62599,62602],{"style":12063},[212,62600],{"className":62601,"style":658},[499],[212,62603,62604],{},[212,62605,35632],{"className":62606},[1682],[212,62608,515],{"className":62609},[514],[212,62611,62613],{"className":62612},[487],[212,62614,62616],{"className":62615,"style":61432},[491],[212,62617],{},[212,62619],{"className":62620,"style":603},[354],[212,62622,62624],{"className":62623},[256],[212,62625,3096],{"className":62626},[616,3918],[212,62628,40437],{"className":62629,"style":1178},[256,257],[212,62631],{"className":62632,"style":603},[354],[212,62634,62636,62639,62698],{"className":62635},[256],[212,62637],{"className":62638},[343,638],[212,62640,62642],{"className":62641},[435],[212,62643,62645,62690],{"className":62644},[482,483],[212,62646,62648,62687],{"className":62647},[487],[212,62649,62651,62665,62673],{"className":62650,"style":651},[491],[212,62652,62653,62656],{"style":654},[212,62654],{"className":62655,"style":658},[499],[212,62657,62659,62662],{"className":62658},[256],[212,62660,441],{"className":62661},[256,257],[212,62663,410],{"className":62664},[256,257],[212,62666,62667,62670],{"style":670},[212,62668],{"className":62669,"style":658},[499],[212,62671],{"className":62672,"style":678},[677],[212,62674,62675,62678],{"style":681},[212,62676],{"className":62677,"style":658},[499],[212,62679,62681,62684],{"className":62680},[256],[212,62682,441],{"className":62683},[256,257],[212,62685,403],{"className":62686,"style":531},[256,257],[212,62688,515],{"className":62689},[514],[212,62691,62693],{"className":62692},[487],[212,62694,62696],{"className":62695,"style":703},[491],[2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",[212,63214,63216,63229],{"className":63215,"translate":216},[215],[212,63217,63219],{"className":63218},[220],[222,63220,63221],{"xmlns":224},[226,63222,63223,63227],{},[229,63224,63225],{},[307,63226,7126],{},[236,63228,55690],{"encoding":238},[212,63230,63232],{"className":63231,"ariaHidden":243},[242],[212,63233,63235,63238],{"className":63234},[247],[212,63236],{"className":63237,"style":43388},[251],[212,63239,7126],{"className":63240},[359],"，因为「积分的上确界 ≥ 上确界的积分」。反向不等式需要一个可测选择\u002F极大值论证：由于 ",[212,63243,63245,63258],{"className":63244,"translate":216},[215],[212,63246,63248],{"className":63247},[220],[222,63249,63250],{"xmlns":224},[226,63251,63252,63256],{},[229,63253,63254],{},[232,63255,234],{},[236,63257,234],{"encoding":238},[212,63259,63261],{"className":63260,"ariaHidden":243},[242],[212,63262,63264,63267],{"className":63263},[247],[212,63265],{"className":63266,"style":252},[251],[212,63268,234],{"className":63269,"style":258},[256,257]," 凸，",[212,63272,63274,63328],{"className":63273,"translate":216},[215],[212,63275,63277],{"className":63276},[220],[222,63278,63279],{"xmlns":224},[226,63280,63281,63325],{},[229,63282,63283,63285,63287,63289,63291,63293,63303,63305,63307,63309,63311,63317,63319,63321,63323],{},[232,63284,234],{},[307,63286,310],{"stretchy":309},[232,63288,966],{},[307,63290,317],{"stretchy":309},[307,63292,320],{},[392,63294,63295,63301],{},[229,63296,63297,63299],{},[232,63298,35632],{},[307,63300,4301],{},[232,63302,40437],{},[307,63304,3096],{"stretchy":309},[232,63306,40437],{},[232,63308,966],{},[307,63310,5011],{},[7012,63312,63313,63315],{},[232,63314,234],{},[307,63316,7771],{},[307,63318,310],{"stretchy":309},[232,63320,40437],{},[307,63322,317],{"stretchy":309},[307,63324,3106],{"stretchy":309},[236,63326,63327],{"encoding":238},"f(t)=\\sup_y\\{yt-f^*(y)\\}",[212,63329,63331,63358,63422],{"className":63330,"ariaHidden":243},[242],[212,63332,63334,63337,63340,63343,63346,63349,63352,63355],{"className":63333},[247],[212,63335],{"className":63336,"style":336},[251],[212,63338,234],{"className":63339,"style":258},[256,257],[212,63341,310],{"className":63342},[343],[212,63344,966],{"className":63345},[256,257],[212,63347,317],{"className":63348},[350],[212,63350],{"className":63351,"style":355},[354],[212,63353,320],{"className":63354},[359],[212,63356],{"className":63357,"style":355},[354],[212,63359,63361,63364,63404,63407,63410,63413,63416,63419],{"className":63360},[247],[212,63362],{"className":63363,"style":57526},[251],[212,63365,63367,63370],{"className":63366},[1682],[212,63368,35632],{"className":63369},[1682],[212,63371,63373],{"className":63372},[478],[212,63374,63376,63396],{"className":63375},[482,483],[212,63377,63379,63393],{"className":63378},[487],[212,63380,63382],{"className":63381,"style":37199},[491],[212,63383,63384,63387],{"style":35778},[212,63385],{"className":63386,"style":500},[499],[212,63388,63390],{"className":63389},[504,505,506,507],[212,63391,40437],{"className":63392,"style":1178},[256,257,507],[212,63394,515],{"className":63395},[514],[212,63397,63399],{"className":63398},[487],[212,63400,63402],{"className":63401,"style":57565},[491],[212,63403],{},[212,63405,3096],{"className":63406},[343],[212,63408,40437],{"className":63409,"style":1178},[256,257],[212,63411,966],{"className":63412},[256,257],[212,63414],{"className":63415,"style":2785},[354],[212,63417,5011],{"className":63418},[2789],[212,63420],{"className":63421,"style":2785},[354],[212,63423,63425,63428,63457,63460,63463],{"className":63424},[247],[212,63426],{"className":63427,"style":336},[251],[212,63429,63431,63434],{"className":63430},[256],[212,63432,234],{"className":63433,"style":258},[256,257],[212,63435,63437],{"className":63436},[478],[212,63438,63440],{"className":63439},[482],[212,63441,63443],{"className":63442},[487],[212,63444,63446],{"className":63445,"style":8697},[491],[212,63447,63448,63451],{"style":7063},[212,63449],{"className":63450,"style":500},[499],[212,63452,63454],{"className":63453},[504,505,506,507],[212,63455,7771],{"className":63456},[2789,507],[212,63458,310],{"className":63459},[343],[212,63461,40437],{"className":63462,"style":1178},[256,257],[212,63464,61209],{"className":63465},[350]," 中的 ",[212,63468,63470,63483],{"className":63469,"translate":216},[215],[212,63471,63473],{"className":63472},[220],[222,63474,63475],{"xmlns":224},[226,63476,63477,63481],{},[229,63478,63479],{},[232,63480,40437],{},[236,63482,40437],{"encoding":238},[212,63484,63486],{"className":63485,"ariaHidden":243},[242],[212,63487,63489,63492],{"className":63488},[247],[212,63490],{"className":63491,"style":2474},[251],[212,63493,40437],{"className":63494,"style":1178},[256,257]," 可取为 ",[212,63497,63499,63523],{"className":63498,"translate":216},[215],[212,63500,63502],{"className":63501},[220],[222,63503,63504],{"xmlns":224},[226,63505,63506,63520],{},[229,63507,63508,63514,63516,63518],{},[7012,63509,63510,63512],{},[232,63511,234],{},[307,63513,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,63515,310],{"stretchy":309},[232,63517,966],{},[307,63519,317],{"stretchy":309},[236,63521,63522],{"encoding":238},"f'(t)",[212,63524,63526],{"className":63525,"ariaHidden":243},[242],[212,63527,63529,63532,63564,63567,63570],{"className":63528},[247],[212,63530],{"className":63531,"style":7041},[251],[212,63533,63535,63538],{"className":63534},[256],[212,63536,234],{"className":63537,"style":258},[256,257],[212,63539,63541],{"className":63540},[478],[212,63542,63544],{"className":63543},[482],[212,63545,63547],{"className":63546},[487],[212,63548,63550],{"className":63549,"style":7060},[491],[212,63551,63552,63555],{"style":7063},[212,63553],{"className":63554,"style":500},[499],[212,63556,63558],{"className":63557},[504,505,506,507],[212,63559,63561],{"className":63560},[256,507],[212,63562,7018],{"className":63563},[256,507],[212,63565,310],{"className":63566},[343],[212,63568,966],{"className":63569},[256,257],[212,63571,317],{"className":63572},[350],"（在可微点），而 ",[212,63575,63577,63605],{"className":63576,"translate":216},[215],[212,63578,63580],{"className":63579},[220],[222,63581,63582],{"xmlns":224},[226,63583,63584,63602],{},[229,63585,63586,63588,63590,63596,63598,63600],{},[232,63587,966],{},[307,63589,8882],{},[7012,63591,63592,63594],{},[232,63593,234],{},[307,63595,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,63597,310],{"stretchy":309},[232,63599,966],{},[307,63601,317],{"stretchy":309},[236,63603,63604],{"encoding":238},"t\\mapsto f'(t)",[212,63606,63608,63626],{"className":63607,"ariaHidden":243},[242],[212,63609,63611,63614,63617,63620,63623],{"className":63610},[247],[212,63612],{"className":63613,"style":8909},[251],[212,63615,966],{"className":63616},[256,257],[212,63618],{"className":63619,"style":355},[354],[212,63621,8882],{"className":63622},[359],[212,63624],{"className":63625,"style":355},[354],[212,63627,63629,63632,63664,63667,63670],{"className":63628},[247],[212,63630],{"className":63631,"style":7041},[251],[212,63633,63635,63638],{"className":63634},[256],[212,63636,234],{"className":63637,"style":258},[256,257],[212,63639,63641],{"className":63640},[478],[212,63642,63644],{"className":63643},[482],[212,63645,63647],{"className":63646},[487],[212,63648,63650],{"className":63649,"style":7060},[491],[212,63651,63652,63655],{"style":7063},[212,63653],{"className":63654,"style":500},[499],[212,63656,63658],{"className":63657},[504,505,506,507],[212,63659,63661],{"className":63660},[256,507],[212,63662,7018],{"className":63663},[256,507],[212,63665,310],{"className":63666},[343],[212,63668,966],{"className":63669},[256,257],[212,63671,317],{"className":63672},[350]," 单调，于是 ",[212,63675,63677,63723],{"className":63676,"translate":216},[215],[212,63678,63680],{"className":63679},[220],[222,63681,63682],{"xmlns":224},[226,63683,63684,63720],{},[229,63685,63686,63692,63694,63696,63698,63700,63702,63708,63710,63712,63714,63716,63718],{},[7012,63687,63688,63690],{},[232,63689,4356],{},[307,63691,7771],{},[307,63693,310],{"stretchy":309},[232,63695,971],{},[307,63697,317],{"stretchy":309},[307,63699,1214],{},[307,63701,320],{},[7012,63703,63704,63706],{},[232,63705,234],{},[307,63707,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,63709,310],{"stretchy":309},[232,63711,966],{},[307,63713,310],{"stretchy":309},[232,63715,971],{},[307,63717,317],{"stretchy":309},[307,63719,317],{"stretchy":309},[236,63721,63722],{"encoding":238},"g^*(x):=f'(t(x))",[212,63724,63726,63780],{"className":63725,"ariaHidden":243},[242],[212,63727,63729,63732,63761,63764,63767,63770,63773,63777],{"className":63728},[247],[212,63730],{"className":63731,"style":336},[251],[212,63733,63735,63738],{"className":63734},[256],[212,63736,4356],{"className":63737,"style":1178},[256,257],[212,63739,63741],{"className":63740},[478],[212,63742,63744],{"className":63743},[482],[212,63745,63747],{"className":63746},[487],[212,63748,63750],{"className":63749,"style":8697},[491],[212,63751,63752,63755],{"style":7063},[212,63753],{"className":63754,"style":500},[499],[212,63756,63758],{"className":63757},[504,505,506,507],[212,63759,7771],{"className":63760},[2789,507],[212,63762,310],{"className":63763},[343],[212,63765,971],{"className":63766},[256,257],[212,63768,317],{"className":63769},[350],[212,63771],{"className":63772,"style":355},[354],[212,63774,63776],{"className":63775},[359],":=",[212,63778],{"className":63779,"style":355},[354],[212,63781,63783,63786,63818,63821,63824,63827,63830],{"className":63782},[247],[212,63784],{"className":63785,"style":7041},[251],[212,63787,63789,63792],{"className":63788},[256],[212,63790,234],{"className":63791,"style":258},[256,257],[212,63793,63795],{"className":63794},[478],[212,63796,63798],{"className":63797},[482],[212,63799,63801],{"className":63800},[487],[212,63802,63804],{"className":63803,"style":7060},[491],[212,63805,63806,63809],{"style":7063},[212,63807],{"className":63808,"style":500},[499],[212,63810,63812],{"className":63811},[504,505,506,507],[212,63813,63815],{"className":63814},[256,507],[212,63816,7018],{"className":63817},[256,507],[212,63819,310],{"className":63820},[343],[212,63822,966],{"className":63823},[256,257],[212,63825,310],{"className":63826},[343],[212,63828,971],{"className":63829},[256,257],[212,63831,19247],{"className":63832},[350]," 是可测的，并且对每个 ",[212,63835,63837,63850],{"className":63836,"translate":216},[215],[212,63838,63840],{"className":63839},[220],[222,63841,63842],{"xmlns":224},[226,63843,63844,63848],{},[229,63845,63846],{},[232,63847,971],{},[236,63849,971],{"encoding":238},[212,63851,63853],{"className":63852,"ariaHidden":243},[242],[212,63854,63856,63859],{"className":63855},[247],[212,63857],{"className":63858,"style":2543},[251],[212,63860,971],{"className":63861},[256,257]," 达到上确界。于是不等式取等号。",[11,63864,63865,63868],{},[1194,63866,63867],{},"最优解。"," 达到上确界的函数为",[212,63870,63872],{"className":63871,"translate":216},[377],[212,63873,63875,63937],{"className":63874,"translate":216},[215],[212,63876,63878],{"className":63877},[220],[222,63879,63880],{"xmlns":224,"display":386},[226,63881,63882,63934],{},[229,63883,63884,63890,63892,63894,63896,63898,63904,63906,63932],{},[7012,63885,63886,63888],{},[232,63887,4356],{},[307,63889,7771],{},[307,63891,310],{"stretchy":309},[232,63893,971],{},[307,63895,317],{"stretchy":309},[307,63897,320],{},[7012,63899,63900,63902],{},[232,63901,234],{},[307,63903,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[1495,63905,1502],{},[229,63907,63908,63910,63924,63926,63928,63930],{},[307,63909,310],{"fence":243},[435,63911,63912,63918],{},[229,63913,63914,63916],{},[232,63915,441],{},[232,63917,403],{},[229,63919,63920,63922],{},[232,63921,441],{},[232,63923,410],{},[307,63925,310],{"stretchy":309},[232,63927,971],{},[307,63929,317],{"stretchy":309},[307,63931,317],{"fence":243},[307,63933,748],{"separator":243},[236,63935,63936],{"encoding":238},"g^*(x)=f'\\!\\left(\\frac{dP}{dQ}(x)\\right),",[212,63938,63940,63993],{"className":63939,"ariaHidden":243},[242],[212,63941,63943,63946,63975,63978,63981,63984,63987,63990],{"className":63942},[247],[212,63944],{"className":63945,"style":336},[251],[212,63947,63949,63952],{"className":63948},[256],[212,63950,4356],{"className":63951,"style":1178},[256,257],[212,63953,63955],{"className":63954},[478],[212,63956,63958],{"className":63957},[482],[212,63959,63961],{"className":63960},[487],[212,63962,63964],{"className":63963,"style":8446},[491],[212,63965,63966,63969],{"style":8475},[212,63967],{"className":63968,"style":500},[499],[212,63970,63972],{"className":63971},[504,505,506,507],[212,63973,7771],{"className":63974},[2789,507],[212,63976,310],{"className":63977},[343],[212,63979,971],{"className":63980},[256,257],[212,63982,317],{"className":63983},[350],[212,63985],{"className":63986,"style":355},[354],[212,63988,320],{"className":63989},[359],[212,63991],{"className":63992,"style":355},[354],[212,63994,63996,63999,64031,64034,64037,64129,64132],{"className":63995},[247],[212,63997],{"className":63998,"style":556},[251],[212,64000,64002,64005],{"className":64001},[256],[212,64003,234],{"className":64004,"style":258},[256,257],[212,64006,64008],{"className":64007},[478],[212,64009,64011],{"className":64010},[482],[212,64012,64014],{"className":64013},[487],[212,64015,64017],{"className":64016,"style":29171},[491],[212,64018,64019,64022],{"style":8475},[212,64020],{"className":64021,"style":500},[499],[212,64023,64025],{"className":64024},[504,505,506,507],[212,64026,64028],{"className":64027},[256,507],[212,64029,7018],{"className":64030},[256,507],[212,64032],{"className":64033,"style":1710},[354],[212,64035],{"className":64036,"style":603},[354],[212,64038,64040,64046,64114,64117,64120,64123],{"className":64039},[607],[212,64041,64043],{"className":64042,"style":612},[343,611],[212,64044,310],{"className":64045},[616,506],[212,64047,64049,64052,64111],{"className":64048},[256],[212,64050],{"className":64051},[343,638],[212,64053,64055],{"className":64054},[435],[212,64056,64058,64103],{"className":64057},[482,483],[212,64059,64061,64100],{"className":64060},[487],[212,64062,64064,64078,64086],{"className":64063,"style":651},[491],[212,64065,64066,64069],{"style":654},[212,64067],{"className":64068,"style":658},[499],[212,64070,64072,64075],{"className":64071},[256],[212,64073,441],{"className":64074},[256,257],[212,64076,410],{"className":64077},[256,257],[212,64079,64080,64083],{"style":670},[212,64081],{"className":64082,"style":658},[499],[212,64084],{"className":64085,"style":678},[677],[212,64087,64088,64091],{"style":681},[212,64089],{"className":64090,"style":658},[499],[212,64092,64094,64097],{"className":64093},[256],[212,64095,441],{"className":64096},[256,257],[212,64098,403],{"className":64099,"style":531},[256,257],[212,64101,515],{"className":64102},[514],[212,64104,64106],{"className":64105},[487],[212,64107,64109],{"className":64108,"style":703},[491],[212,64110],{},[212,64112],{"className":64113},[350,638],[212,64115,310],{"className":64116},[343],[212,64118,971],{"className":64119},[256,257],[212,64121,317],{"className":64122},[350],[212,64124,64126],{"className":64125,"style":612},[350,611],[212,64127,317],{"className":64128},[616,506],[212,64130],{"className":64131,"style":603},[354],[212,64133,748],{"className":64134},[770],[11,64136,64137,64138,4051,64166,64194,64195,64255,64256,64328,64329,45807,64448,64632],{},"条件是 ",[212,64139,64141,64154],{"className":64140,"translate":216},[215],[212,64142,64144],{"className":64143},[220],[222,64145,64146],{"xmlns":224},[226,64147,64148,64152],{},[229,64149,64150],{},[232,64151,234],{},[236,64153,234],{"encoding":238},[212,64155,64157],{"className":64156,"ariaHidden":243},[242],[212,64158,64160,64163],{"className":64159},[247],[212,64161],{"className":64162,"style":252},[251],[212,64164,234],{"className":64165,"style":258},[256,257],[212,64167,64169,64182],{"className":64168,"translate":216},[215],[212,64170,64172],{"className":64171},[220],[222,64173,64174],{"xmlns":224},[226,64175,64176,64180],{},[229,64177,64178],{},[232,64179,966],{},[236,64181,966],{"encoding":238},[212,64183,64185],{"className":64184,"ariaHidden":243},[242],[212,64186,64188,64191],{"className":64187},[247],[212,64189],{"className":64190,"style":5541},[251],[212,64192,966],{"className":64193},[256,257]," 处可微、且 ",[212,64196,64198,64216],{"className":64197,"translate":216},[215],[212,64199,64201],{"className":64200},[220],[222,64202,64203],{"xmlns":224},[226,64204,64205,64213],{},[229,64206,64207],{},[7012,64208,64209,64211],{},[232,64210,4356],{},[307,64212,7771],{},[236,64214,64215],{"encoding":238},"g^*",[212,64217,64219],{"className":64218,"ariaHidden":243},[242],[212,64220,64222,64226],{"className":64221},[247],[212,64223],{"className":64224,"style":64225},[251],"height:0.8831em;vertical-align:-0.1944em;",[212,64227,64229,64232],{"className":64228},[256],[212,64230,4356],{"className":64231,"style":1178},[256,257],[212,64233,64235],{"className":64234},[478],[212,64236,64238],{"className":64237},[482],[212,64239,64241],{"className":64240},[487],[212,64242,64244],{"className":64243,"style":8697},[491],[212,64245,64246,64249],{"style":7063},[212,64247],{"className":64248,"style":500},[499],[212,64250,64252],{"className":64251},[504,505,506,507],[212,64253,7771],{"className":64254},[2789,507]," 落在 ",[212,64257,64259,64281],{"className":64258,"translate":216},[215],[212,64260,64262],{"className":64261},[220],[222,64263,64264],{"xmlns":224},[226,64265,64266,64278],{},[229,64267,64268,64270,64272],{},[232,64269,61617],{"mathvariant":406},[307,64271,4301],{},[7012,64273,64274,64276],{},[232,64275,234],{},[307,64277,7771],{},[236,64279,64280],{"encoding":238},"\\operatorname{dom} f^*",[212,64282,64284],{"className":64283,"ariaHidden":243},[242],[212,64285,64287,64290,64296,64299],{"className":64286},[247],[212,64288],{"className":64289,"style":252},[251],[212,64291,64293],{"className":64292},[1682],[212,64294,61617],{"className":64295},[256,32862],[212,64297],{"className":64298,"style":603},[354],[212,64300,64302,64305],{"className":64301},[256],[212,64303,234],{"className":64304,"style":258},[256,257],[212,64306,64308],{"className":64307},[478],[212,64309,64311],{"className":64310},[482],[212,64312,64314],{"className":64313},[487],[212,64315,64317],{"className":64316,"style":8697},[491],[212,64318,64319,64322],{"style":7063},[212,64320],{"className":64321,"style":500},[499],[212,64323,64325],{"className":64324},[504,505,506,507],[212,64326,7771],{"className":64327},[2789,507]," 内。例如 KL（",[212,64330,64332,64362],{"className":64331,"translate":216},[215],[212,64333,64335],{"className":64334},[220],[222,64336,64337],{"xmlns":224},[226,64338,64339,64359],{},[229,64340,64341,64347,64349,64351,64353,64355,64357],{},[7012,64342,64343,64345],{},[232,64344,234],{},[307,64346,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,64348,320],{},[232,64350,4298],{},[307,64352,4301],{},[232,64354,966],{},[307,64356,2668],{},[312,64358,314],{},[236,64360,64361],{"encoding":238},"f'=\\log t+1",[212,64363,64365,64413,64439],{"className":64364,"ariaHidden":243},[242],[212,64366,64368,64372,64404,64407,64410],{"className":64367},[247],[212,64369],{"className":64370,"style":64371},[251],"height:0.9463em;vertical-align:-0.1944em;",[212,64373,64375,64378],{"className":64374},[256],[212,64376,234],{"className":64377,"style":258},[256,257],[212,64379,64381],{"className":64380},[478],[212,64382,64384],{"className":64383},[482],[212,64385,64387],{"className":64386},[487],[212,64388,64390],{"className":64389,"style":7060},[491],[212,64391,64392,64395],{"style":7063},[212,64393],{"className":64394,"style":500},[499],[212,64396,64398],{"className":64397},[504,505,506,507],[212,64399,64401],{"className":64400},[256,507],[212,64402,7018],{"className":64403},[256,507],[212,64405],{"className":64406,"style":355},[354],[212,64408,320],{"className":64409},[359],[212,64411],{"className":64412,"style":355},[354],[212,64414,64416,64419,64424,64427,64430,64433,64436],{"className":64415},[247],[212,64417],{"className":64418,"style":252},[251],[212,64420,4352,64422],{"className":64421},[1682],[212,64423,4356],{"style":4355},[212,64425],{"className":64426,"style":603},[354],[212,64428,966],{"className":64429},[256,257],[212,64431],{"className":64432,"style":2785},[354],[212,64434,2668],{"className":64435},[2789],[212,64437],{"className":64438,"style":2785},[354],[212,64440,64442,64445],{"className":64441},[247],[212,64443],{"className":64444,"style":369},[251],[212,64446,314],{"className":64447},[256],[212,64449,64451,64485],{"className":64450,"translate":216},[215],[212,64452,64454],{"className":64453},[220],[222,64455,64456],{"xmlns":224},[226,64457,64458,64482],{},[229,64459,64460,64466,64468,64470,64472,64478,64480],{},[7012,64461,64462,64464],{},[232,64463,4356],{},[307,64465,7771],{},[307,64467,320],{},[232,64469,4298],{},[307,64471,4301],{},[435,64473,64474,64476],{},[232,64475,11],{},[232,64477,1141],{},[307,64479,2668],{},[312,64481,314],{},[236,64483,64484],{"encoding":238},"g^*=\\log\\frac{p}{q}+1",[212,64486,64488,64532,64623],{"className":64487,"ariaHidden":243},[242],[212,64489,64491,64494,64523,64526,64529],{"className":64490},[247],[212,64492],{"className":64493,"style":64225},[251],[212,64495,64497,64500],{"className":64496},[256],[212,64498,4356],{"className":64499,"style":1178},[256,257],[212,64501,64503],{"className":64502},[478],[212,64504,64506],{"className":64505},[482],[212,64507,64509],{"className":64508},[487],[212,64510,64512],{"className":64511,"style":8697},[491],[212,64513,64514,64517],{"style":7063},[212,64515],{"className":64516,"style":500},[499],[212,64518,64520],{"className":64519},[504,505,506,507],[212,64521,7771],{"className":64522},[2789,507],[212,64524],{"className":64525,"style":355},[354],[212,64527,320],{"className":64528},[359],[212,64530],{"className":64531,"style":355},[354],[212,64533,64535,64538,64543,64546,64614,64617,64620],{"className":64534},[247],[212,64536],{"className":64537,"style":3282},[251],[212,64539,4352,64541],{"className":64540},[1682],[212,64542,4356],{"style":4355},[212,64544],{"className":64545,"style":603},[354],[212,64547,64549,64552,64611],{"className":64548},[256],[212,64550],{"className":64551},[343,638],[212,64553,64555],{"className":64554},[435],[212,64556,64558,64603],{"className":64557},[482,483],[212,64559,64561,64600],{"className":64560},[487],[212,64562,64564,64578,64586],{"className":64563,"style":3301},[491],[212,64565,64566,64569],{"style":2725},[212,64567],{"className":64568,"style":658},[499],[212,64570,64572],{"className":64571},[504,505,506,507],[212,64573,64575],{"className":64574},[256,507],[212,64576,1141],{"className":64577,"style":1178},[256,257,507],[212,64579,64580,64583],{"style":670},[212,64581],{"className":64582,"style":658},[499],[212,64584],{"className":64585,"style":678},[677],[212,64587,64588,64591],{"style":3051},[212,64589],{"className":64590,"style":658},[499],[212,64592,64594],{"className":64593},[504,505,506,507],[212,64595,64597],{"className":64596},[256,507],[212,64598,11],{"className":64599},[256,257,507],[212,64601,515],{"className":64602},[514],[212,64604,64606],{"className":64605},[487],[212,64607,64609],{"className":64608,"style":2937},[491],[212,64610],{},[212,64612],{"className":64613},[350,638],[212,64615],{"className":64616,"style":2785},[354],[212,64618,2668],{"className":64619},[2789],[212,64621],{"className":64622,"style":2785},[354],[212,64624,64626,64629],{"className":64625},[247],[212,64627],{"className":64628,"style":369},[251],[212,64630,314],{"className":64631},[256],"；这解释了为什么「对判别器做 log 密度比」是 f-GAN 的最佳策略。",[11,64634,64635,64697,64698,64797,64798,45807],{},[1194,64636,64637,64638,64696],{},"常用 ",[212,64639,64641,64658],{"className":64640,"translate":216},[215],[212,64642,64644],{"className":64643},[220],[222,64645,64646],{"xmlns":224},[226,64647,64648,64656],{},[229,64649,64650],{},[7012,64651,64652,64654],{},[232,64653,234],{},[307,64655,7771],{},[236,64657,60918],{"encoding":238},[212,64659,64661],{"className":64660,"ariaHidden":243},[242],[212,64662,64664,64667],{"className":64663},[247],[212,64665],{"className":64666,"style":252},[251],[212,64668,64670,64673],{"className":64669},[256],[212,64671,234],{"className":64672,"style":258},[256,257],[212,64674,64676],{"className":64675},[478],[212,64677,64679],{"className":64678},[482],[212,64680,64682],{"className":64681},[487],[212,64683,64685],{"className":64684,"style":8697},[491],[212,64686,64687,64690],{"style":7063},[212,64688],{"className":64689,"style":500},[499],[212,64691,64693],{"className":64692},[504,505,506,507],[212,64694,7771],{"className":64695},[2789,507]," 表","（结合 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dQ=1",[212,64732,64734,64761,64788],{"className":64733,"ariaHidden":243},[242],[212,64735,64737,64740,64743,64746,64749,64752,64755,64758],{"className":64736},[247],[212,64738],{"className":64739,"style":5810},[251],[212,64741,1485],{"className":64742,"style":5815},[1682,1683,5814],[212,64744],{"className":64745,"style":603},[354],[212,64747,441],{"className":64748},[256,257],[212,64750,403],{"className":64751,"style":531},[256,257],[212,64753],{"className":64754,"style":355},[354],[212,64756,320],{"className":64757},[359],[212,64759],{"className":64760,"style":355},[354],[212,64762,64764,64767,64770,64773,64776,64779,64782,64785],{"className":64763},[247],[212,64765],{"className":64766,"style":5810},[251],[212,64768,1485],{"className":64769,"style":5815},[1682,1683,5814],[212,64771],{"className":64772,"style":603},[354],[212,64774,441],{"className":64775},[256,257],[212,64777,410],{"className":64778},[256,257],[212,64780],{"className":64781,"style":355},[354],[212,64783,320],{"className":64784},[359],[212,64786],{"className":64787,"style":355},[354],[212,64789,64791,64794],{"className":64790},[247],[212,64792],{"className":64793,"style":369},[251],[212,64795,314],{"className":64796},[256]," 可加任意常数 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GAN 损失",[52789,65030,65031,65194,65435,66068,66372,66711],{},[52697,65032,65033,65084,65160,65191],{},[52794,65034,65035,65083],{},[212,65036,65038,65057],{"className":65037,"translate":216},[215],[212,65039,65041],{"className":65040},[220],[222,65042,65043],{"xmlns":224},[226,65044,65045,65055],{},[229,65046,65047,65049,65051,65053],{},[232,65048,966],{},[232,65050,4298],{},[307,65052,4301],{},[232,65054,966],{},[236,65056,52925],{"encoding":238},[212,65058,65060],{"className":65059,"ariaHidden":243},[242],[212,65061,65063,65066,65069,65072,65077,65080],{"className":65062},[247],[212,65064],{"className":65065,"style":252},[251],[212,65067,966],{"className":65068},[256,257],[212,65070],{"className":65071,"style":603},[354],[212,65073,4352,65075],{"className":65074},[1682],[212,65076,4356],{"style":4355},[212,65078],{"className":65079,"style":603},[354],[212,65081,966],{"className":65082},[256,257],"（KL）",[52794,65085,65086],{},[212,65087,65089,65113],{"className":65088,"translate":216},[215],[212,65090,65092],{"className":65091},[220],[222,65093,65094],{"xmlns":224},[226,65095,65096,65110],{},[229,65097,65098],{},[7012,65099,65100,65102],{},[232,65101,7765],{},[229,65103,65104,65106,65108],{},[232,65105,40437],{},[307,65107,5011],{},[312,65109,314],{},[236,65111,65112],{"encoding":238},"e^{y-1}",[212,65114,65116],{"className":65115,"ariaHidden":243},[242],[212,65117,65119,65122],{"className":65118},[247],[212,65120],{"className":65121,"style":20228},[251],[212,65123,65125,65128],{"className":65124},[256],[212,65126,7765],{"className":65127},[256,257],[212,65129,65131],{"className":65130},[478],[212,65132,65134],{"className":65133},[482],[212,65135,65137],{"className":65136},[487],[212,65138,65140],{"className":65139,"style":20228},[491],[212,65141,65142,65145],{"style":7063},[212,65143],{"className":65144,"style":500},[499],[212,65146,65148],{"className":65147},[504,505,506,507],[212,65149,65151,65154,65157],{"className":65150},[256,507],[212,65152,40437],{"className":65153,"style":1178},[256,257,507],[212,65155,5011],{"className":65156},[2789,507],[212,65158,314],{"className":65159},[256,507],[52794,65161,65162],{},[212,65163,65165,65179],{"className":65164,"translate":216},[215],[212,65166,65168],{"className":65167},[220],[222,65169,65170],{"xmlns":224},[226,65171,65172,65176],{},[229,65173,65174],{},[232,65175,1231],{"mathvariant":419},[236,65177,65178],{"encoding":238},"\\mathbb R",[212,65180,65182],{"className":65181,"ariaHidden":243},[242],[212,65183,65185,65188],{"className":65184},[247],[212,65186],{"className":65187,"style":1295},[251],[212,65189,1231],{"className":65190},[256,563],[52794,65192,65193],{},"MINE-f \u002F 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y\\rvert\\le\\frac12",[212,66269,66271,66295],{"className":66270,"ariaHidden":243},[242],[212,66272,66274,66277,66280,66283,66286,66289,66292],{"className":66273},[247],[212,66275],{"className":66276,"style":336},[251],[212,66278,5006],{"className":66279},[343],[212,66281,40437],{"className":66282,"style":1178},[256,257],[212,66284,5006],{"className":66285},[350],[212,66287],{"className":66288,"style":355},[354],[212,66290,10150],{"className":66291},[359],[212,66293],{"className":66294,"style":355},[354],[212,66296,66298,66301],{"className":66297},[247],[212,66299],{"className":66300,"style":2703},[251],[212,66302,66304,66307,66366],{"className":66303},[256],[212,66305],{"className":66306},[343,638],[212,66308,66310],{"className":66309},[435],[212,66311,66313,66358],{"className":66312},[482,483],[212,66314,66316,66355],{"className":66315},[487],[212,66317,66319,66333,66341],{"className":66318,"style":2722},[491],[212,66320,66321,66324],{"style":2725},[212,66322],{"className":66323,"style":658},[499],[212,66325,66327],{"className":66326},[504,505,506,507],[212,66328,66330],{"className":66329},[256,507],[212,66331,2661],{"className":66332},[256,507],[212,66334,66335,66338],{"style":670},[212,66336],{"className":66337,"style":658},[499],[212,66339],{"className":66340,"style":678},[677],[212,66342,66343,66346],{"style":2748},[212,66344],{"className":66345,"style":658},[499],[212,66347,66349],{"className":66348},[504,505,506,507],[212,66350,66352],{"className":66351},[256,507],[212,66353,314],{"className":66354},[256,507],[212,66356,515],{"className":66357},[514],[212,66359,66361],{"className":66360},[487],[212,66362,66364],{"className":66363,"style":2770},[491],[212,66365],{},[212,66367],{"className":66368},[350,638],[52794,66370,66371],{},"—",[52697,66373,66374,66524,66678,66708],{},[52794,66375,66376,15995,66466,53674],{},[212,66377,66379,66404],{"className":66378,"translate":216},[215],[212,66380,66382],{"className":66381},[220],[222,66383,66384],{"xmlns":224},[226,66385,66386,66402],{},[229,66387,66388,66390,66392,66394,66396],{},[307,66389,310],{"stretchy":309},[232,66391,966],{},[307,66393,5011],{},[312,66395,314],{},[7012,66397,66398,66400],{},[307,66399,317],{"stretchy":309},[312,66401,2661],{},[236,66403,54029],{"encoding":238},[212,66405,66407,66428],{"className":66406,"ariaHidden":243},[242],[212,66408,66410,66413,66416,66419,66422,66425],{"className":66409},[247],[212,66411],{"className":66412,"style":336},[251],[212,66414,310],{"className":66415},[343],[212,66417,966],{"className":66418},[256,257],[212,66420],{"className":66421,"style":2785},[354],[212,66423,5011],{"className":66424},[2789],[212,66426],{"className":66427,"style":2785},[354],[212,66429,66431,66434,66437],{"className":66430},[247],[212,66432],{"className":66433,"style":20203},[251],[212,66435,314],{"className":66436},[256],[212,66438,66440,66443],{"className":66439},[350],[212,66441,317],{"className":66442},[350],[212,66444,66446],{"className":66445},[478],[212,66447,66449],{"className":66448},[482],[212,66450,66452],{"className":66451},[487],[212,66453,66455],{"className":66454,"style":20228},[491],[212,66456,66457,66460],{"style":7063},[212,66458],{"className":66459,"style":500},[499],[212,66461,66463],{"className":66462},[504,505,506,507],[212,66464,2661],{"className":66465},[256,507],[212,66467,66469,66486],{"className":66468,"translate":216},[215],[212,66470,66472],{"className":66471},[220],[222,66473,66474],{"xmlns":224},[226,66475,66476,66484],{},[229,66477,66478],{},[7012,66479,66480,66482],{},[232,66481,37649],{},[312,66483,2661],{},[236,66485,40594],{"encoding":238},[212,66487,66489],{"className":66488,"ariaHidden":243},[242],[212,66490,66492,66495],{"className":66491},[247],[212,66493],{"className":66494,"style":40604},[251],[212,66496,66498,66501],{"className":66497},[256],[212,66499,37649],{"className":66500},[256,257],[212,66502,66504],{"className":66503},[478],[212,66505,66507],{"className":66506},[482],[212,66508,66510],{"className":66509},[487],[212,66511,66513],{"className":66512,"style":20228},[491],[212,66514,66515,66518],{"style":7063},[212,66516],{"className":66517,"style":500},[499],[212,66519,66521],{"className":66520},[504,505,506,507],[212,66522,2661],{"className":66523},[256,507],[52794,66525,66526],{},[212,66527,66529,66555],{"className":66528,"translate":216},[215],[212,66530,66532],{"className":66531},[220],[222,66533,66534],{"xmlns":224},[226,66535,66536,66552],{},[229,66537,66538,66540,66542],{},[232,66539,40437],{},[307,66541,2668],{},[435,66543,66544,66550],{},[7012,66545,66546,66548],{},[232,66547,40437],{},[312,66549,2661],{},[312,66551,39189],{},[236,66553,66554],{"encoding":238},"y+\\frac{y^2}{4}",[212,66556,66558,66576],{"className":66557,"ariaHidden":243},[242],[212,66559,66561,66564,66567,66570,66573],{"className":66560},[247],[212,66562],{"className":66563,"style":40521},[251],[212,66565,40437],{"className":66566,"style":1178},[256,257],[212,66568],{"className":66569,"style":2785},[354],[212,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29,66868,66869,66871,66873],{},[312,66870,314],{},[307,66872,5011],{},[232,66874,40437],{},[236,66876,66877],{"encoding":238},"\\frac{y}{1-y}",[212,66879,66881],{"className":66880,"ariaHidden":243},[242],[212,66882,66884,66887],{"className":66883},[247],[212,66885],{"className":66886,"style":3282},[251],[212,66888,66890,66893,66958],{"className":66889},[256],[212,66891],{"className":66892},[343,638],[212,66894,66896],{"className":66895},[435],[212,66897,66899,66950],{"className":66898},[482,483],[212,66900,66902,66947],{"className":66901},[487],[212,66903,66905,66925,66933],{"className":66904,"style":3301},[491],[212,66906,66907,66910],{"style":2725},[212,66908],{"className":66909,"style":658},[499],[212,66911,66913],{"className":66912},[504,505,506,507],[212,66914,66916,66919,66922],{"className":66915},[256,507],[212,66917,314],{"className":66918},[256,507],[212,66920,5011],{"className":66921},[2789,507],[212,66923,40437],{"className":66924,"style":1178},[256,257,507],[212,66926,66927,66930],{"style":670},[212,66928],{"className":66929,"style":658},[499],[212,66931],{"className":66932,"style":678},[677],[212,66934,66935,66938],{"style":3051},[212,66936],{"className":66937,"style":658},[499],[212,66939,66941],{"className":66940},[504,505,506,507],[212,66942,66944],{"className":66943},[256,507],[212,66945,40437],{"className":66946,"style":1178},[256,257,507],[212,66948,515],{"className":66949},[514],[212,66951,66953],{"className":66952},[487],[212,66954,66956],{"className":66955,"style":2937},[491],[212,66957],{},[212,66959],{"className":66960},[350,638],[52794,66962,66963],{},[212,66964,66966,66984],{"className":66965,"translate":216},[215],[212,66967,66969],{"className":66968},[220],[222,66970,66971],{"xmlns":224},[226,66972,66973,66981],{},[229,66974,66975,66977,66979],{},[232,66976,40437],{},[307,66978,7449],{},[312,66980,314],{},[236,66982,66983],{"encoding":238},"y\u003C1",[212,66985,66987,67005],{"className":66986,"ariaHidden":243},[242],[212,66988,66990,66993,66996,66999,67002],{"className":66989},[247],[212,66991],{"className":66992,"style":31892},[251],[212,66994,40437],{"className":66995,"style":1178},[256,257],[212,66997],{"className":66998,"style":355},[354],[212,67000,7449],{"className":67001},[359],[212,67003],{"className":67004,"style":355},[354],[212,67006,67008,67011],{"className":67007},[247],[212,67009],{"className":67010,"style":369},[251],[212,67012,314],{"className":67013},[256],[52794,67015,66371],{},[11,67017,67018,67019,67077,67078,67324,67325,67486,67487,67752,67753,21156,67913,68029],{},"以 ",[212,67020,67022,67039],{"className":67021,"translate":216},[215],[212,67023,67025],{"className":67024},[220],[222,67026,67027],{"xmlns":224},[226,67028,67029,67037],{},[229,67030,67031],{},[7012,67032,67033,67035],{},[232,67034,37649],{},[312,67036,2661],{},[236,67038,40594],{"encoding":238},[212,67040,67042],{"className":67041,"ariaHidden":243},[242],[212,67043,67045,67048],{"className":67044},[247],[212,67046],{"className":67047,"style":40604},[251],[212,67049,67051,67054],{"className":67050},[256],[212,67052,37649],{"className":67053},[256,257],[212,67055,67057],{"className":67056},[478],[212,67058,67060],{"className":67059},[482],[212,67061,67063],{"className":67062},[487],[212,67064,67066],{"className":67065,"style":20228},[491],[212,67067,67068,67071],{"style":7063},[212,67069],{"className":67070,"style":500},[499],[212,67072,67074],{"className":67073},[504,505,506,507],[212,67075,2661],{"className":67076},[256,507]," 为例验证：",[212,67079,67081,67141],{"className":67080,"translate":216},[215],[212,67082,67084],{"className":67083},[220],[222,67085,67086],{"xmlns":224},[226,67087,67088,67138],{},[229,67089,67090,67096,67098,67100,67102,67104,67114,67116,67118,67120,67122,67124,67126,67128,67130,67136],{},[7012,67091,67092,67094],{},[232,67093,234],{},[307,67095,7771],{},[307,67097,310],{"stretchy":309},[232,67099,40437],{},[307,67101,317],{"stretchy":309},[307,67103,320],{},[392,67105,67106,67112],{},[229,67107,67108,67110],{},[232,67109,35632],{},[307,67111,4301],{},[232,67113,966],{},[307,67115,3096],{"stretchy":309},[232,67117,966],{},[232,67119,40437],{},[307,67121,5011],{},[307,67123,310],{"stretchy":309},[232,67125,966],{},[307,67127,5011],{},[312,67129,314],{},[7012,67131,67132,67134],{},[307,67133,317],{"stretchy":309},[312,67135,2661],{},[307,67137,3106],{"stretchy":309},[236,67139,67140],{"encoding":238},"f^*(y)=\\sup_t\\{ty-(t-1)^2\\}",[212,67142,67144,67197,67262,67283],{"className":67143,"ariaHidden":243},[242],[212,67145,67147,67150,67179,67182,67185,67188,67191,67194],{"className":67146},[247],[212,67148],{"className":67149,"style":336},[251],[212,67151,67153,67156],{"className":67152},[256],[212,67154,234],{"className":67155,"style":258},[256,257],[212,67157,67159],{"className":67158},[478],[212,67160,67162],{"className":67161},[482],[212,67163,67165],{"className":67164},[487],[212,67166,67168],{"className":67167,"style":8697},[491],[212,67169,67170,67173],{"style":7063},[212,67171],{"className":67172,"style":500},[499],[212,67174,67176],{"className":67175},[504,505,506,507],[212,67177,7771],{"className":67178},[2789,507],[212,67180,310],{"className":67181},[343],[212,67183,40437],{"className":67184,"style":1178},[256,257],[212,67186,317],{"className":67187},[350],[212,67189],{"className":67190,"style":355},[354],[212,67192,320],{"className":67193},[359],[212,67195],{"className":67196,"style":355},[354],[212,67198,67200,67203,67244,67247,67250,67253,67256,67259],{"className":67199},[247],[212,67201],{"className":67202,"style":336},[251],[212,67204,67206,67209],{"className":67205},[1682],[212,67207,35632],{"className":67208},[1682],[212,67210,67212],{"className":67211},[478],[212,67213,67215,67236],{"className":67214},[482,483],[212,67216,67218,67233],{"className":67217},[487],[212,67219,67222],{"className":67220,"style":67221},[491],"height:0.1864em;",[212,67223,67224,67227],{"style":35778},[212,67225],{"className":67226,"style":500},[499],[212,67228,67230],{"className":67229},[504,505,506,507],[212,67231,966],{"className":67232},[256,257,507],[212,67234,515],{"className":67235},[514],[212,67237,67239],{"className":67238},[487],[212,67240,67242],{"className":67241,"style":37220},[491],[212,67243],{},[212,67245,3096],{"className":67246},[343],[212,67248,966],{"className":67249},[256,257],[212,67251,40437],{"className":67252,"style":1178},[256,257],[212,67254],{"className":67255,"style":2785},[354],[212,67257,5011],{"className":67258},[2789],[212,67260],{"className":67261,"style":2785},[354],[212,67263,67265,67268,67271,67274,67277,67280],{"className":67264},[247],[212,67266],{"className":67267,"style":336},[251],[212,67269,310],{"className":67270},[343],[212,67272,966],{"className":67273},[256,257],[212,67275],{"className":67276,"style":2785},[354],[212,67278,5011],{"className":67279},[2789],[212,67281],{"className":67282,"style":2785},[354],[212,67284,67286,67289,67292,67321],{"className":67285},[247],[212,67287],{"className":67288,"style":20203},[251],[212,67290,314],{"className":67291},[256],[212,67293,67295,67298],{"className":67294},[350],[212,67296,317],{"className":67297},[350],[212,67299,67301],{"className":67300},[478],[212,67302,67304],{"className":67303},[482],[212,67305,67307],{"className":67306},[487],[212,67308,67310],{"className":67309,"style":20228},[491],[212,67311,67312,67315],{"style":7063},[212,67313],{"className":67314,"style":500},[499],[212,67316,67318],{"className":67317},[504,505,506,507],[212,67319,2661],{"className":67320},[256,507],[212,67322,3106],{"className":67323},[350],"，驻点 ",[212,67326,67328,67372],{"className":67327,"translate":216},[215],[212,67329,67331],{"className":67330},[220],[222,67332,67333],{"xmlns":224},[226,67334,67335,67369],{},[229,67336,67337,67339,67341,67343,67345,67347,67349,67351,67353,67355,67357,67359,67361,67363,67365,67367],{},[232,67338,40437],{},[307,67340,320],{},[312,67342,2661],{},[307,67344,310],{"stretchy":309},[232,67346,966],{},[307,67348,5011],{},[312,67350,314],{},[307,67352,317],{"stretchy":309},[307,67354,11190],{},[232,67356,966],{},[307,67358,320],{},[312,67360,314],{},[307,67362,2668],{},[232,67364,40437],{},[232,67366,1138],{"mathvariant":406},[312,67368,2661],{},[236,67370,67371],{"encoding":238},"y=2(t-1)\\Rightarrow t=1+y\u002F2",[212,67373,67375,67393,67417,67438,67456,67474],{"className":67374,"ariaHidden":243},[242],[212,67376,67378,67381,67384,67387,67390],{"className":67377},[247],[212,67379],{"className":67380,"style":2474},[251],[212,67382,40437],{"className":67383,"style":1178},[256,257],[212,67385],{"className":67386,"style":355},[354],[212,67388,320],{"className":67389},[359],[212,67391],{"className":67392,"style":355},[354],[212,67394,67396,67399,67402,67405,67408,67411,67414],{"className":67395},[247],[212,67397],{"className":67398,"style":336},[251],[212,67400,2661],{"className":67401},[256],[212,67403,310],{"className":67404},[343],[212,67406,966],{"className":67407},[256,257],[212,67409],{"className":67410,"style":2785},[354],[212,67412,5011],{"className":67413},[2789],[212,67415],{"className":67416,"style":2785},[354],[212,67418,67420,67423,67426,67429,67432,67435],{"className":67419},[247],[212,67421],{"className":67422,"style":336},[251],[212,67424,314],{"className":67425},[256],[212,67427,317],{"className":67428},[350],[212,67430],{"className":67431,"style":355},[354],[212,67433,11190],{"className":67434},[359],[212,67436],{"className":67437,"style":355},[354],[212,67439,67441,67444,67447,67450,67453],{"className":67440},[247],[212,67442],{"className":67443,"style":5541},[251],[212,67445,966],{"className":67446},[256,257],[212,67448],{"className":67449,"style":355},[354],[212,67451,320],{"className":67452},[359],[212,67454],{"className":67455,"style":355},[354],[212,67457,67459,67462,67465,67468,67471],{"className":67458},[247],[212,67460],{"className":67461,"style":12778},[251],[212,67463,314],{"className":67464},[256],[212,67466],{"className":67467,"style":2785},[354],[212,67469,2668],{"className":67470},[2789],[212,67472],{"className":67473,"style":2785},[354],[212,67475,67477,67480,67483],{"className":67476},[247],[212,67478],{"className":67479,"style":336},[251],[212,67481,40437],{"className":67482,"style":1178},[256,257],[212,67484,45350],{"className":67485},[256],"，得 ",[212,67488,67490,67554],{"className":67489,"translate":216},[215],[212,67491,67493],{"className":67492},[220],[222,67494,67495],{"xmlns":224},[226,67496,67497,67551],{},[229,67498,67499,67505,67507,67509,67511,67513,67515,67517,67519,67521,67523,67525,67531,67533,67535,67537,67539,67541,67547,67549],{},[7012,67500,67501,67503],{},[232,67502,234],{},[307,67504,7771],{},[307,67506,320],{},[232,67508,40437],{},[307,67510,310],{"stretchy":309},[312,67512,314],{},[307,67514,2668],{},[232,67516,40437],{},[232,67518,1138],{"mathvariant":406},[312,67520,2661],{},[307,67522,317],{"stretchy":309},[307,67524,5011],{},[7012,67526,67527,67529],{},[232,67528,40437],{},[312,67530,2661],{},[232,67532,1138],{"mathvariant":406},[312,67534,39189],{},[307,67536,320],{},[232,67538,40437],{},[307,67540,2668],{},[7012,67542,67543,67545],{},[232,67544,40437],{},[312,67546,2661],{},[232,67548,1138],{"mathvariant":406},[312,67550,39189],{},[236,67552,67553],{"encoding":238},"f^*=y(1+y\u002F2)-y^2\u002F4=y+y^2\u002F4",[212,67555,67557,67601,67625,67649,67696,67714],{"className":67556,"ariaHidden":243},[242],[212,67558,67560,67563,67592,67595,67598],{"className":67559},[247],[212,67561],{"className":67562,"style":252},[251],[212,67564,67566,67569],{"className":67565},[256],[212,67567,234],{"className":67568,"style":258},[256,257],[212,67570,67572],{"className":67571},[478],[212,67573,67575],{"className":67574},[482],[212,67576,67578],{"className":67577},[487],[212,67579,67581],{"className":67580,"style":8697},[491],[212,67582,67583,67586],{"style":7063},[212,67584],{"className":67585,"style":500},[499],[212,67587,67589],{"className":67588},[504,505,506,507],[212,67590,7771],{"className":67591},[2789,507],[212,67593],{"className":67594,"style":355},[354],[212,67596,320],{"className":67597},[359],[212,67599],{"className":67600,"style":355},[354],[212,67602,67604,67607,67610,67613,67616,67619,67622],{"className":67603},[247],[212,67605],{"className":67606,"style":336},[251],[212,67608,40437],{"className":67609,"style":1178},[256,257],[212,67611,310],{"className":67612},[343],[212,67614,314],{"className":67615},[256],[212,67617],{"className":67618,"style":2785},[354],[212,67620,2668],{"className":67621},[2789],[212,67623],{"className":67624,"style":2785},[354],[212,67626,67628,67631,67634,67637,67640,67643,67646],{"className":67627},[247],[212,67629],{"className":67630,"style":336},[251],[212,67632,40437],{"className":67633,"style":1178},[256,257],[212,67635,45350],{"className":67636},[256],[212,67638,317],{"className":67639},[350],[212,67641],{"className":67642,"style":2785},[354],[212,67644,5011],{"className":67645},[2789],[212,67647],{"className":67648,"style":2785},[354],[212,67650,67652,67655,67684,67687,67690,67693],{"className":67651},[247],[212,67653],{"className":67654,"style":20203},[251],[212,67656,67658,67661],{"className":67657},[256],[212,67659,40437],{"className":67660,"style":1178},[256,257],[212,67662,67664],{"className":67663},[478],[212,67665,67667],{"className":67666},[482],[212,67668,67670],{"className":67669},[487],[212,67671,67673],{"className":67672,"style":20228},[491],[212,67674,67675,67678],{"style":7063},[212,67676],{"className":67677,"style":500},[499],[212,67679,67681],{"className":67680},[504,505,506,507],[212,67682,2661],{"className":67683},[256,507],[212,67685,40572],{"className":67686},[256],[212,67688],{"className":67689,"style":355},[354],[212,67691,320],{"className":67692},[359],[212,67694],{"className":67695,"style":355},[354],[212,67697,67699,67702,67705,67708,67711],{"className":67698},[247],[212,67700],{"className":67701,"style":40521},[251],[212,67703,40437],{"className":67704,"style":1178},[256,257],[212,67706],{"className":67707,"style":2785},[354],[212,67709,2668],{"className":67710},[2789],[212,67712],{"className":67713,"style":2785},[354],[212,67715,67717,67720,67749],{"className":67716},[247],[212,67718],{"className":67719,"style":20203},[251],[212,67721,67723,67726],{"className":67722},[256],[212,67724,40437],{"className":67725,"style":1178},[256,257],[212,67727,67729],{"className":67728},[478],[212,67730,67732],{"className":67731},[482],[212,67733,67735],{"className":67734},[487],[212,67736,67738],{"className":67737,"style":20228},[491],[212,67739,67740,67743],{"style":7063},[212,67741],{"className":67742,"style":500},[499],[212,67744,67746],{"className":67745},[504,505,506,507],[212,67747,2661],{"className":67748},[256,507],[212,67750,40572],{"className":67751},[256],"。以 Hellinger² 为例：",[212,67754,67756,67792],{"className":67755,"translate":216},[215],[212,67757,67759],{"className":67758},[220],[222,67760,67761],{"xmlns":224},[226,67762,67763,67789],{},[229,67764,67765,67767,67769,67771,67773,67775,67777,67779,67781,67785,67787],{},[232,67766,234],{},[307,67768,310],{"stretchy":309},[232,67770,966],{},[307,67772,317],{"stretchy":309},[307,67774,320],{},[232,67776,966],{},[307,67778,5011],{},[312,67780,2661],{},[34539,67782,67783],{},[232,67784,966],{},[307,67786,2668],{},[312,67788,314],{},[236,67790,67791],{"encoding":238},"f(t)=t-2\\sqrt t+1",[212,67793,67795,67822,67841,67904],{"className":67794,"ariaHidden":243},[242],[212,67796,67798,67801,67804,67807,67810,67813,67816,67819],{"className":67797},[247],[212,67799],{"className":67800,"style":336},[251],[212,67802,234],{"className":67803,"style":258},[256,257],[212,67805,310],{"className":67806},[343],[212,67808,966],{"className":67809},[256,257],[212,67811,317],{"className":67812},[350],[212,67814],{"className":67815,"style":355},[354],[212,67817,320],{"className":67818},[359],[212,67820],{"className":67821,"style":355},[354],[212,67823,67825,67829,67832,67835,67838],{"className":67824},[247],[212,67826],{"className":67827,"style":67828},[251],"height:0.6984em;vertical-align:-0.0833em;",[212,67830,966],{"className":67831},[256,257],[212,67833],{"className":67834,"style":2785},[354],[212,67836,5011],{"className":67837},[2789],[212,67839],{"className":67840,"style":2785},[354],[212,67842,67844,67848,67851,67895,67898,67901],{"className":67843},[247],[212,67845],{"className":67846,"style":67847},[251],"height:1.04em;vertical-align:-0.1475em;",[212,67849,2661],{"className":67850},[256],[212,67852,67854],{"className":67853},[256,34567],[212,67855,67857,67887],{"className":67856},[482,483],[212,67858,67860,67884],{"className":67859},[487],[212,67861,67863,67872],{"className":67862,"style":42883},[491],[212,67864,67866,67869],{"className":67865,"style":12063},[6505],[212,67867],{"className":67868,"style":658},[499],[212,67870,966],{"className":67871,"style":34587},[256,257],[212,67873,67874,67877],{"style":42895},[212,67875],{"className":67876,"style":658},[499],[212,67878,67880],{"className":67879,"style":34644},[34643],[6521,67881,67882],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,67883],{"d":34651},[212,67885,515],{"className":67886},[514],[212,67888,67890],{"className":67889},[487],[212,67891,67893],{"className":67892,"style":42915},[491],[212,67894],{},[212,67896],{"className":67897,"style":2785},[354],[212,67899,2668],{"className":67900},[2789],[212,67902],{"className":67903,"style":2785},[354],[212,67905,67907,67910],{"className":67906},[247],[212,67908],{"className":67909,"style":369},[251],[212,67911,314],{"className":67912},[256],[212,67914,67916,67940],{"className":67915,"translate":216},[215],[212,67917,67919],{"className":67918},[220],[222,67920,67921],{"xmlns":224},[226,67922,67923,67937],{},[229,67924,67925,67927,67929,67933,67935],{},[232,67926,15600],{},[307,67928,320],{},[34539,67930,67931],{},[232,67932,966],{},[307,67934,7126],{},[312,67936,323],{},[236,67938,67939],{"encoding":238},"u=\\sqrt t\\ge0",[212,67941,67943,67961,68020],{"className":67942,"ariaHidden":243},[242],[212,67944,67946,67949,67952,67955,67958],{"className":67945},[247],[212,67947],{"className":67948,"style":2543},[251],[212,67950,15600],{"className":67951},[256,257],[212,67953],{"className":67954,"style":355},[354],[212,67956,320],{"className":67957},[359],[212,67959],{"className":67960,"style":355},[354],[212,67962,67964,67967,68011,68014,68017],{"className":67963},[247],[212,67965],{"className":67966,"style":67847},[251],[212,67968,67970],{"className":67969},[256,34567],[212,67971,67973,68003],{"className":67972},[482,483],[212,67974,67976,68000],{"className":67975},[487],[212,67977,67979,67988],{"className":67978,"style":42883},[491],[212,67980,67982,67985],{"className":67981,"style":12063},[6505],[212,67983],{"className":67984,"style":658},[499],[212,67986,966],{"className":67987,"style":34587},[256,257],[212,67989,67990,67993],{"style":42895},[212,67991],{"className":67992,"style":658},[499],[212,67994,67996],{"className":67995,"style":34644},[34643],[6521,67997,67998],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,67999],{"d":34651},[212,68001,515],{"className":68002},[514],[212,68004,68006],{"className":68005},[487],[212,68007,68009],{"className":68008,"style":42915},[491],[212,68010],{},[212,68012],{"className":68013,"style":355},[354],[212,68015,7126],{"className":68016},[359],[212,68018],{"className":68019,"style":355},[354],[212,68021,68023,68026],{"className":68022},[247],[212,68024],{"className":68025,"style":369},[251],[212,68027,323],{"className":68028},[256],"，把共轭写成有限上确界",[212,68031,68033],{"className":68032,"translate":216},[377],[212,68034,68036,68110],{"className":68035,"translate":216},[215],[212,68037,68039],{"className":68038},[220],[222,68040,68041],{"xmlns":224,"display":386},[226,68042,68043,68107],{},[229,68044,68045,68051,68053,68055,68057,68059,68075,68077,68079,68081,68083,68085,68087,68093,68095,68097,68099,68101,68103,68105],{},[7012,68046,68047,68049],{},[232,68048,234],{},[307,68050,7771],{},[307,68052,310],{"stretchy":309},[232,68054,40437],{},[307,68056,317],{"stretchy":309},[307,68058,320],{},[6214,68060,68061,68067],{},[229,68062,68063,68065],{},[232,68064,35632],{},[307,68066,4301],{},[229,68068,68069,68071,68073],{},[232,68070,15600],{},[307,68072,7126],{},[312,68074,323],{},[307,68076,3096],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[307,68078,310],{"stretchy":309},[232,68080,40437],{},[307,68082,5011],{},[312,68084,314],{},[307,68086,317],{"stretchy":309},[7012,68088,68089,68091],{},[232,68090,15600],{},[312,68092,2661],{},[307,68094,2668],{},[312,68096,2661],{},[232,68098,15600],{},[307,68100,5011],{},[312,68102,314],{},[307,68104,3106],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[307,68106,748],{"separator":243},[236,68108,68109],{"encoding":238},"f^*(y)=\\sup_{u\\ge0}\\Big\\{(y-1)u^2+2u-1\\Big\\},",[212,68111,68113,68166,68250,68300,68321],{"className":68112,"ariaHidden":243},[242],[212,68114,68116,68119,68148,68151,68154,68157,68160,68163],{"className":68115},[247],[212,68117],{"className":68118,"style":336},[251],[212,68120,68122,68125],{"className":68121},[256],[212,68123,234],{"className":68124,"style":258},[256,257],[212,68126,68128],{"className":68127},[478],[212,68129,68131],{"className":68130},[482],[212,68132,68134],{"className":68133},[487],[212,68135,68137],{"className":68136,"style":8446},[491],[212,68138,68139,68142],{"style":8475},[212,68140],{"className":68141,"style":500},[499],[212,68143,68145],{"className":68144},[504,505,506,507],[212,68146,7771],{"className":68147},[2789,507],[212,68149,310],{"className":68150},[343],[212,68152,40437],{"className":68153,"style":1178},[256,257],[212,68155,317],{"className":68156},[350],[212,68158],{"className":68159,"style":355},[354],[212,68161,320],{"className":68162},[359],[212,68164],{"className":68165,"style":355},[354],[212,68167,68169,68173,68226,68229,68235,68238,68241,68244,68247],{"className":68168},[247],[212,68170],{"className":68171,"style":68172},[251],"height:2.1567em;vertical-align:-1.0067em;",[212,68174,68176],{"className":68175},[1682,13916],[212,68177,68179,68218],{"className":68178},[482,483],[212,68180,68182,68215],{"className":68181},[487],[212,68183,68185,68205],{"className":68184,"style":2543},[491],[212,68186,68187,68190],{"style":61132},[212,68188],{"className":68189,"style":658},[499],[212,68191,68193],{"className":68192},[504,505,506,507],[212,68194,68196,68199,68202],{"className":68195},[256,507],[212,68197,15600],{"className":68198},[256,257,507],[212,68200,7126],{"className":68201},[359,507],[212,68203,323],{"className":68204},[256,507],[212,68206,68207,68210],{"style":12063},[212,68208],{"className":68209,"style":658},[499],[212,68211,68212],{},[212,68213,35632],{"className":68214},[1682],[212,68216,515],{"className":68217},[514],[212,68219,68221],{"className":68220},[487],[212,68222,68224],{"className":68223,"style":61170},[491],[212,68225],{},[212,68227],{"className":68228,"style":603},[354],[212,68230,68232],{"className":68231},[256],[212,68233,3096],{"className":68234},[616,3918],[212,68236,310],{"className":68237},[343],[212,68239,40437],{"className":68240,"style":1178},[256,257],[212,68242],{"className":68243,"style":2785},[354],[212,68245,5011],{"className":68246},[2789],[212,68248],{"className":68249,"style":2785},[354],[212,68251,68253,68256,68259,68262,68291,68294,68297],{"className":68252},[247],[212,68254],{"className":68255,"style":37451},[251],[212,68257,314],{"className":68258},[256],[212,68260,317],{"className":68261},[350],[212,68263,68265,68268],{"className":68264},[256],[212,68266,15600],{"className":68267},[256,257],[212,68269,68271],{"className":68270},[478],[212,68272,68274],{"className":68273},[482],[212,68275,68277],{"className":68276},[487],[212,68278,68280],{"className":68279,"style":19935},[491],[212,68281,68282,68285],{"style":8475},[212,68283],{"className":68284,"style":500},[499],[212,68286,68288],{"className":68287},[504,505,506,507],[212,68289,2661],{"className":68290},[256,507],[212,68292],{"className":68293,"style":2785},[354],[212,68295,2668],{"className":68296},[2789],[212,68298],{"className":68299,"style":2785},[354],[212,68301,68303,68306,68309,68312,68315,68318],{"className":68302},[247],[212,68304],{"className":68305,"style":12778},[251],[212,68307,2661],{"className":68308},[256],[212,68310,15600],{"className":68311},[256,257],[212,68313],{"className":68314,"style":2785},[354],[212,68316,5011],{"className":68317},[2789],[212,68319],{"className":68320,"style":2785},[354],[212,68322,68324,68328,68331,68337],{"className":68323},[247],[212,68325],{"className":68326,"style":68327},[251],"height:1.8em;vertical-align:-0.65em;",[212,68329,314],{"className":68330},[256],[212,68332,68334],{"className":68333},[256],[212,68335,3106],{"className":68336},[616,3918],[212,68338,748],{"className":68339},[770],[11,68341,68342,68343,68394,68395,68428,68429,68479,68480,68614],{},"当 ",[212,68344,68346,68364],{"className":68345,"translate":216},[215],[212,68347,68349],{"className":68348},[220],[222,68350,68351],{"xmlns":224},[226,68352,68353,68361],{},[229,68354,68355,68357,68359],{},[232,68356,40437],{},[307,68358,7126],{},[312,68360,314],{},[236,68362,68363],{"encoding":238},"y\\ge1",[212,68365,68367,68385],{"className":68366,"ariaHidden":243},[242],[212,68368,68370,68373,68376,68379,68382],{"className":68369},[247],[212,68371],{"className":68372,"style":15617},[251],[212,68374,40437],{"className":68375,"style":1178},[256,257],[212,68377],{"className":68378,"style":355},[354],[212,68380,7126],{"className":68381},[359],[212,68383],{"className":68384,"style":355},[354],[212,68386,68388,68391],{"className":68387},[247],[212,68389],{"className":68390,"style":369},[251],[212,68392,314],{"className":68393},[256]," 时上确界为 ",[212,68396,68398,68413],{"className":68397,"translate":216},[215],[212,68399,68401],{"className":68400},[220],[222,68402,68403],{"xmlns":224},[226,68404,68405,68411],{},[229,68406,68407,68409],{},[307,68408,2668],{},[232,68410,1223],{"mathvariant":406},[236,68412,4439],{"encoding":238},[212,68414,68416],{"className":68415,"ariaHidden":243},[242],[212,68417,68419,68422,68425],{"className":68418},[247],[212,68420],{"className":68421,"style":4449},[251],[212,68423,2668],{"className":68424},[256],[212,68426,1223],{"className":68427},[256],"；当 ",[212,68430,68432,68449],{"className":68431,"translate":216},[215],[212,68433,68435],{"className":68434},[220],[222,68436,68437],{"xmlns":224},[226,68438,68439,68447],{},[229,68440,68441,68443,68445],{},[232,68442,40437],{},[307,68444,7449],{},[312,68446,314],{},[236,68448,66983],{"encoding":238},[212,68450,68452,68470],{"className":68451,"ariaHidden":243},[242],[212,68453,68455,68458,68461,68464,68467],{"className":68454},[247],[212,68456],{"className":68457,"style":31892},[251],[212,68459,40437],{"className":68460,"style":1178},[256,257],[212,68462],{"className":68463,"style":355},[354],[212,68465,7449],{"className":68466},[359],[212,68468],{"className":68469,"style":355},[354],[212,68471,68473,68476],{"className":68472},[247],[212,68474],{"className":68475,"style":369},[251],[212,68477,314],{"className":68478},[256]," 时上式是开口向下的二次函数，最大点 ",[212,68481,68483,68513],{"className":68482,"translate":216},[215],[212,68484,68486],{"className":68485},[220],[222,68487,68488],{"xmlns":224},[226,68489,68490,68510],{},[229,68491,68492,68494,68496],{},[232,68493,15600],{},[307,68495,320],{},[1453,68497,68498],{"scriptlevel":323,"displaystyle":243},[435,68499,68500,68502],{},[312,68501,314],{},[229,68503,68504,68506,68508],{},[312,68505,314],{},[307,68507,5011],{},[232,68509,40437],{},[236,68511,68512],{"encoding":238},"u=\\dfrac{1}{1-y}",[212,68514,68516,68534],{"className":68515,"ariaHidden":243},[242],[212,68517,68519,68522,68525,68528,68531],{"className":68518},[247],[212,68520],{"className":68521,"style":2543},[251],[212,68523,15600],{"className":68524},[256,257],[212,68526],{"className":68527,"style":355},[354],[212,68529,320],{"className":68530},[359],[212,68532],{"className":68533,"style":355},[354],[212,68535,68537,68540],{"className":68536},[247],[212,68538],{"className":68539,"style":31503},[251],[212,68541,68543,68546,68611],{"className":68542},[256],[212,68544],{"className":68545},[343,638],[212,68547,68549],{"className":68548},[435],[212,68550,68552,68603],{"className":68551},[482,483],[212,68553,68555,68600],{"className":68554},[487],[212,68556,68558,68581,68589],{"className":68557,"style":23089},[491],[212,68559,68560,68563],{"style":654},[212,68561],{"className":68562,"style":658},[499],[212,68564,68566,68569,68572,68575,68578],{"className":68565},[256],[212,68567,314],{"className":68568},[256],[212,68570],{"className":68571,"style":2785},[354],[212,68573,5011],{"className":68574},[2789],[212,68576],{"className":68577,"style":2785},[354],[212,68579,40437],{"className":68580,"style":1178},[256,257],[212,68582,68583,68586],{"style":670},[212,68584],{"className":68585,"style":658},[499],[212,68587],{"className":68588,"style":678},[677],[212,68590,68591,68594],{"style":681},[212,68592],{"className":68593,"style":658},[499],[212,68595,68597],{"className":68596},[256],[212,68598,314],{"className":68599},[256],[212,68601,515],{"className":68602},[514],[212,68604,68606],{"className":68605},[487],[212,68607,68609],{"className":68608,"style":703},[491],[212,68610],{},[212,68612],{"className":68613},[350,638],"，代回得",[212,68616,68618],{"className":68617,"translate":216},[377],[212,68619,68621,68717],{"className":68620,"translate":216},[215],[212,68622,68624],{"className":68623},[220],[222,68625,68626],{"xmlns":224,"display":386},[226,68627,68628,68714],{},[229,68629,68630,68636,68638,68640,68642,68644,68670,68672,68674,68686,68688,68690,68692,68704,68706,68708,68710,68712],{},[7012,68631,68632,68634],{},[232,68633,234],{},[307,68635,7771],{},[307,68637,310],{"stretchy":309},[232,68639,40437],{},[307,68641,317],{"stretchy":309},[307,68643,320],{},[435,68645,68646,68654],{},[229,68647,68648,68650,68652],{},[232,68649,40437],{},[307,68651,5011],{},[312,68653,314],{},[229,68655,68656,68658,68660,68662,68664],{},[307,68657,310],{"stretchy":309},[312,68659,314],{},[307,68661,5011],{},[232,68663,40437],{},[7012,68665,68666,68668],{},[307,68667,317],{"stretchy":309},[312,68669,2661],{},[307,68671,2668],{},[312,68673,2661],{},[435,68675,68676,68678],{},[312,68677,314],{},[229,68679,68680,68682,68684],{},[312,68681,314],{},[307,68683,5011],{},[232,68685,40437],{},[307,68687,5011],{},[312,68689,314],{},[307,68691,320],{},[435,68693,68694,68696],{},[232,68695,40437],{},[229,68697,68698,68700,68702],{},[312,68699,314],{},[307,68701,5011],{},[232,68703,40437],{},[307,68705,748],{"separator":243},[354,68707],{"width":3460},[232,68709,40437],{},[307,68711,7449],{},[312,68713,49709],{},[236,68715,68716],{"encoding":238},"f^*(y)=\\frac{y-1}{(1-y)^2}+2\\frac{1}{1-y}-1\n=\\frac{y}{1-y},\\qquad y\u003C1 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",[212,69820,69822,69856],{"className":69821,"translate":216},[215],[212,69823,69825],{"className":69824},[220],[222,69826,69827],{"xmlns":224},[226,69828,69829,69853],{},[229,69830,69831,69833,69835,69847,69849,69851],{},[232,69832,40437],{},[307,69834,320],{},[7751,69836,69837,69839,69845],{},[232,69838,234],{},[229,69840,69841,69843],{},[232,69842,23943],{},[232,69844,25937],{},[307,69846,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,69848,310],{"stretchy":309},[232,69850,966],{},[307,69852,317],{"stretchy":309},[236,69854,69855],{"encoding":238},"y=f_{JS}'(t)",[212,69857,69859,69877],{"className":69858,"ariaHidden":243},[242],[212,69860,69862,69865,69868,69871,69874],{"className":69861},[247],[212,69863],{"className":69864,"style":2474},[251],[212,69866,40437],{"className":69867,"style":1178},[256,257],[212,69869],{"className":69870,"style":355},[354],[212,69872,320],{"className":69873},[359],[212,69875],{"className":69876,"style":355},[354],[212,69878,69880,69883,69943,69946,69949],{"className":69879},[247],[212,69881],{"className":69882,"style":69576},[251],[212,69884,69886,69889],{"className":69885},[256],[212,69887,234],{"className":69888,"style":258},[256,257],[212,69890,69892],{"className":69891},[478],[212,69893,69895,69935],{"className":69894},[482,483],[212,69896,69898,69932],{"className":69897},[487],[212,69899,69901,69918],{"className":69900,"style":7060},[491],[212,69902,69903,69906],{"style":69597},[212,69904],{"className":69905,"style":500},[499],[212,69907,69909],{"className":69908},[504,505,506,507],[212,69910,69912,69915],{"className":69911},[256,507],[212,69913,23943],{"className":69914,"style":24353},[256,257,507],[212,69916,25937],{"className":69917,"style":26061},[256,257,507],[212,69919,69920,69923],{"style":7063},[212,69921],{"className":69922,"style":500},[499],[212,69924,69926],{"className":69925},[504,505,506,507],[212,69927,69929],{"className":69928},[256,507],[212,69930,7018],{"className":69931},[256,507],[212,69933,515],{"className":69934},[514],[212,69936,69938],{"className":69937},[487],[212,69939,69941],{"className":69940,"style":38590},[491],[212,69942],{},[212,69944,310],{"className":69945},[343],[212,69947,966],{"className":69948},[256,257],[212,69950,317],{"className":69951},[350],[212,69953,69955,69995],{"className":69954,"translate":216},[215],[212,69956,69958],{"className":69957},[220],[222,69959,69960],{"xmlns":224},[226,69961,69962,69992],{},[229,69963,69964,69974,69976],{},[7012,69965,69966,69968],{},[232,69967,7765],{},[229,69969,69970,69972],{},[312,69971,2661],{},[232,69973,40437],{},[307,69975,320],{},[435,69977,69978,69984],{},[229,69979,69980,69982],{},[312,69981,2661],{},[232,69983,966],{},[229,69985,69986,69988,69990],{},[232,69987,966],{},[307,69989,2668],{},[312,69991,314],{},[236,69993,69994],{"encoding":238},"e^{2y}=\\frac{2t}{t+1}",[212,69996,69998,70048],{"className":69997,"ariaHidden":243},[242],[212,69999,70001,70004,70039,70042,70045],{"className":70000},[247],[212,70002],{"className":70003,"style":20228},[251],[212,70005,70007,70010],{"className":70006},[256],[212,70008,7765],{"className":70009},[256,257],[212,70011,70013],{"className":70012},[478],[212,70014,70016],{"className":70015},[482],[212,70017,70019],{"className":70018},[487],[212,70020,70022],{"className":70021,"style":20228},[491],[212,70023,70024,70027],{"style":7063},[212,70025],{"className":70026,"style":500},[499],[212,70028,70030],{"className":70029},[504,505,506,507],[212,70031,70033,70036],{"className":70032},[256,507],[212,70034,2661],{"className":70035},[256,507],[212,70037,40437],{"className":70038,"style":1178},[256,257,507],[212,70040],{"className":70041,"style":355},[354],[212,70043,320],{"className":70044},[359],[212,70046],{"className":70047,"style":355},[354],[212,70049,70051,70054],{"className":70050},[247],[212,70052],{"className":70053,"style":45604},[251],[212,70055,70057,70060,70128],{"className":70056},[256],[212,70058],{"className":70059},[343,638],[212,70061,70063],{"className":70062},[435],[212,70064,70066,70120],{"className":70065},[482,483],[212,70067,70069,70117],{"className":70068},[487],[212,70070,70072,70092,70100],{"className":70071,"style":2722},[491],[212,70073,70074,70077],{"style":2725},[212,70075],{"className":70076,"style":658},[499],[212,70078,70080],{"className":70079},[504,505,506,507],[212,70081,70083,70086,70089],{"className":70082},[256,507],[212,70084,966],{"className":70085},[256,257,507],[212,70087,2668],{"className":70088},[2789,507],[212,70090,314],{"className":70091},[256,507],[212,70093,70094,70097],{"style":670},[212,70095],{"className":70096,"style":658},[499],[212,70098],{"className":70099,"style":678},[677],[212,70101,70102,70105],{"style":2748},[212,70103],{"className":70104,"style":658},[499],[212,70106,70108],{"className":70107},[504,505,506,507],[212,70109,70111,70114],{"className":70110},[256,507],[212,70112,2661],{"className":70113},[256,507],[212,70115,966],{"className":70116},[256,257,507],[212,70118,515],{"className":70119},[514],[212,70121,70123],{"className":70122},[487],[212,70124,70126],{"className":70125,"style":16629},[491],[212,70127],{},[212,70129],{"className":70130},[350,638],"，解得 ",[212,70133,70135,70181],{"className":70134,"translate":216},[215],[212,70136,70138],{"className":70137},[220],[222,70139,70140],{"xmlns":224},[226,70141,70142,70178],{},[229,70143,70144,70146,70148],{},[232,70145,966],{},[307,70147,320],{},[1453,70149,70150],{"scriptlevel":323,"displaystyle":243},[435,70151,70152,70162],{},[7012,70153,70154,70156],{},[232,70155,7765],{},[229,70157,70158,70160],{},[312,70159,2661],{},[232,70161,40437],{},[229,70163,70164,70166,70168],{},[312,70165,2661],{},[307,70167,5011],{},[7012,70169,70170,70172],{},[232,70171,7765],{},[229,70173,70174,70176],{},[312,70175,2661],{},[232,70177,40437],{},[236,70179,70180],{"encoding":238},"t=\\dfrac{e^{2y}}{2-e^{2y}}",[212,70182,70184,70202],{"className":70183,"ariaHidden":243},[242],[212,70185,70187,70190,70193,70196,70199],{"className":70186},[247],[212,70188],{"className":70189,"style":5541},[251],[212,70191,966],{"className":70192},[256,257],[212,70194],{"className":70195,"style":355},[354],[212,70197,320],{"className":70198},[359],[212,70200],{"className":70201,"style":355},[354],[212,70203,70205,70209],{"className":70204},[247],[212,70206],{"className":70207,"style":70208},[251],"height:2.2604em;vertical-align:-0.7693em;",[212,70210,70212,70215,70344],{"className":70211},[256],[212,70213],{"className":70214},[343,638],[212,70216,70218],{"className":70217},[435],[212,70219,70221,70336],{"className":70220},[482,483],[212,70222,70224,70333],{"className":70223},[487],[212,70225,70227,70282,70290],{"className":70226,"style":37923},[491],[212,70228,70229,70232],{"style":654},[212,70230],{"className":70231,"style":658},[499],[212,70233,70235,70238,70241,70244,70247],{"className":70234},[256],[212,70236,2661],{"className":70237},[256],[212,70239],{"className":70240,"style":2785},[354],[212,70242,5011],{"className":70243},[2789],[212,70245],{"className":70246,"style":2785},[354],[212,70248,70250,70253],{"className":70249},[256],[212,70251,7765],{"className":70252},[256,257],[212,70254,70256],{"className":70255},[478],[212,70257,70259],{"className":70258},[482],[212,70260,70262],{"className":70261},[487],[212,70263,70265],{"className":70264,"style":45232},[491],[212,70266,70267,70270],{"style":45235},[212,70268],{"className":70269,"style":500},[499],[212,70271,70273],{"className":70272},[504,505,506,507],[212,70274,70276,70279],{"className":70275},[256,507],[212,70277,2661],{"className":70278},[256,507],[212,70280,40437],{"className":70281,"style":1178},[256,257,507],[212,70283,70284,70287],{"style":670},[212,70285],{"className":70286,"style":658},[499],[212,70288],{"className":70289,"style":678},[677],[212,70291,70292,70295],{"style":681},[212,70293],{"className":70294,"style":658},[499],[212,70296,70298],{"className":70297},[256],[212,70299,70301,70304],{"className":70300},[256],[212,70302,7765],{"className":70303},[256,257],[212,70305,70307],{"className":70306},[478],[212,70308,70310],{"className":70309},[482],[212,70311,70313],{"className":70312},[487],[212,70314,70316],{"className":70315,"style":20228},[491],[212,70317,70318,70321],{"style":7063},[212,70319],{"className":70320,"style":500},[499],[212,70322,70324],{"className":70323},[504,505,506,507],[212,70325,70327,70330],{"className":70326},[256,507],[212,70328,2661],{"className":70329},[256,507],[212,70331,40437],{"className":70332,"style":1178},[256,257,507],[212,70334,515],{"className":70335},[514],[212,70337,70339],{"className":70338},[487],[212,70340,70342],{"className":70341,"style":17215},[491],[212,70343],{},[212,70345],{"className":70346},[350,638],"（这要求 ",[212,70349,70351,70377],{"className":70350,"translate":216},[215],[212,70352,70354],{"className":70353},[220],[222,70355,70356],{"xmlns":224},[226,70357,70358,70374],{},[229,70359,70360,70370,70372],{},[7012,70361,70362,70364],{},[232,70363,7765],{},[229,70365,70366,70368],{},[312,70367,2661],{},[232,70369,40437],{},[307,70371,7449],{},[312,70373,2661],{},[236,70375,70376],{"encoding":238},"e^{2y}\u003C2",[212,70378,70380,70431],{"className":70379,"ariaHidden":243},[242],[212,70381,70383,70387,70422,70425,70428],{"className":70382},[247],[212,70384],{"className":70385,"style":70386},[251],"height:0.8532em;vertical-align:-0.0391em;",[212,70388,70390,70393],{"className":70389},[256],[212,70391,7765],{"className":70392},[256,257],[212,70394,70396],{"className":70395},[478],[212,70397,70399],{"className":70398},[482],[212,70400,70402],{"className":70401},[487],[212,70403,70405],{"className":70404,"style":20228},[491],[212,70406,70407,70410],{"style":7063},[212,70408],{"className":70409,"style":500},[499],[212,70411,70413],{"className":70412},[504,505,506,507],[212,70414,70416,70419],{"className":70415},[256,507],[212,70417,2661],{"className":70418},[256,507],[212,70420,40437],{"className":70421,"style":1178},[256,257,507],[212,70423],{"className":70424,"style":355},[354],[212,70426,7449],{"className":70427},[359],[212,70429],{"className":70430,"style":355},[354],[212,70432,70434,70437],{"className":70433},[247],[212,70435],{"className":70436,"style":369},[251],[212,70438,2661],{"className":70439},[256],[212,70441,70443,70470],{"className":70442,"translate":216},[215],[212,70444,70446],{"className":70445},[220],[222,70447,70448],{"xmlns":224},[226,70449,70450,70468],{},[229,70451,70452,70454,70456],{},[232,70453,40437],{},[307,70455,7449],{},[435,70457,70458,70466],{},[229,70459,70460,70462,70464],{},[232,70461,4298],{},[307,70463,4301],{},[312,70465,2661],{},[312,70467,2661],{},[236,70469,65953],{"encoding":238},[212,70471,70473,70491],{"className":70472,"ariaHidden":243},[242],[212,70474,70476,70479,70482,70485,70488],{"className":70475},[247],[212,70477],{"className":70478,"style":31892},[251],[212,70480,40437],{"className":70481,"style":1178},[256,257],[212,70483],{"className":70484,"style":355},[354],[212,70486,7449],{"className":70487},[359],[212,70489],{"className":70490,"style":355},[354],[212,70492,70494,70497],{"className":70493},[247],[212,70495],{"className":70496,"style":65981},[251],[212,70498,70500,70503,70577],{"className":70499},[256],[212,70501],{"className":70502},[343,638],[212,70504,70506],{"className":70505},[435],[212,70507,70509,70569],{"className":70508},[482,483],[212,70510,70512,70566],{"className":70511},[487],[212,70513,70515,70529,70537],{"className":70514,"style":3023},[491],[212,70516,70517,70520],{"style":2725},[212,70518],{"className":70519,"style":658},[499],[212,70521,70523],{"className":70522},[504,505,506,507],[212,70524,70526],{"className":70525},[256,507],[212,70527,2661],{"className":70528},[256,507],[212,70530,70531,70534],{"style":670},[212,70532],{"className":70533,"style":658},[499],[212,70535],{"className":70536,"style":678},[677],[212,70538,70539,70542],{"style":3051},[212,70540],{"className":70541,"style":658},[499],[212,70543,70545],{"className":70544},[504,505,506,507],[212,70546,70548,70560,70563],{"className":70547},[256,507],[212,70549,70551,70554,70557],{"className":70550},[1682,507],[212,70552,47857],{"className":70553},[507],[212,70555,47861],{"className":70556},[507],[212,70558,4356],{"className":70559,"style":4355},[507],[212,70561],{"className":70562,"style":42566},[354,507],[212,70564,2661],{"className":70565},[256,507],[212,70567,515],{"className":70568},[514],[212,70570,70572],{"className":70571},[487],[212,70573,70575],{"className":70574,"style":2770},[491],[212,70576],{},[212,70578],{"className":70579},[350,638],"）。于是 ",[212,70582,70584,70638],{"className":70583,"translate":216},[215],[212,70585,70587],{"className":70586},[220],[222,70588,70589],{"xmlns":224},[226,70590,70591,70635],{},[229,70592,70593,70595,70597,70609,70611,70613,70615,70617,70619,70621,70623,70633],{},[232,70594,4298],{},[307,70596,4301],{},[435,70598,70599,70607],{},[229,70600,70601,70603,70605],{},[232,70602,966],{},[307,70604,2668],{},[312,70606,314],{},[312,70608,2661],{},[307,70610,320],{},[307,70612,5011],{},[232,70614,4298],{},[307,70616,4301],{},[307,70618,310],{"stretchy":309},[312,70620,2661],{},[307,70622,5011],{},[7012,70624,70625,70627],{},[232,70626,7765],{},[229,70628,70629,70631],{},[312,70630,2661],{},[232,70632,40437],{},[307,70634,317],{"stretchy":309},[236,70636,70637],{"encoding":238},"\\log\\frac{t+1}{2}=-\\log(2-e^{2y})",[212,70639,70641,70738,70770],{"className":70640,"ariaHidden":243},[242],[212,70642,70644,70647,70652,70655,70729,70732,70735],{"className":70643},[247],[212,70645],{"className":70646,"style":2703},[251],[212,70648,4352,70650],{"className":70649},[1682],[212,70651,4356],{"style":4355},[212,70653],{"className":70654,"style":603},[354],[212,70656,70658,70661,70726],{"className":70657},[256],[212,70659],{"className":70660},[343,638],[212,70662,70664],{"className":70663},[435],[212,70665,70667,70718],{"className":70666},[482,483],[212,70668,70670,70715],{"className":70669},[487],[212,70671,70673,70687,70695],{"className":70672,"style":2722},[491],[212,70674,70675,70678],{"style":2725},[212,70676],{"className":70677,"style":658},[499],[212,70679,70681],{"className":70680},[504,505,506,507],[212,70682,70684],{"className":70683},[256,507],[212,70685,2661],{"className":70686},[256,507],[212,70688,70689,70692],{"style":670},[212,70690],{"className":70691,"style":658},[499],[212,70693],{"className":70694,"style":678},[677],[212,70696,70697,70700],{"style":2748},[212,70698],{"className":70699,"style":658},[499],[212,70701,70703],{"className":70702},[504,505,506,507],[212,70704,70706,70709,70712],{"className":70705},[256,507],[212,70707,966],{"className":70708},[256,257,507],[212,70710,2668],{"className":70711},[2789,507],[212,70713,314],{"className":70714},[256,507],[212,70716,515],{"className":70717},[514],[212,70719,70721],{"className":70720},[487],[212,70722,70724],{"className":70723,"style":2770},[491],[212,70725],{},[212,70727],{"className":70728},[350,638],[212,70730],{"className":70731,"style":355},[354],[212,70733,320],{"className":70734},[359],[212,70736],{"className":70737,"style":355},[354],[212,70739,70741,70744,70747,70750,70755,70758,70761,70764,70767],{"className":70740},[247],[212,70742],{"className":70743,"style":336},[251],[212,70745,5011],{"className":70746},[256],[212,70748],{"className":70749,"style":603},[354],[212,70751,4352,70753],{"className":70752},[1682],[212,70754,4356],{"style":4355},[212,70756,310],{"className":70757},[343],[212,70759,2661],{"className":70760},[256],[212,70762],{"className":70763,"style":2785},[354],[212,70765,5011],{"className":70766},[2789],[212,70768],{"className":70769,"style":2785},[354],[212,70771,70773,70776,70811],{"className":70772},[247],[212,70774],{"className":70775,"style":20203},[251],[212,70777,70779,70782],{"className":70778},[256],[212,70780,7765],{"className":70781},[256,257],[212,70783,70785],{"className":70784},[478],[212,70786,70788],{"className":70787},[482],[212,70789,70791],{"className":70790},[487],[212,70792,70794],{"className":70793,"style":20228},[491],[212,70795,70796,70799],{"style":7063},[212,70797],{"className":70798,"style":500},[499],[212,70800,70802],{"className":70801},[504,505,506,507],[212,70803,70805,70808],{"className":70804},[256,507],[212,70806,2661],{"className":70807},[256,507],[212,70809,40437],{"className":70810,"style":1178},[256,257,507],[212,70812,317],{"className":70813},[350],"，代入",[212,70816,70818],{"className":70817,"translate":216},[377],[212,70819,70821,71019],{"className":70820,"translate":216},[215],[212,70822,70824],{"className":70823},[220],[222,70825,70826],{"xmlns":224,"display":386},[226,70827,70828,71016],{},[1441,70829,70830,70882,70964],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,70831,70832,70850],{},[1450,70833,70834],{},[1453,70835,70836],{"scriptlevel":323,"displaystyle":243},[229,70837,70838,70844,70846,70848],{},[7012,70839,70840,70842],{},[232,70841,234],{},[307,70843,7771],{},[307,70845,310],{"stretchy":309},[232,70847,40437],{},[307,70849,317],{"stretchy":309},[1450,70851,70852],{},[1453,70853,70854],{"scriptlevel":323,"displaystyle":243},[229,70855,70856,70858,70860,70862,70864,70866,70876,70878,70880],{},[229,70857],{},[307,70859,320],{},[232,70861,40437],{},[232,70863,966],{},[307,70865,5011],{},[392,70867,70868,70870],{},[232,70869,234],{},[229,70871,70872,70874],{},[232,70873,23943],{},[232,70875,25937],{},[307,70877,310],{"stretchy":309},[232,70879,966],{},[307,70881,317],{"stretchy":309},[1447,70883,70884,70890],{},[1450,70885,70886],{},[1453,70887,70888],{"scriptlevel":323,"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,{"className":72008},[256],[212,72010,3106],{"className":72011},[350],"。在 ",[212,72014,72016,72034],{"className":72015,"translate":216},[215],[212,72017,72019],{"className":72018},[220],[222,72020,72021],{"xmlns":224},[226,72022,72023,72031],{},[229,72024,72025,72027,72029],{},[232,72026,966],{},[307,72028,10150],{},[312,72030,314],{},[236,72032,72033],{"encoding":238},"t\\le1",[212,72035,72037,72055],{"className":72036,"ariaHidden":243},[242],[212,72038,72040,72043,72046,72049,72052],{"className":72039},[247],[212,72041],{"className":72042,"style":43388},[251],[212,72044,966],{"className":72045},[256,257],[212,72047],{"className":72048,"style":355},[354],[212,72050,10150],{"className":72051},[359],[212,72053],{"className":72054,"style":355},[354],[212,72056,72058,72061],{"className":72057},[247],[212,72059],{"className":72060,"style":369},[251],[212,72062,314],{"className":72063},[256]," 一侧，",[212,72066,72068,72124],{"className":72067,"translate":216},[215],[212,72069,72071],{"className":72070},[220],[222,72072,72073],{"xmlns":224},[226,72074,72075,72121],{},[229,72076,72077,72079,72081,72083,72095,72097,72099,72101,72103,72105,72111,72113,72115],{},[232,72078,40437],{},[232,72080,966],{},[307,72082,5011],{},[435,72084,72085,72093],{},[229,72086,72087,72089,72091],{},[312,72088,314],{},[307,72090,5011],{},[232,72092,966],{},[312,72094,2661],{},[307,72096,320],{},[232,72098,966],{},[307,72100,310],{"stretchy":309},[232,72102,40437],{},[307,72104,2668],{},[435,72106,72107,72109],{},[312,72108,314],{},[312,72110,2661],{},[307,72112,317],{"stretchy":309},[307,72114,5011],{},[435,72116,72117,72119],{},[312,72118,314],{},[312,72120,2661],{},[236,72122,72123],{"encoding":238},"yt-\\frac{1-t}{2}=t(y+\\frac12)-\\frac12",[212,72125,72127,72148,72237,72261,72347],{"className":72126,"ariaHidden":243},[242],[212,72128,72130,72133,72136,72139,72142,72145],{"className":72129},[247],[212,72131],{"className":72132,"style":26474},[251],[212,72134,40437],{"className":72135,"style":1178},[256,257],[212,72137,966],{"className":72138},[256,257],[212,72140],{"className":72141,"style":2785},[354],[212,72143,5011],{"className":72144},[2789],[212,72146],{"className":72147,"style":2785},[354],[212,72149,72151,72154,72228,72231,72234],{"className":72150},[247],[212,72152],{"className":72153,"style":2703},[251],[212,72155,72157,72160,72225],{"className":72156},[256],[212,72158],{"className":72159},[343,638],[212,72161,72163],{"className":72162},[435],[212,72164,72166,72217],{"className":72165},[482,483],[212,72167,72169,72214],{"className":72168},[487],[212,72170,72172,72186,72194],{"className":72171,"style":2722},[491],[212,72173,72174,72177],{"style":2725},[212,72175],{"className":72176,"style":658},[499],[212,72178,72180],{"className":72179},[504,505,506,507],[212,72181,72183],{"className":72182},[256,507],[212,72184,2661],{"className":72185},[256,507],[212,72187,72188,72191],{"style":670},[212,72189],{"className":72190,"style":658},[499],[212,72192],{"className":72193,"style":678},[677],[212,72195,72196,72199],{"style":2748},[212,72197],{"className":72198,"style":658},[499],[212,72200,72202],{"className":72201},[504,505,506,507],[212,72203,72205,72208,72211],{"className":72204},[256,507],[212,72206,314],{"className":72207},[256,507],[212,72209,5011],{"className":72210},[2789,507],[212,72212,966],{"className":72213},[256,257,507],[212,72215,515],{"className":72216},[514],[212,72218,72220],{"className":72219},[487],[212,72221,72223],{"className":72222,"style":2770},[491],[212,72224],{},[212,72226],{"className":72227},[350,638],[212,72229],{"className":72230,"style":355},[354],[212,72232,320],{"className":72233},[359],[212,72235],{"className":72236,"style":355},[354],[212,72238,72240,72243,72246,72249,72252,72255,72258],{"className":72239},[247],[212,72241],{"className":72242,"style":336},[251],[212,72244,966],{"className":72245},[256,257],[212,72247,310],{"className":72248},[343],[212,72250,40437],{"className":72251,"style":1178},[256,257],[212,72253],{"className":72254,"style":2785},[354],[212,72256,2668],{"className":72257},[2789],[212,72259],{"className":72260,"style":2785},[354],[212,72262,72264,72267,72335,72338,72341,72344],{"className":72263},[247],[212,72265],{"className":72266,"style":2703},[251],[212,72268,72270,72273,72332],{"className":72269},[256],[212,72271],{"className":72272},[343,638],[212,72274,72276],{"className":72275},[435],[212,72277,72279,72324],{"className":72278},[482,483],[212,72280,72282,72321],{"className":72281},[487],[212,72283,72285,72299,72307],{"className":72284,"style":2722},[491],[212,72286,72287,72290],{"style":2725},[212,72288],{"className":72289,"style":658},[499],[212,72291,72293],{"className":72292},[504,505,506,507],[212,72294,72296],{"className":72295},[256,507],[212,72297,2661],{"className":72298},[256,507],[212,72300,72301,72304],{"style":670},[212,72302],{"className":72303,"style":658},[499],[212,72305],{"className":72306,"style":678},[677],[212,72308,72309,72312],{"style":2748},[212,72310],{"className":72311,"style":658},[499],[212,72313,72315],{"className":72314},[504,505,506,507],[212,72316,72318],{"className":72317},[256,507],[212,72319,314],{"className":72320},[256,507],[212,72322,515],{"className":72323},[514],[212,72325,72327],{"className":72326},[487],[212,72328,72330],{"className":72329,"style":2770},[491],[212,72331],{},[212,72333],{"className":72334},[350,638],[212,72336,317],{"className":72337},[350],[212,72339],{"className":72340,"style":2785},[354],[212,72342,5011],{"className":72343},[2789],[212,72345],{"className":72346,"style":2785},[354],[212,72348,72350,72353],{"className":72349},[247],[212,72351],{"className":72352,"style":2703},[251],[212,72354,72356,72359,72418],{"className":72355},[256],[212,72357],{"className":72358},[343,638],[212,72360,72362],{"className":72361},[435],[212,72363,72365,72410],{"className":72364},[482,483],[212,72366,72368,72407],{"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",[212,72423,72425,72443],{"className":72424,"translate":216},[215],[212,72426,72428],{"className":72427},[220],[222,72429,72430],{"xmlns":224},[226,72431,72432,72440],{},[229,72433,72434,72436,72438],{},[232,72435,966],{},[307,72437,7126],{},[312,72439,314],{},[236,72441,72442],{"encoding":238},"t\\ge1",[212,72444,72446,72464],{"className":72445,"ariaHidden":243},[242],[212,72447,72449,72452,72455,72458,72461],{"className":72448},[247],[212,72450],{"className":72451,"style":43388},[251],[212,72453,966],{"className":72454},[256,257],[212,72456],{"className":72457,"style":355},[354],[212,72459,7126],{"className":72460},[359],[212,72462],{"className":72463,"style":355},[354],[212,72465,72467,72470],{"className":72466},[247],[212,72468],{"className":72469,"style":369},[251],[212,72471,314],{"className":72472},[256],[212,72474,72476,72532],{"className":72475,"translate":216},[215],[212,72477,72479],{"className":72478},[220],[222,72480,72481],{"xmlns":224},[226,72482,72483,72529],{},[229,72484,72485,72487,72489,72491,72503,72505,72507,72509,72511,72513,72519,72521,72523],{},[232,72486,40437],{},[232,72488,966],{},[307,72490,5011],{},[435,72492,72493,72501],{},[229,72494,72495,72497,72499],{},[232,72496,966],{},[307,72498,5011],{},[312,72500,314],{},[312,72502,2661],{},[307,72504,320],{},[232,72506,966],{},[307,72508,310],{"stretchy":309},[232,72510,40437],{},[307,72512,5011],{},[435,72514,72515,72517],{},[312,72516,314],{},[312,72518,2661],{},[307,72520,317],{"stretchy":309},[307,72522,2668],{},[435,72524,72525,72527],{},[312,72526,314],{},[312,72528,2661],{},[236,72530,72531],{"encoding":238},"yt-\\frac{t-1}{2}=t(y-\\frac12)+\\frac12",[212,72533,72535,72556,72645,72669,72755],{"className":72534,"ariaHidden":243},[242],[212,72536,72538,72541,72544,72547,72550,72553],{"className":72537},[247],[212,72539],{"className":72540,"style":26474},[251],[212,72542,40437],{"className":72543,"style":1178},[256,257],[212,72545,966],{"className":72546},[256,257],[212,72548],{"className":72549,"style":2785},[354],[212,72551,5011],{"className":72552},[2789],[212,72554],{"className":72555,"style":2785},[354],[212,72557,72559,72562,72636,72639,72642],{"className":72558},[247],[212,72560],{"className":72561,"style":2703},[251],[212,72563,72565,72568,72633],{"className":72564},[256],[212,72566],{"className":72567},[343,638],[212,72569,72571],{"className":72570},[435],[212,72572,72574,72625],{"className":72573},[482,483],[212,72575,72577,72622],{"className":72576},[487],[212,72578,72580,72594,72602],{"className":72579,"style":2722},[491],[212,72581,72582,72585],{"style":2725},[212,72583],{"className":72584,"style":658},[499],[212,72586,72588],{"className":72587},[504,505,506,507],[212,72589,72591],{"className":72590},[256,507],[212,72592,2661],{"className":72593},[256,507],[212,72595,72596,72599],{"style":670},[212,72597],{"className":72598,"style":658},[499],[212,72600],{"className":72601,"style":678},[677],[212,72603,72604,72607],{"style":2748},[212,72605],{"className":72606,"style":658},[499],[212,72608,72610],{"className":72609},[504,505,506,507],[212,72611,72613,72616,72619],{"className":72612},[256,507],[212,72614,966],{"className":72615},[256,257,507],[212,72617,5011],{"className":72618},[2789,507],[212,72620,314],{"className":72621},[256,507],[212,72623,515],{"className":72624},[514],[212,72626,72628],{"className":72627},[487],[212,72629,72631],{"className":72630,"style":2770},[491],[212,72632],{},[212,72634],{"className":72635},[350,638],[212,72637],{"className":72638,"style":355},[354],[212,72640,320],{"className":72641},[359],[212,72643],{"className":72644,"style":355},[354],[212,72646,72648,72651,72654,72657,72660,72663,72666],{"className":72647},[247],[212,72649],{"className":72650,"style":336},[251],[212,72652,966],{"className":72653},[256,257],[212,72655,310],{"className":72656},[343],[212,72658,40437],{"className":72659,"style":1178},[256,257],[212,72661],{"className":72662,"style":2785},[354],[212,72664,5011],{"className":72665},[2789],[212,72667],{"className":72668,"style":2785},[354],[212,72670,72672,72675,72743,72746,72749,72752],{"className":72671},[247],[212,72673],{"className":72674,"style":2703},[251],[212,72676,72678,72681,72740],{"className":72677},[256],[212,72679],{"className":72680},[343,638],[212,72682,72684],{"className":72683},[435],[212,72685,72687,72732],{"className":72686},[482,483],[212,72688,72690,72729],{"className":72689},[487],[212,72691,72693,72707,72715],{"className":72692,"style":2722},[491],[212,72694,72695,72698],{"style":2725},[212,72696],{"className":72697,"style":658},[499],[212,72699,72701],{"className":72700},[504,505,506,507],[212,72702,72704],{"className":72703},[256,507],[212,72705,2661],{"className":72706},[256,507],[212,72708,72709,72712],{"style":670},[212,72710],{"className":72711,"style":658},[499],[212,72713],{"className":72714,"style":678},[677],[212,72716,72717,72720],{"style":2748},[212,72718],{"className":72719,"style":658},[499],[212,72721,72723],{"className":72722},[504,505,506,507],[212,72724,72726],{"className":72725},[256,507],[212,72727,314],{"className":72728},[256,507],[212,72730,515],{"className":72731},[514],[212,72733,72735],{"className":72734},[487],[212,72736,72738],{"className":72737,"style":2770},[491],[212,72739],{},[212,72741],{"className":72742},[350,638],[212,72744,317],{"className":72745},[350],[212,72747],{"className":72748,"style":2785},[354],[212,72750,2668],{"className":72751},[2789],[212,72753],{"className":72754,"style":2785},[354],[212,72756,72758,72761],{"className":72757},[247],[212,72759],{"className":72760,"style":2703},[251],[212,72762,72764,72767,72826],{"className":72763},[256],[212,72765],{"className":72766},[343,638],[212,72768,72770],{"className":72769},[435],[212,72771,72773,72818],{"className":72772},[482,483],[212,72774,72776,72815],{"className":72775},[487],[212,72777,72779,72793,72801],{"className":72778,"style":2722},[491],[212,72780,72781,72784],{"style":2725},[212,72782],{"className":72783,"style":658},[499],[212,72785,72787],{"className":72786},[504,505,506,507],[212,72788,72790],{"className":72789},[256,507],[212,72791,2661],{"className":72792},[256,507],[212,72794,72795,72798],{"style":670},[212,72796],{"className":72797,"style":658},[499],[212,72799],{"className":72800,"style":678},[677],[212,72802,72803,72806],{"style":2748},[212,72804],{"className":72805,"style":658},[499],[212,72807,72809],{"className":72808},[504,505,506,507],[212,72810,72812],{"className":72811},[256,507],[212,72813,314],{"className":72814},[256,507],[212,72816,515],{"className":72817},[514],[212,72819,72821],{"className":72820},[487],[212,72822,72824],{"className":72823,"style":2770},[491],[212,72825],{},[212,72827],{"className":72828},[350,638],"。两段都是线性的：当 ",[212,72831,72833,72858],{"className":72832,"translate":216},[215],[212,72834,72836],{"className":72835},[220],[222,72837,72838],{"xmlns":224},[226,72839,72840,72856],{},[229,72841,72842,72844,72846,72848,72850],{},[307,72843,5006],{"stretchy":309},[232,72845,40437],{},[307,72847,5006],{"stretchy":309},[307,72849,10150],{},[435,72851,72852,72854],{},[312,72853,314],{},[312,72855,2661],{},[236,72857,66267],{"encoding":238},[212,72859,72861,72885],{"className":72860,"ariaHidden":243},[242],[212,72862,72864,72867,72870,72873,72876,72879,72882],{"className":72863},[247],[212,72865],{"className":72866,"style":336},[251],[212,72868,5006],{"className":72869},[343],[212,72871,40437],{"className":72872,"style":1178},[256,257],[212,72874,5006],{"className":72875},[350],[212,72877],{"className":72878,"style":355},[354],[212,72880,10150],{"className":72881},[359],[212,72883],{"className":72884,"style":355},[354],[212,72886,72888,72891],{"className":72887},[247],[212,72889],{"className":72890,"style":2703},[251],[212,72892,72894,72897,72956],{"className":72893},[256],[212,72895],{"className":72896},[343,638],[212,72898,72900],{"className":72899},[435],[212,72901,72903,72948],{"className":72902},[482,483],[212,72904,72906,72945],{"className":72905},[487],[212,72907,72909,72923,72931],{"className":72908,"style":2722},[491],[212,72910,72911,72914],{"style":2725},[212,72912],{"className":72913,"style":658},[499],[212,72915,72917],{"className":72916},[504,505,506,507],[212,72918,72920],{"className":72919},[256,507],[212,72921,2661],{"className":72922},[256,507],[212,72924,72925,72928],{"style":670},[212,72926],{"className":72927,"style":658},[499],[212,72929],{"className":72930,"style":678},[677],[212,72932,72933,72936],{"style":2748},[212,72934],{"className":72935,"style":658},[499],[212,72937,72939],{"className":72938},[504,505,506,507],[212,72940,72942],{"className":72941},[256,507],[212,72943,314],{"className":72944},[256,507],[212,72946,515],{"className":72947},[514],[212,72949,72951],{"className":72950},[487],[212,72952,72954],{"className":72953,"style":2770},[491],[212,72955],{},[212,72957],{"className":72958},[350,638]," 时两段的最大值都在 ",[212,72961,72963,72981],{"className":72962,"translate":216},[215],[212,72964,72966],{"className":72965},[220],[222,72967,72968],{"xmlns":224},[226,72969,72970,72978],{},[229,72971,72972,72974,72976],{},[232,72973,966],{},[307,72975,320],{},[312,72977,314],{},[236,72979,72980],{"encoding":238},"t=1",[212,72982,72984,73002],{"className":72983,"ariaHidden":243},[242],[212,72985,72987,72990,72993,72996,72999],{"className":72986},[247],[212,72988],{"className":72989,"style":5541},[251],[212,72991,966],{"className":72992},[256,257],[212,72994],{"className":72995,"style":355},[354],[212,72997,320],{"className":72998},[359],[212,73000],{"className":73001,"style":355},[354],[212,73003,73005,73008],{"className":73004},[247],[212,73006],{"className":73007,"style":369},[251],[212,73009,314],{"className":73010},[256]," 取到，为 ",[212,73013,73015,73028],{"className":73014,"translate":216},[215],[212,73016,73018],{"className":73017},[220],[222,73019,73020],{"xmlns":224},[226,73021,73022,73026],{},[229,73023,73024],{},[232,73025,40437],{},[236,73027,40437],{"encoding":238},[212,73029,73031],{"className":73030,"ariaHidden":243},[242],[212,73032,73034,73037],{"className":73033},[247],[212,73035],{"className":73036,"style":2474},[251],[212,73038,40437],{"className":73039,"style":1178},[256,257],[212,73041,73043,73065],{"className":73042,"translate":216},[215],[212,73044,73046],{"className":73045},[220],[222,73047,73048],{"xmlns":224},[226,73049,73050,73062],{},[229,73051,73052,73054,73056],{},[232,73053,40437],{},[307,73055,3101],{},[435,73057,73058,73060],{},[312,73059,314],{},[312,73061,2661],{},[236,73063,73064],{"encoding":238},"y>\\frac12",[212,73066,73068,73086],{"className":73067,"ariaHidden":243},[242],[212,73069,73071,73074,73077,73080,73083],{"className":73070},[247],[212,73072],{"className":73073,"style":31892},[251],[212,73075,40437],{"className":73076,"style":1178},[256,257],[212,73078],{"className":73079,"style":355},[354],[212,73081,3101],{"className":73082},[359],[212,73084],{"className":73085,"style":355},[354],[212,73087,73089,73092],{"className":73088},[247],[212,73090],{"className":73091,"style":2703},[251],[212,73093,73095,73098,73157],{"className":73094},[256],[212,73096],{"className":73097},[343,638],[212,73099,73101],{"className":73100},[435],[212,73102,73104,73149],{"className":73103},[482,483],[212,73105,73107,73146],{"className":73106},[487],[212,73108,73110,73124,73132],{"className":73109,"style":2722},[491],[212,73111,73112,73115],{"style":2725},[212,73113],{"className":73114,"style":658},[499],[212,73116,73118],{"className":73117},[504,505,506,507],[212,73119,73121],{"className":73120},[256,507],[212,73122,2661],{"className":73123},[256,507],[212,73125,73126,73129],{"style":670},[212,73127],{"className":73128,"style":658},[499],[212,73130],{"className":73131,"style":678},[677],[212,73133,73134,73137],{"style":2748},[212,73135],{"className":73136,"style":658},[499],[212,73138,73140],{"className":73139},[504,505,506,507],[212,73141,73143],{"className":73142},[256,507],[212,73144,314],{"className":73145},[256,507],[212,73147,515],{"className":73148},[514],[212,73150,73152],{"className":73151},[487],[212,73153,73155],{"className":73154,"style":2770},[491],[212,73156],{},[212,73158],{"className":73159},[350,638]," 时第二段严格递增，上确界为 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e":500},[499],[212,74621,74623],{"className":74622},[504,505,506,507],[212,74624,410],{"className":74625},[256,257,507],[212,74627,515],{"className":74628},[514],[212,74630,74632],{"className":74631},[487],[212,74633,74635],{"className":74634,"style":522},[491],[212,74636],{},[212,74638,427],{"className":74639},[343],[212,74641,4356],{"className":74642,"style":1178},[256,257],[212,74644,454],{"className":74645},[350],[212,74647,74649],{"className":74648},[256],[212,74650,3106],{"className":74651},[616,9872],[11,74653,74654],{},"的 Kantorovich 型对偶。",[11,74656,74657],{},"这个对偶表示在机器学习中非常有用，例如 f-GAN 就是基于此构造的（第 5 节详述）。",[2509,74659,74661],{"id":74660},"_45-数据处理不等式","4.5 数据处理不等式",[24,74663,74664,74767],{},[11,74665,74666,11260,74669,74697,74698,5843,74732,74766],{},[1194,74667,74668],{},"命题 4.4（数据处理不等式）",[212,74670,74672,74685],{"className":74671,"translate":216},[215],[212,74673,74675],{"className":74674},[220],[222,74676,74677],{"xmlns":224},[226,74678,74679,74683],{},[229,74680,74681],{},[232,74682,10894],{},[236,74684,10894],{"encoding":238},[212,74686,74688],{"className":74687,"ariaHidden":243},[242],[212,74689,74691,74694],{"className":74690},[247],[212,74692],{"className":74693,"style":861},[251],[212,74695,10894],{"className":74696,"style":10982},[256,257]," 是一个马尔可夫核（随机变换），记 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为输出分布，则",[212,74768,74770],{"className":74769,"translate":216},[377],[212,74771,74773,74825],{"className":74772,"translate":216},[215],[212,74774,74776],{"className":74775},[220],[222,74777,74778],{"xmlns":224,"display":386},[226,74779,74780,74822],{},[229,74781,74782,74788,74790,74792,74794,74796,74798,74800,74802,74804,74810,74812,74814,74816,74818,74820],{},[392,74783,74784,74786],{},[232,74785,396],{},[232,74787,234],{},[307,74789,310],{"stretchy":309},[232,74791,403],{},[232,74793,10894],{},[232,74795,407],{"mathvariant":406},[232,74797,410],{},[232,74799,10894],{},[307,74801,317],{"stretchy":309},[307,74803,10150],{},[392,74805,74806,74808],{},[232,74807,396],{},[232,74809,234],{},[307,74811,310],{"stretchy":309},[232,74813,403],{},[232,74815,407],{"mathvariant":406},[232,74817,410],{},[307,74819,317],{"stretchy":309},[232,74821,4573],{"mathvariant":406},[236,74823,74824],{"encoding":238},"D_f(PK\\|QK)\\le 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E_{QK}\\Big[\nf\\big(\\mathbb E_Q[t|Y]\\big)\\Big]\\\\\n&\\le \\mathbb E_{QK}\\Big[\n\\mathbb E_Q[f(t)|Y]\\Big]\\\\\n&=\\mathbb 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1},[491],[212,77814],{},[11,77816,77817,56346,77820,77848,77849,77944,77945,77989,77990,78018,78019,78089,78090,78118,78119,78147,78148,34025,78189,78192],{},[1194,77818,77819],{},"等号条件。",[212,77821,77823,77836],{"className":77822,"translate":216},[215],[212,77824,77826],{"className":77825},[220],[222,77827,77828],{"xmlns":224},[226,77829,77830,77834],{},[229,77831,77832],{},[232,77833,234],{},[236,77835,234],{"encoding":238},[212,77837,77839],{"className":77838,"ariaHidden":243},[242],[212,77840,77842,77845],{"className":77841},[247],[212,77843],{"className":77844,"style":252},[251],[212,77846,234],{"className":77847,"style":258},[256,257]," 严格凸，等号成立当且仅当 ",[212,77850,77852,77880],{"className":77851,"translate":216},[215],[212,77853,77855],{"className":77854},[220],[222,77856,77857],{"xmlns":224},[226,77858,77859,77877],{},[229,77860,77861,77867,77869,77871,77873,77875],{},[392,77862,77863,77865],{},[232,77864,420],{"mathvariant":419},[232,77866,410],{},[307,77868,427],{"stretchy":309},[232,77870,966],{},[232,77872,5006],{"mathvariant":406},[232,77874,5599],{},[307,77876,454],{"stretchy":309},[236,77878,77879],{"encoding":238},"\\mathbb E_Q[t|Y]",[212,77881,77883],{"className":77882,"ariaHidden":243},[242],[212,77884,77886,77889,77929,77932,77935,77938,77941],{"className":77885},[247],[212,77887],{"className":77888,"style":467},[251],[212,77890,77892,77895],{"className":77891},[256],[212,77893,420],{"className":77894},[256,563],[212,77896,77898],{"className":77897},[478],[212,77899,77901,77921],{"className":77900},[482,483],[212,77902,77904,77918],{"className":77903},[487],[212,77905,77907],{"className":77906,"style":576},[491],[212,77908,77909,77912],{"style":579},[212,77910],{"className":77911,"style":500},[499],[212,77913,77915],{"className":77914},[504,505,506,507],[212,77916,410],{"className":77917},[256,257,507],[212,77919,515],{"className":77920},[514],[212,77922,77924],{"className":77923},[487],[212,77925,77927],{"className":77926,"style":522},[491],[212,77928],{},[212,77930,427],{"className":77931},[343],[212,77933,966],{"className":77934},[256,257],[212,77936,5006],{"className":77937},[256],[212,77939,5599],{"className":77940,"style":2785},[256,257],[212,77942,454],{"className":77943},[350]," 本身是 ",[212,77946,77948,77968],{"className":77947,"translate":216},[215],[212,77949,77951],{"className":77950},[220],[222,77952,77953],{"xmlns":224},[226,77954,77955,77965],{},[229,77956,77957,77959,77961,77963],{},[232,77958,2530],{},[307,77960,310],{"stretchy":309},[232,77962,5599],{},[307,77964,317],{"stretchy":309},[236,77966,77967],{"encoding":238},"\\sigma(Y)",[212,77969,77971],{"className":77970,"ariaHidden":243},[242],[212,77972,77974,77977,77980,77983,77986],{"className":77973},[247],[212,77975],{"className":77976,"style":336},[251],[212,77978,2530],{"className":77979,"style":1178},[256,257],[212,77981,310],{"className":77982},[343],[212,77984,5599],{"className":77985,"style":2785},[256,257],[212,77987,317],{"className":77988},[350],"-可测的（对每个 ",[212,77991,77993,78006],{"className":77992,"translate":216},[215],[212,77994,77996],{"className":77995},[220],[222,77997,77998],{"xmlns":224},[226,77999,78000,78004],{},[229,78001,78002],{},[232,78003,40437],{},[236,78005,40437],{"encoding":238},[212,78007,78009],{"className":78008,"ariaHidden":243},[242],[212,78010,78012,78015],{"className":78011},[247],[212,78013],{"className":78014,"style":2474},[251],[212,78016,40437],{"className":78017,"style":1178},[256,257]," 是常数），即 ",[212,78020,78022,78047],{"className":78021,"translate":216},[215],[212,78023,78025],{"className":78024},[220],[222,78026,78027],{"xmlns":224},[226,78028,78029,78045],{},[229,78030,78031,78033,78035,78037,78039,78041,78043],{},[232,78032,966],{},[307,78034,320],{},[232,78036,441],{},[232,78038,403],{},[232,78040,1138],{"mathvariant":406},[232,78042,441],{},[232,78044,410],{},[236,78046,5531],{"encoding":238},[212,78048,78050,78068],{"className":78049,"ariaHidden":243},[242],[212,78051,78053,78056,78059,78062,78065],{"className":78052},[247],[212,78054],{"className":78055,"style":5541},[251],[212,78057,966],{"className":78058},[256,257],[212,78060],{"className":78061,"style":355},[354],[212,78063,320],{"className":78064},[359],[212,78066],{"className":78067,"style":355},[354],[212,78069,78071,78074,78077,78080,78083,78086],{"className":78070},[247],[212,78072],{"className":78073,"style":336},[251],[212,78075,441],{"className":78076},[256,257],[212,78078,403],{"className":78079,"style":531},[256,257],[212,78081,1138],{"className":78082},[256],[212,78084,441],{"className":78085},[256,257],[212,78087,410],{"className":78088},[256,257]," 可表为 ",[212,78091,78093,78106],{"className":78092,"translate":216},[215],[212,78094,78096],{"className":78095},[220],[222,78097,78098],{"xmlns":224},[226,78099,78100,78104],{},[229,78101,78102],{},[232,78103,5599],{},[236,78105,5599],{"encoding":238},[212,78107,78109],{"className":78108,"ariaHidden":243},[242],[212,78110,78112,78115],{"className":78111},[247],[212,78113],{"className":78114,"style":861},[251],[212,78116,5599],{"className":78117,"style":2785},[256,257]," 的函数。此时 ",[212,78120,78122,78135],{"className":78121,"translate":216},[215],[212,78123,78125],{"className":78124},[220],[222,78126,78127],{"xmlns":224},[226,78128,78129,78133],{},[229,78130,78131],{},[232,78132,5599],{},[236,78134,5599],{"encoding":238},[212,78136,78138],{"className":78137,"ariaHidden":243},[242],[212,78139,78141,78144],{"className":78140},[247],[212,78142],{"className":78143,"style":861},[251],[212,78145,5599],{"className":78146,"style":2785},[256,257]," 是关于 ",[212,78149,78151,78168],{"className":78150,"translate":216},[215],[212,78152,78154],{"className":78153},[220],[222,78155,78156],{"xmlns":224},[226,78157,78158,78166],{},[229,78159,78160,78162,78164],{},[232,78161,403],{},[307,78163,748],{"separator":243},[232,78165,410],{},[236,78167,753],{"encoding":238},[212,78169,78171],{"className":78170,"ariaHidden":243},[242],[212,78172,78174,78177,78180,78183,78186],{"className":78173},[247],[212,78175],{"className":78176,"style":763},[251],[212,78178,403],{"className":78179,"style":531},[256,257],[212,78181,748],{"className":78182},[770],[212,78184],{"className":78185,"style":603},[354],[212,78187,410],{"className":78188},[256,257],[1194,78190,78191],{},"充分统计量","：随机变换没有丢信息。这正是 f-散度能担当「信息量」的原因。",[11,78194,78195,78198,78199,78240],{},[1194,78196,78197],{},"信息单调性（Csiszár 的更进一步结果）。"," 对 α-散度族，还有更强的「信息单调性」：把 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4.5（局部二次展开）",[212,78253,78255,78268],{"className":78254,"translate":216},[215],[212,78256,78258],{"className":78257},[220],[222,78259,78260],{"xmlns":224},[226,78261,78262,78266],{},[229,78263,78264],{},[232,78265,38865],{},[236,78267,38865],{"encoding":238},[212,78269,78271],{"className":78270,"ariaHidden":243},[242],[212,78272,78274,78277],{"className":78273},[247],[212,78275],{"className":78276,"style":12797},[251],[212,78278,38865],{"className":78279},[256,257]," 满足 ",[212,78282,78284,78310],{"className":78283,"translate":216},[215],[212,78285,78287],{"className":78286},[220],[222,78288,78289],{"xmlns":224},[226,78290,78291,78307],{},[229,78292,78293,78295,78297,78299,78301,78303,78305],{},[307,78294,1485],{},[232,78296,38865],{},[1495,78298,1497],{},[232,78300,441],{},[232,78302,403],{},[307,78304,320],{},[312,78306,323],{},[236,78308,78309],{"encoding":238},"\\int 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h^2\\,dP\u003C\\infty",[212,78389,78391,78450],{"className":78390,"ariaHidden":243},[242],[212,78392,78394,78397,78400,78403,78432,78435,78438,78441,78444,78447],{"className":78393},[247],[212,78395],{"className":78396,"style":50527},[251],[212,78398,1485],{"className":78399,"style":5815},[1682,1683,5814],[212,78401],{"className":78402,"style":603},[354],[212,78404,78406,78409],{"className":78405},[256],[212,78407,38865],{"className":78408},[256,257],[212,78410,78412],{"className":78411},[478],[212,78413,78415],{"className":78414},[482],[212,78416,78418],{"className":78417},[487],[212,78419,78421],{"className":78420,"style":20228},[491],[212,78422,78423,78426],{"style":7063},[212,78424],{"className":78425,"style":500},[499],[212,78427,78429],{"className":78428},[504,505,506,507],[212,78430,2661],{"className":78431},[256,507],[212,78433],{"className":78434,"style":603},[354],[212,78436,441],{"className":78437},[256,257],[212,78439,403],{"className":78440,"style":531},[256,257],[212,78442],{"className":78443,"style":355},[354],[212,78445,7449],{"className":78446},[359],[212,78448],{"className":78449,"style":355},[354],[212,78451,78453,78456],{"className":78452},[247],[212,78454],{"className":78455,"style":2543},[251],[212,78457,1223],{"className":78458},[256],[212,78460,78462,78502],{"className":78461,"translate":216},[215],[212,78463,78465],{"className":78464},[220],[222,78466,78467],{"xmlns":224},[226,78468,78469,78499],{},[229,78470,78471,78473,78479,78481,78483,78485,78487,78489,78491,78493,78495,78497],{},[232,78472,441],{},[392,78474,78475,78477],{},[232,78476,410],{},[232,78478,38862],{},[307,78480,320],{},[307,78482,310],{"stretchy":309},[312,78484,314],{},[307,78486,2668],{},[232,78488,38862],{},[232,78490,38865],{},[307,78492,317],{"stretchy":309},[1495,78494,1497],{},[232,78496,441],{},[232,78498,403],{},[236,78500,78501],{"encoding":238},"dQ_\\varepsilon=(1+\\varepsilon h)\\,dP",[212,78503,78505,78563,78584],{"className":78504,"ariaHidden":243},[242],[212,78506,78508,78511,78514,78554,78557,78560],{"className":78507},[247],[212,78509],{"className":78510,"style":252},[251],[212,78512,441],{"className":78513},[256,257],[212,78515,78517,78520],{"className":78516},[256],[212,78518,410],{"className":78519},[256,257],[212,78521,78523],{"className":78522},[478],[212,78524,78526,78546],{"className":78525},[482,483],[212,78527,78529,78543],{"className":78528},[487],[212,78530,78532],{"className":78531,"style":45129},[491],[212,78533,78534,78537],{"style":579},[212,78535],{"className":78536,"style":500},[499],[212,78538,78540],{"className":78539},[504,505,506,507],[212,78541,38862],{"className":78542},[256,257,507],[212,78544,515],{"className":78545},[514],[212,78547,78549],{"className":78548},[487],[212,78550,78552],{"className":78551,"style":8166},[491],[212,78553],{},[212,78555],{"className":78556,"style":355},[354],[212,78558,320],{"className":78559},[359],[212,78561],{"className":78562,"style":355},[354],[212,78564,78566,78569,78572,78575,78578,78581],{"className":78565},[247],[212,78567],{"className":78568,"style":336},[251],[212,78570,310],{"className":78571},[343],[212,78573,314],{"className":78574},[256],[212,78576],{"className":78577,"style":2785},[354],[212,78579,2668],{"className":78580},[2789],[212,78582],{"className":78583,"style":2785},[354],[212,78585,78587,78590,78593,78596,78599,78602,78605],{"className":78586},[247],[212,78588],{"className":78589,"style":336},[251],[212,78591,38862],{"className":78592},[256,257],[212,78594,38865],{"className":78595},[256,257],[212,78597,317],{"className":78598},[350],[212,78600],{"className":78601,"style":603},[354],[212,78603,441],{"className":78604},[256,257],[212,78606,403],{"className":78607,"style":531},[256,257],"，则当 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记 ",[212,79133,79135,79175],{"className":79134,"translate":216},[215],[212,79136,79138],{"className":79137},[220],[222,79139,79140],{"xmlns":224},[226,79141,79142,79172],{},[229,79143,79144,79146,79148,79150,79156,79158,79160,79162,79164,79166,79168,79170],{},[232,79145,966],{},[307,79147,320],{},[232,79149,441],{},[392,79151,79152,79154],{},[232,79153,410],{},[232,79155,38862],{},[232,79157,1138],{"mathvariant":406},[232,79159,441],{},[232,79161,403],{},[307,79163,320],{},[312,79165,314],{},[307,79167,2668],{},[232,79169,38862],{},[232,79171,38865],{},[236,79173,79174],{"encoding":238},"t=dQ_\\varepsilon\u002FdP=1+\\varepsilon h",[212,79176,79178,79196,79263,79281],{"className":79177,"ariaHidden":243},[242],[212,79179,79181,79184,79187,79190,79193],{"className":79180},[247],[212,79182],{"className":79183,"style":5541},[251],[212,79185,966],{"className":79186},[256,257],[212,79188],{"className":79189,"style":355},[354],[212,79191,320],{"className":79192},[359],[212,79194],{"className":79195,"style":355},[354],[212,79197,79199,79202,79205,79245,79248,79251,79254,79257,79260],{"className":79198},[247],[212,79200],{"className":79201,"style":336},[251],[212,79203,441],{"className":79204},[256,257],[212,79206,79208,79211],{"className":79207},[256],[212,79209,410],{"className":79210},[256,257],[212,79212,79214],{"className":79213},[478],[212,79215,79217,79237],{"className":79216},[482,483],[212,79218,79220,79234],{"className":79219},[487],[212,79221,79223],{"className":79222,"style":45129},[491],[212,79224,79225,79228],{"style":579},[212,79226],{"className":79227,"style":500},[499],[212,79229,79231],{"className":79230},[504,505,506,507],[212,79232,38862],{"className":79233},[256,257,507],[212,79235,515],{"className":79236},[514],[212,79238,79240],{"className":79239},[487],[212,79241,79243],{"className":79242,"style":8166},[491],[212,79244],{},[212,79246,1138],{"className":79247},[256],[212,79249,441],{"className":79250},[256,257],[212,79252,403],{"className":79253,"style":531},[256,257],[212,79255],{"className":79256,"style":355},[354],[212,79258,320],{"className":79259},[359],[212,79261],{"className":79262,"style":355},[354],[212,79264,79266,79269,79272,79275,79278],{"className":79265},[247],[212,79267],{"className":79268,"style":12778},[251],[212,79270,314],{"className":79271},[256],[212,79273],{"className":79274,"style":2785},[354],[212,79276,2668],{"className":79277},[2789],[212,79279],{"className":79280,"style":2785},[354],[212,79282,79284,79287,79290],{"className":79283},[247],[212,79285],{"className":79286,"style":12797},[251],[212,79288,38862],{"className":79289},[256,257],[212,79291,38865],{"className":79292},[256,257],"，由 ",[212,79295,79297,79320],{"className":79296,"translate":216},[215],[212,79298,79300],{"className":79299},[220],[222,79301,79302],{"xmlns":224},[226,79303,79304,79318],{},[229,79305,79306,79308,79310,79312,79314,79316],{},[232,79307,234],{},[307,79309,310],{"stretchy":309},[312,79311,314],{},[307,79313,317],{"stretchy":309},[307,79315,320],{},[312,79317,323],{},[236,79319,326],{"encoding":238},[212,79321,79323,79350],{"className":79322,"ariaHidden":243},[242],[212,79324,79326,79329,79332,79335,79338,79341,79344,79347],{"className":79325},[247],[212,79327],{"className":79328,"style":336},[251],[212,79330,234],{"className":79331,"style":258},[256,257],[212,79333,310],{"className":79334},[343],[212,79336,314],{"className":79337},[256],[212,79339,317],{"className":79340},[350],[212,79342],{"className":79343,"style":355},[354],[212,79345,320],{"className":79346},[359],[212,79348],{"className":79349,"style":355},[354],[212,79351,79353,79356],{"className":79352},[247],[212,79354],{"className":79355,"style":369},[251],[212,79357,323],{"className":79358},[256],[212,79360,79362,79387],{"className":79361,"translate":216},[215],[212,79363,79365],{"className":79364},[220],[222,79366,79367],{"xmlns":224},[226,79368,79369,79385],{},[229,79370,79371,79373,79375,79377,79379,79381,79383],{},[307,79372,1485],{},[232,79374,38865],{},[1495,79376,1497],{},[232,79378,441],{},[232,79380,403],{},[307,79382,320],{},[312,79384,323],{},[236,79386,78309],{"encoding":238},[212,79388,79390,79423],{"className":79389,"ariaHidden":243},[242],[212,79391,79393,79396,79399,79402,79405,79408,79411,79414,79417,79420],{"className":79392},[247],[212,79394],{"className":79395,"style":5810},[251],[212,79397,1485],{"className":79398,"style":5815},[1682,1683,5814],[212,79400],{"className":79401,"style":603},[354],[212,79403,38865],{"className":79404},[256,257],[212,79406],{"className":79407,"style":603},[354],[212,79409,441],{"className":79410},[256,257],[212,79412,403],{"className":79413,"style":531},[256,257],[212,79415],{"className":79416,"style":355},[354],[212,79418,320],{"className":79419},[359],[212,79421],{"className":79422,"style":355},[354],[212,79424,79426,79429],{"className":79425},[247],[212,79427],{"className":79428,"style":369},[251],[212,79430,323],{"className":79431},[256]," 做 Taylor 展开：",[212,79434,79436],{"className":79435,"translate":216},[377],[212,79437,79439,79667],{"className":79438,"translate":216},[215],[212,79440,79442],{"className":79441},[220],[222,79443,79444],{"xmlns":224,"display":386},[226,79445,79446,79664],{},[1441,79447,79448,79510,79584],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,79449,79450,79476],{},[1450,79451,79452],{},[1453,79453,79454],{"scriptlevel":323,"displaystyle":243},[229,79455,79456,79462,79464,79470,79472,79474],{},[392,79457,79458,79460],{},[232,79459,396],{},[232,79461,234],{},[307,79463,310],{"stretchy":309},[392,79465,79466,79468],{},[232,79467,410],{},[232,79469,38862],{},[232,79471,407],{"mathvariant":406},[232,79473,403],{},[307,79475,317],{"stretchy":309},[1450,79477,79478],{},[1453,79479,79480],{"scriptlevel":323,"displaystyle":243},[229,79481,79482,79484,79486,79492,79494,79496,79498,79500,79502,79504,79506,79508],{},[229,79483],{},[307,79485,320],{},[392,79487,79488,79490],{},[232,79489,420],{"mathvariant":419},[232,79491,403],{},[307,79493,427],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,79495,234],{},[307,79497,310],{"stretchy":309},[312,79499,314],{},[307,79501,2668],{},[232,79503,38862],{},[232,79505,38865],{},[307,79507,317],{"stretchy":309},[307,79509,454],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[1447,79511,79512,79518],{},[1450,79513,79514],{},[1453,79515,79516],{"scriptlevel":323,"displaystyle":243},[229,79517],{},[1450,79519,79520],{},[1453,79521,79522],{"scriptlevel":323,"displaystyle":243},[229,79523,79524,79526,79528,79546,79548,79550,79556,79558,79560,79562],{},[229,79525],{},[307,79527,320],{},[6214,79529,79530,79544],{},[6214,79531,79532,79542],{},[229,79533,79534,79536,79538,79540],{},[232,79535,234],{},[307,79537,310],{"stretchy":309},[312,79539,314],{},[307,79541,317],{"stretchy":309},[307,79543,6238],{"stretchy":243},[312,79545,323],{},[307,79547,2668],{},[232,79549,38862],{},[7012,79551,79552,79554],{},[232,79553,234],{},[307,79555,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,79557,310],{"stretchy":309},[312,79559,314],{},[307,79561,317],{"stretchy":309},[6214,79563,79564,79582],{},[6214,79565,79566,79580],{},[229,79567,79568,79574,79576,79578],{},[392,79569,79570,79572],{},[232,79571,420],{"mathvariant":419},[232,79573,403],{},[307,79575,427],{"stretchy":309},[232,79577,38865],{},[307,79579,454],{"stretchy":309},[307,79581,6238],{"stretchy":243},[312,79583,323],{},[1447,79585,79586,79592],{},[1450,79587,79588],{},[1453,79589,79590],{"scriptlevel":323,"displaystyle":243},[229,79591],{},[1450,79593,79594],{},[1453,79595,79596],{"scriptlevel":323,"displaystyle":243},[229,79597,79598,79600,79602,79604,79614,79624,79626,79628,79630,79632,79638,79640,79646,79648,79650,79652,79654,79660,79662],{},[229,79599],{},[354,79601],{"width":3460},[307,79603,2668],{},[435,79605,79606,79612],{},[7012,79607,79608,79610],{},[232,79609,38862],{},[312,79611,2661],{},[312,79613,2661],{},[7012,79615,79616,79618],{},[232,79617,234],{},[229,79619,79620,79622],{},[307,79621,7018],{"mathvariant":406},[307,79623,7018],{"mathvariant":406},[307,79625,310],{"stretchy":309},[312,79627,314],{},[307,79629,317],{"stretchy":309},[1495,79631,1497],{},[392,79633,79634,79636],{},[232,79635,420],{"mathvariant":419},[232,79637,403],{},[307,79639,427],{"stretchy":309},[7012,79641,79642,79644],{},[232,79643,38865],{},[312,79645,2661],{},[307,79647,454],{"stretchy":309},[307,79649,2668],{},[232,79651,19421],{},[307,79653,310],{"stretchy":309},[7012,79655,79656,79658],{},[232,79657,38862],{},[312,79659,40935],{},[307,79661,317],{"stretchy":309},[232,79663,4573],{"mathvariant":406},[236,79665,79666],{"encoding":238},"\\begin{aligned}\nD_f(Q_\\varepsilon\\|P)\n&=\\mathbb E_P\\big[f(1+\\varepsilon h)\\big]\\\\[2pt]\n&=\\underbrace{f(1)}_{0}\n+\\varepsilon f'(1)\n\\underbrace{\\mathbb E_P[h]}_{0}\\\\\n&\\qquad+\\frac{\\varepsilon^2}{2}f''(1)\\,\n\\mathbb 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ssName":80525,"style":474},[256,257],[212,80527,310],{"className":80528},[343],[212,80530,80532,80535],{"className":80531},[256],[212,80533,38862],{"className":80534},[256,257],[212,80536,80538],{"className":80537},[478],[212,80539,80541],{"className":80540},[482],[212,80542,80544],{"className":80543},[487],[212,80545,80547],{"className":80546,"style":19935},[491],[212,80548,80549,80552],{"style":8475},[212,80550],{"className":80551,"style":500},[499],[212,80553,80555],{"className":80554},[504,505,506,507],[212,80556,40935],{"className":80557},[256,507],[212,80559,317],{"className":80560},[350],[212,80562,4573],{"className":80563},[256],[212,80565,515],{"className":80566},[514],[212,80568,80570],{"className":80569},[487],[212,80571,80573],{"className":80572,"style":79825},[491],[212,80574],{},[11,80576,80577,23545,80661,15995,80746,80849,80850,81056,81057,15995,81227,80849,81399,81706,81707,81763,81764,81949,81950,82183,82184,82187,82188,82268],{},[1194,80578,80579,80580,80660],{},"这说明：在无穷小尺度上，所有 f-散度都只差一个常数 ",[212,80581,80583,80610],{"className":80582,"translate":216},[215],[212,80584,80586],{"className":80585},[220],[222,80587,80588],{"xmlns":224},[226,80589,80590,80608],{},[229,80591,80592,80602,80604,80606],{},[7012,80593,80594,80596],{},[232,80595,234],{},[229,80597,80598,80600],{},[307,80599,7018],{"mathvariant":406},[307,80601,7018],{"mathvariant":406},[307,80603,310],{"stretchy":309},[312,80605,314],{},[307,80607,317],{"stretchy":309},[236,80609,39734],{"encoding":238},[212,80611,80613],{"className":80612,"ariaHidden":243},[242],[212,80614,80616,80619,80651,80654,80657],{"className":80615},[247],[212,80617],{"className":80618,"style":7041},[251],[212,80620,80622,80625],{"className":80621},[256],[212,80623,234],{"className":80624,"style":258},[256,257],[212,80626,80628],{"className":80627},[478],[212,80629,80631],{"className":80630},[482],[212,80632,80634],{"className":80633},[487],[212,80635,80637],{"className":80636,"style":7060},[491],[212,80638,80639,80642],{"style":7063},[212,80640],{"className":80641,"style":500},[499],[212,80643,80645],{"className":80644},[504,505,506,507],[212,80646,80648],{"className":80647},[256,507],[212,80649,21948],{"className":80650},[256,507],[212,80652,310],{"className":80653},[343],[212,80655,314],{"className":80656},[256],[212,80658,317],{"className":80659},[350],"，形状完全一致。",[212,80662,80664,80693],{"className":80663,"translate":216},[215],[212,80665,80667],{"className":80666},[220],[222,80668,80669],{"xmlns":224},[226,80670,80671,80691],{},[229,80672,80673,80675,80677,80679,80681,80683,80685,80687,80689],{},[232,80674,234],{},[307,80676,310],{"stretchy":309},[232,80678,966],{},[307,80680,317],{"stretchy":309},[307,80682,320],{},[232,80684,966],{},[232,80686,4298],{},[307,80688,4301],{},[232,80690,966],{},[236,80692,4306],{"encoding":238},[212,80694,80696,80723],{"className":80695,"ariaHidden":243},[242],[212,80697,80699,80702,80705,80708,80711,80714,80717,80720],{"className":80698},[247],[212,80700],{"className":80701,"style":336},[251],[212,80703,234],{"className":80704,"style":258},[256,257],[212,80706,310],{"className":80707},[343],[212,80709,966],{"className":80710},[256,257],[212,80712,317],{"className":80713},[350],[212,80715],{"className":80716,"style":355},[354],[212,80718,320],{"className":80719},[359],[212,80721],{"className":80722,"style":355},[354],[212,80724,80726,80729,80732,80735,80740,80743],{"className":80725},[247],[212,80727],{"className":80728,"style":252},[251],[212,80730,966],{"className":80731},[256,257],[212,80733],{"className":80734,"style":603},[354],[212,80736,4352,80738],{"className":80737},[1682],[212,80739,4356],{"style":4355},[212,80741],{"className":80742,"style":603},[354],[212,80744,966],{"className":80745},[256,257],[212,80747,80749,80781],{"className":80748,"translate":216},[215],[212,80750,80752],{"className":80751},[220],[222,80753,80754],{"xmlns":224},[226,80755,80756,80778],{},[229,80757,80758,80768,80770,80772,80774,80776],{},[7012,80759,80760,80762],{},[232,80761,234],{},[229,80763,80764,80766],{},[307,80765,7018],{"mathvariant":406},[307,80767,7018],{"mathvariant":406},[307,80769,310],{"stretchy":309},[312,80771,314],{},[307,80773,317],{"stretchy":309},[307,80775,320],{},[312,80777,314],{},[236,80779,80780],{"encoding":238},"f''(1)=1",[212,80782,80784,80840],{"className":80783,"ariaHidden":243},[242],[212,80785,80787,80790,80822,80825,80828,80831,80834,80837],{"className":80786},[247],[212,80788],{"className":80789,"style":7041},[251],[212,80791,80793,80796],{"className":80792},[256],[212,80794,234],{"className":80795,"style":258},[256,257],[212,80797,80799],{"className":80798},[478],[212,80800,80802],{"className":80801},[482],[212,80803,80805],{"className":80804},[487],[212,80806,80808],{"className":80807,"style":7060},[491],[212,80809,80810,80813],{"style":7063},[212,80811],{"className":80812,"style":500},[499],[212,80814,80816],{"className":80815},[504,505,506,507],[212,80817,80819],{"className":80818},[256,507],[212,80820,21948],{"className":80821},[256,507],[212,80823,310],{"className":80824},[343],[212,80826,314],{"className":80827},[256],[212,80829,317],{"className":80830},[350],[212,80832],{"className":80833,"style":355},[354],[212,80835,320],{"className":80836},[359],[212,80838],{"className":80839,"style":355},[354],[212,80841,80843,80846],{"className":80842},[247],[212,80844],{"className":80845,"style":369},[251],[212,80847,314],{"className":80848},[256],"）即得 ",[212,80851,80853,80889],{"className":80852,"translate":216},[215],[212,80854,80856],{"className":80855},[220],[222,80857,80858],{"xmlns":224},[226,80859,80860,80886],{},[229,80861,80862,80872,80874,80880],{},[392,80863,80864,80866],{},[232,80865,396],{},[229,80867,80868,80870],{},[232,80869,10894],{},[232,80871,22093],{},[307,80873,33159],{},[435,80875,80876,80878],{},[312,80877,314],{},[312,80879,2661],{},[7012,80881,80882,80884],{},[232,80883,37649],{},[312,80885,2661],{},[236,80887,80888],{"encoding":238},"D_{KL}\\approx\\frac12\\chi^2",[212,80890,80892,80953],{"className":80891,"ariaHidden":243},[242],[212,80893,80895,80898,80944,80947,80950],{"className":80894},[247],[212,80896],{"className":80897,"style":16161},[251],[212,80899,80901,80904],{"className":80900},[256],[212,80902,396],{"className":80903,"style":474},[256,257],[212,80905,80907],{"className":80906},[478],[212,80908,80910,80936],{"className":80909},[482,483],[212,80911,80913,80933],{"className":80912},[487],[212,80914,80916],{"className":80915,"style":576},[491],[212,80917,80918,80921],{"style":495},[212,80919],{"className":80920,"style":500},[499],[212,80922,80924],{"className":80923},[504,505,506,507],[212,80925,80927,80930],{"className":80926},[256,507],[212,80928,10894],{"className":80929,"style":10982},[256,257,507],[212,80931,22093],{"className":80932},[256,257,507],[212,80934,515],{"className":80935},[514],[212,80937,80939],{"className":80938},[487],[212,80940,80942],{"className":80941,"style":8166},[491],[212,80943],{},[212,80945],{"className":80946,"style":355},[354],[212,80948,33159],{"className":80949},[359],[212,80951],{"className":80952,"style":355},[354],[212,80954,80956,80959,81027],{"className":80955},[247],[212,80957],{"className":80958,"style":2703},[251],[212,80960,80962,80965,81024],{"className":80961},[256],[212,80963],{"className":80964},[343,638],[212,80966,80968],{"className":80967},[435],[212,80969,80971,81016],{"className":80970},[482,483],[212,80972,80974,81013],{"className":80973},[487],[212,80975,80977,80991,80999],{"className":80976,"style":2722},[491],[212,80978,80979,80982],{"style":2725},[212,80980],{"className":80981,"style":658},[499],[212,80983,80985],{"className":80984},[504,505,506,507],[212,80986,80988],{"className":80987},[256,507],[212,80989,2661],{"className":80990},[256,507],[212,80992,80993,80996],{"style":670},[212,80994],{"className":80995,"style":658},[499],[212,80997],{"className":80998,"style":678},[677],[212,81000,81001,81004],{"style":2748},[212,81002],{"className":81003,"style":658},[499],[212,81005,81007],{"className":81006},[504,505,506,507],[212,81008,81010],{"className":81009},[256,507],[212,81011,314],{"className":81012},[256,507],[212,81014,515],{"className":81015},[514],[212,81017,81019],{"className":81018},[487],[212,81020,81022],{"className":81021,"style":2770},[491],[212,81023],{},[212,81025],{"className":81026},[350,638],[212,81028,81030,81033],{"className":81029},[256],[212,81031,37649],{"className":81032},[256,257],[212,81034,81036],{"className":81035},[478],[212,81037,81039],{"className":81038},[482],[212,81040,81042],{"className":81041},[487],[212,81043,81045],{"className":81044,"style":20228},[491],[212,81046,81047,81050],{"style":7063},[212,81048],{"className":81049,"style":500},[499],[212,81051,81053],{"className":81052},[504,505,506,507],[212,81054,2661],{"className":81055},[256,507],"；取 ",[212,81058,81060,81097],{"className":81059,"translate":216},[215],[212,81061,81063],{"className":81062},[220],[222,81064,81065],{"xmlns":224},[226,81066,81067,81095],{},[229,81068,81069,81071,81073,81075,81077,81079,81081,81085,81087,81089],{},[232,81070,234],{},[307,81072,310],{"stretchy":309},[232,81074,966],{},[307,81076,317],{"stretchy":309},[307,81078,320],{},[307,81080,310],{"stretchy":309},[34539,81082,81083],{},[232,81084,966],{},[307,81086,5011],{},[312,81088,314],{},[7012,81090,81091,81093],{},[307,81092,317],{"stretchy":309},[312,81094,2661],{},[236,81096,42830],{"encoding":238},[212,81098,81100,81127,81189],{"className":81099,"ariaHidden":243},[242],[212,81101,81103,81106,81109,81112,81115,81118,81121,81124],{"className":81102},[247],[212,81104],{"className":81105,"style":336},[251],[212,81107,234],{"className":81108,"style":258},[256,257],[212,81110,310],{"className":81111},[343],[212,81113,966],{"className":81114},[256,257],[212,81116,317],{"className":81117},[350],[212,81119],{"className":81120,"style":355},[354],[212,81122,320],{"className":81123},[359],[212,81125],{"className":81126,"style":355},[354],[212,81128,81130,81133,81136,81180,81183,81186],{"className":81129},[247],[212,81131],{"className":81132,"style":42867},[251],[212,81134,310],{"className":81135},[343],[212,81137,81139],{"className":81138},[256,34567],[212,81140,81142,81172],{"className":81141},[482,483],[212,81143,81145,81169],{"className":81144},[487],[212,81146,81148,81157],{"className":81147,"style":42883},[491],[212,81149,81151,81154],{"className":81150,"style":12063},[6505],[212,81152],{"className":81153,"style":658},[499],[212,81155,966],{"className":81156,"style":34587},[256,257],[212,81158,81159,81162],{"style":42895},[212,81160],{"className":81161,"style":658},[499],[212,81163,81165],{"className":81164,"style":34644},[34643],[6521,81166,81167],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,81168],{"d":34651},[212,81170,515],{"className":81171},[514],[212,81173,81175],{"className":81174},[487],[212,81176,81178],{"className":81177,"style":42915},[491],[212,81179],{},[212,81181],{"className":81182,"style":2785},[354],[212,81184,5011],{"className":81185},[2789],[212,81187],{"className":81188,"style":2785},[354],[212,81190,81192,81195,81198],{"className":81191},[247],[212,81193],{"className":81194,"style":20203},[251],[212,81196,314],{"className":81197},[256],[212,81199,81201,81204],{"className":81200},[350],[212,81202,317],{"className":81203},[350],[212,81205,81207],{"className":81206},[478],[212,81208,81210],{"className":81209},[482],[212,81211,81213],{"className":81212},[487],[212,81214,81216],{"className":81215,"style":20228},[491],[212,81217,81218,81221],{"style":7063},[212,81219],{"className":81220,"style":500},[499],[212,81222,81224],{"className":81223},[504,505,506,507],[212,81225,2661],{"className":81226},[256,507],[212,81228,81230,81266],{"className":81229,"translate":216},[215],[212,81231,81233],{"className":81232},[220],[222,81234,81235],{"xmlns":224},[226,81236,81237,81263],{},[229,81238,81239,81249,81251,81253,81255,81257],{},[7012,81240,81241,81243],{},[232,81242,234],{},[229,81244,81245,81247],{},[307,81246,7018],{"mathvariant":406},[307,81248,7018],{"mathvariant":406},[307,81250,310],{"stretchy":309},[312,81252,314],{},[307,81254,317],{"stretchy":309},[307,81256,320],{},[435,81258,81259,81261],{},[312,81260,314],{},[312,81262,2661],{},[236,81264,81265],{"encoding":238},"f''(1)=\\frac12",[212,81267,81269,81325],{"className":81268,"ariaHidden":243},[242],[212,81270,81272,81275,81307,81310,81313,81316,81319,81322],{"className":81271},[247],[212,81273],{"className":81274,"style":7041},[251],[212,81276,81278,81281],{"className":81277},[256],[212,81279,234],{"className":81280,"style":258},[256,257],[212,81282,81284],{"className":81283},[478],[212,81285,81287],{"className":81286},[482],[212,81288,81290],{"className":81289},[487],[212,81291,81293],{"className":81292,"style":7060},[491],[212,81294,81295,81298],{"style":7063},[212,81296],{"className":81297,"style":500},[499],[212,81299,81301],{"className":81300},[504,505,506,507],[212,81302,81304],{"className":81303},[256,507],[212,81305,21948],{"className":81306},[256,507],[212,81308,310],{"className":81309},[343],[212,81311,314],{"className":81312},[256],[212,81314,317],{"className":81315},[350],[212,81317],{"className":81318,"style":355},[354],[212,81320,320],{"className":81321},[359],[212,81323],{"className":81324,"style":355},[354],[212,81326,81328,81331],{"className":81327},[247],[212,81329],{"className":81330,"style":2703},[251],[212,81332,81334,81337,81396],{"className":81333},[256],[212,81335],{"className":81336},[343,638],[212,81338,81340],{"className":81339},[435],[212,81341,81343,81388],{"className":81342},[482,483],[212,81344,81346,81385],{"className":81345},[487],[212,81347,81349,81363,81371],{"className":81348,"style":2722},[491],[212,81350,81351,81354],{"style":2725},[212,81352],{"className":81353,"style":658},[499],[212,81355,81357],{"className":81356},[504,505,506,507],[212,81358,81360],{"className":81359},[256,507],[212,81361,2661],{"className":81362},[256,507],[212,81364,81365,81368],{"style":670},[212,81366],{"className":81367,"style":658},[499],[212,81369],{"className":81370,"style":678},[677],[212,81372,81373,81376],{"style":2748},[212,81374],{"className":81375,"style":658},[499],[212,81377,81379],{"className":81378},[504,505,506,507],[212,81380,81382],{"className":81381},[256,507],[212,81383,314],{"className":81384},[256,507],[212,81386,515],{"className":81387},[514],[212,81389,81391],{"className":81390},[487],[212,81392,81394],{"className":81393,"style":2770},[491],[212,81395],{},[212,81397],{"className":81398},[350,638],[212,81400,81402,81447],{"className":81401,"translate":216},[215],[212,81403,81405],{"className":81404},[220],[222,81406,81407],{"xmlns":224},[226,81408,81409,81445],{},[229,81410,81411,81413,81415,81419,81421,81425,81431,81433,81439],{},[307,81412,1485],{},[307,81414,310],{"stretchy":309},[34539,81416,81417],{},[232,81418,11],{},[307,81420,5011],{},[34539,81422,81423],{},[232,81424,1141],{},[7012,81426,81427,81429],{},[307,81428,317],{"stretchy":309},[312,81430,2661],{},[307,81432,33159],{},[435,81434,81435,81437],{},[312,81436,314],{},[312,81438,39189],{},[7012,81440,81441,81443],{},[232,81442,37649],{},[312,81444,2661],{},[236,81446,39198],{"encoding":238},[212,81448,81450,81515,81603],{"className":81449,"ariaHidden":243},[242],[212,81451,81453,81456,81459,81462,81506,81509,81512],{"className":81452},[247],[212,81454],{"className":81455,"style":39208},[251],[212,81457,1485],{"className":81458,"style":5815},[1682,1683,5814],[212,81460,310],{"className":81461},[343],[212,81463,81465],{"className":81464},[256,34567],[212,81466,81468,81498],{"className":81467},[482,483],[212,81469,81471,81495],{"className":81470},[487],[212,81472,81474,81483],{"className":81473,"style":39227},[491],[212,81475,81477,81480],{"className":81476,"style":12063},[6505],[212,81478],{"className":81479,"style":658},[499],[212,81481,11],{"className":81482,"style":34587},[256,257],[212,81484,81485,81488],{"style":39239},[212,81486],{"className":81487,"style":658},[499],[212,81489,81491],{"className":81490,"style":34644},[34643],[6521,81492,81493],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,81494],{"d":34651},[212,81496,515],{"className":81497},[514],[212,81499,81501],{"className":81500},[487],[212,81502,81504],{"className":81503,"style":39259},[491],[212,81505],{},[212,81507],{"className":81508,"style":2785},[354],[212,81510,5011],{"className":81511},[2789],[212,81513],{"className":81514,"style":2785},[354],[212,81516,81518,81521,81565,81594,81597,81600],{"className":81517},[247],[212,81519],{"className":81520,"style":39277},[251],[212,81522,81524],{"className":81523},[256,34567],[212,81525,81527,81557],{"className":81526},[482,483],[212,81528,81530,81554],{"className":81529},[487],[212,81531,81533,81542],{"className":81532,"style":39227},[491],[212,81534,81536,81539],{"className":81535,"style":12063},[6505],[212,81537],{"className":81538,"style":658},[499],[212,81540,1141],{"className":81541,"style":39299},[256,257],[212,81543,81544,81547],{"style":39239},[212,81545],{"className":81546,"style":658},[499],[212,81548,81550],{"className":81549,"style":34644},[34643],[6521,81551,81552],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,81553],{"d":34651},[212,81555,515],{"className":81556},[514],[212,81558,81560],{"className":81559},[487],[212,81561,81563],{"className":81562,"style":39259},[491],[212,81564],{},[212,81566,81568,81571],{"className":81567},[350],[212,81569,317],{"className":81570},[350],[212,81572,81574],{"className":81573},[478],[212,81575,81577],{"className":81576},[482],[212,81578,81580],{"className":81579},[487],[212,81581,81583],{"className":81582,"style":20228},[491],[212,81584,81585,81588],{"style":7063},[212,81586],{"className":81587,"style":500},[499],[212,81589,81591],{"className":81590},[504,505,506,507],[212,81592,2661],{"className":81593},[256,507],[212,81595],{"className":81596,"style":355},[354],[212,81598,33159],{"className":81599},[359],[212,81601],{"className":81602,"style":355},[354],[212,81604,81606,81609,81677],{"className":81605},[247],[212,81607],{"className":81608,"style":2703},[251],[212,81610,81612,81615,81674],{"className":81611},[256],[212,81613],{"className":81614},[343,638],[212,81616,81618],{"className":81617},[435],[212,81619,81621,81666],{"className":81620},[482,483],[212,81622,81624,81663],{"className":81623},[487],[212,81625,81627,81641,81649],{"className":81626,"style":2722},[491],[212,81628,81629,81632],{"style":2725},[212,81630],{"className":81631,"style":658},[499],[212,81633,81635],{"className":81634},[504,505,506,507],[212,81636,81638],{"className":81637},[256,507],[212,81639,39189],{"className":81640},[256,507],[212,81642,81643,81646],{"style":670},[212,81644],{"className":81645,"style":658},[499],[212,81647],{"className":81648,"style":678},[677],[212,81650,81651,81654],{"style":2748},[212,81652],{"className":81653,"style":658},[499],[212,81655,81657],{"className":81656},[504,505,506,507],[212,81658,81660],{"className":81659},[256,507],[212,81661,314],{"className":81662},[256,507],[212,81664,515],{"className":81665},[514],[212,81667,81669],{"className":81668},[487],[212,81670,81672],{"className":81671,"style":2770},[491],[212,81673],{},[212,81675],{"className":81676},[350,638],[212,81678,81680,81683],{"className":81679},[256],[212,81681,37649],{"className":81682},[256,257],[212,81684,81686],{"className":81685},[478],[212,81687,81689],{"className":81688},[482],[212,81690,81692],{"className":81691},[487],[212,81693,81695],{"className":81694,"style":20228},[491],[212,81696,81697,81700],{"style":7063},[212,81698],{"className":81699,"style":500},[499],[212,81701,81703],{"className":81702},[504,505,506,507],[212,81704,2661],{"className":81705},[256,507],"，除以 2 或换算成 ",[212,81708,81710,81730],{"className":81709,"translate":216},[215],[212,81711,81713],{"className":81712},[220],[222,81714,81715],{"xmlns":224},[226,81716,81717,81727],{},[229,81718,81719,81721,81723,81725],{},[312,81720,314],{},[307,81722,5011],{},[232,81724,39491],{},[232,81726,39494],{},[236,81728,81729],{"encoding":238},"1-BC",[212,81731,81733,81751],{"className":81732,"ariaHidden":243},[242],[212,81734,81736,81739,81742,81745,81748],{"className":81735},[247],[212,81737],{"className":81738,"style":12778},[251],[212,81740,314],{"className":81741},[256],[212,81743],{"className":81744,"style":2785},[354],[212,81746,5011],{"className":81747},[2789],[212,81749],{"className":81750,"style":2785},[354],[212,81752,81754,81757,81760],{"className":81753},[247],[212,81755],{"className":81756,"style":861},[251],[212,81758,39491],{"className":81759,"style":39587},[256,257],[212,81761,39494],{"className":81762,"style":10982},[256,257]," 就是 3.4 节引用的 Bhattacharyya 约定 ",[212,81765,81767,81799],{"className":81766,"translate":216},[215],[212,81768,81770],{"className":81769},[220],[222,81771,81772],{"xmlns":224},[226,81773,81774,81796],{},[229,81775,81776,81782,81784,81790],{},[7012,81777,81778,81780],{},[232,81779,34084],{},[312,81781,2661],{},[307,81783,33159],{},[435,81785,81786,81788],{},[312,81787,314],{},[312,81789,39503],{},[7012,81791,81792,81794],{},[232,81793,37649],{},[312,81795,2661],{},[236,81797,81798],{"encoding":238},"H^2\\approx\\frac18\\chi^2",[212,81800,81802,81846],{"className":81801,"ariaHidden":243},[242],[212,81803,81805,81808,81837,81840,81843],{"className":81804},[247],[212,81806],{"className":81807,"style":20228},[251],[212,81809,81811,81814],{"className":81810},[256],[212,81812,34084],{"className":81813,"style":34238},[256,257],[212,81815,81817],{"className":81816},[478],[212,81818,81820],{"className":81819},[482],[212,81821,81823],{"className":81822},[487],[212,81824,81826],{"className":81825,"style":20228},[491],[212,81827,81828,81831],{"style":7063},[212,81829],{"className":81830,"style":500},[499],[212,81832,81834],{"className":81833},[504,505,506,507],[212,81835,2661],{"className":81836},[256,507],[212,81838],{"className":81839,"style":355},[354],[212,81841,33159],{"className":81842},[359],[212,81844],{"className":81845,"style":355},[354],[212,81847,81849,81852,81920],{"className":81848},[247],[212,81850],{"className":81851,"style":2703},[251],[212,81853,81855,81858,81917],{"className":81854},[256],[212,81856],{"className":81857},[343,638],[212,81859,81861],{"className":81860},[435],[212,81862,81864,81909],{"className":81863},[482,483],[212,81865,81867,81906],{"className":81866},[487],[212,81868,81870,81884,81892],{"className":81869,"style":2722},[491],[212,81871,81872,81875],{"style":2725},[212,81873],{"className":81874,"style":658},[499],[212,81876,81878],{"className":81877},[504,505,506,507],[212,81879,81881],{"className":81880},[256,507],[212,81882,39503],{"className":81883},[256,507],[212,81885,81886,81889],{"style":670},[212,81887],{"className":81888,"style":658},[499],[212,81890],{"className":81891,"style":678},[677],[212,81893,81894,81897],{"style":2748},[212,81895],{"className":81896,"style":658},[499],[212,81898,81900],{"className":81899},[504,505,506,507],[212,81901,81903],{"className":81902},[256,507],[212,81904,314],{"className":81905},[256,507],[212,81907,515],{"className":81908},[514],[212,81910,81912],{"className":81911},[487],[212,81913,81915],{"className":81914,"style":2770},[491],[212,81916],{},[212,81918],{"className":81919},[350,638],[212,81921,81923,81926],{"className":81922},[256],[212,81924,37649],{"className":81925},[256,257],[212,81927,81929],{"className":81928},[478],[212,81930,81932],{"className":81931},[482],[212,81933,81935],{"className":81934},[487],[212,81936,81938],{"className":81937,"style":20228},[491],[212,81939,81940,81943],{"style":7063},[212,81941],{"className":81942,"style":500},[499],[212,81944,81946],{"className":81945},[504,505,506,507],[212,81947,2661],{"className":81948},[256,507],"。共同因子 ",[212,81951,81953,82005],{"className":81952,"translate":216},[215],[212,81954,81956],{"className":81955},[220],[222,81957,81958],{"xmlns":224},[226,81959,81960,82002],{},[229,81961,81962,81968,81970,81976,81978,81980,81982,81988,81990,81996,81998,82000],{},[7012,81963,81964,81966],{},[232,81965,38862],{},[312,81967,2661],{},[307,81969,1485],{},[7012,81971,81972,81974],{},[232,81973,38865],{},[312,81975,2661],{},[232,81977,441],{},[232,81979,403],{},[307,81981,320],{},[7012,81983,81984,81986],{},[232,81985,37649],{},[312,81987,2661],{},[307,81989,310],{"stretchy":309},[392,81991,81992,81994],{},[232,81993,410],{},[232,81995,38862],{},[232,81997,407],{"mathvariant":406},[232,81999,403],{},[307,82001,317],{"stretchy":309},[236,82003,82004],{"encoding":238},"\\varepsilon^2\\int h^2 dP=\\chi^2(Q_\\varepsilon\\|P)",[212,82006,82008,82096],{"className":82007,"ariaHidden":243},[242],[212,82009,82011,82014,82043,82046,82049,82052,82081,82084,82087,82090,82093],{"className":82010},[247],[212,82012],{"className":82013,"style":50527},[251],[212,82015,82017,82020],{"className":82016},[256],[212,82018,38862],{"className":82019},[256,257],[212,82021,82023],{"className":82022},[478],[212,82024,82026],{"className":82025},[482],[212,82027,82029],{"className":82028},[487],[212,82030,82032],{"className":82031,"style":20228},[491],[212,82033,82034,82037],{"style":7063},[212,82035],{"className":82036,"style":500},[499],[212,82038,82040],{"className":82039},[504,505,506,507],[212,82041,2661],{"className":82042},[256,507],[212,82044],{"className":82045,"style":603},[354],[212,82047,1485],{"className":82048,"style":5815},[1682,1683,5814],[212,82050],{"className":82051,"style":603},[354],[212,82053,82055,82058],{"className":82054},[256],[212,82056,38865],{"className":82057},[256,257],[212,82059,82061],{"className":82060},[478],[212,82062,82064],{"className":82063},[482],[212,82065,82067],{"className":82066},[487],[212,82068,82070],{"className":82069,"style":20228},[491],[212,82071,82072,82075],{"style":7063},[212,82073],{"className":82074,"style":500},[499],[212,82076,82078],{"className":82077},[504,505,506,507],[212,82079,2661],{"className":82080},[256,507],[212,82082,441],{"className":82083},[256,257],[212,82085,403],{"className":82086,"style":531},[256,257],[212,82088],{"className":82089,"style":355},[354],[212,82091,320],{"className":82092},[359],[212,82094],{"className":82095,"style":355},[354],[212,82097,82099,82102,82131,82134,82174,82177,82180],{"className":82098},[247],[212,82100],{"className":82101,"style":20203},[251],[212,82103,82105,82108],{"className":82104},[256],[212,82106,37649],{"className":82107},[256,257],[212,82109,82111],{"className":82110},[478],[212,82112,82114],{"className":82113},[482],[212,82115,82117],{"className":82116},[487],[212,82118,82120],{"className":82119,"style":20228},[491],[212,82121,82122,82125],{"style":7063},[212,82123],{"className":82124,"style":500},[499],[212,82126,82128],{"className":82127},[504,505,506,507],[212,82129,2661],{"className":82130},[256,507],[212,82132,310],{"className":82133},[343],[212,82135,82137,82140],{"className":82136},[256],[212,82138,410],{"className":82139},[256,257],[212,82141,82143],{"className":82142},[478],[212,82144,82146,82166],{"className":82145},[482,483],[212,82147,82149,82163],{"className":82148},[487],[212,82150,82152],{"className":82151,"style":45129},[491],[212,82153,82154,82157],{"style":579},[212,82155],{"className":82156,"style":500},[499],[212,82158,82160],{"className":82159},[504,505,506,507],[212,82161,38862],{"className":82162},[256,257,507],[212,82164,515],{"className":82165},[514],[212,82167,82169],{"className":82168},[487],[212,82170,82172],{"className":82171,"style":8166},[491],[212,82173],{},[212,82175,407],{"className":82176},[256],[212,82178,403],{"className":82179,"style":531},[256,257],[212,82181,317],{"className":82182},[350]," 就是",[1194,82185,82186],{},"Fisher 信息度量","：它给出统计流形上的黎曼度量，而 ",[212,82189,82191,82218],{"className":82190,"translate":216},[215],[212,82192,82194],{"className":82193},[220],[222,82195,82196],{"xmlns":224},[226,82197,82198,82216],{},[229,82199,82200,82210,82212,82214],{},[7012,82201,82202,82204],{},[232,82203,234],{},[229,82205,82206,82208],{},[307,82207,7018],{"mathvariant":406},[307,82209,7018],{"mathvariant":406},[307,82211,310],{"stretchy":309},[312,82213,314],{},[307,82215,317],{"stretchy":309},[236,82217,39734],{"encoding":238},[212,82219,82221],{"className":82220,"ariaHidden":243},[242],[212,82222,82224,82227,82259,82262,82265],{"className":82223},[247],[212,82225],{"className":82226,"style":7041},[251],[212,82228,82230,82233],{"className":82229},[256],[212,82231,234],{"className":82232,"style":258},[256,257],[212,82234,82236],{"className":82235},[478],[212,82237,82239],{"className":82238},[482],[212,82240,82242],{"className":82241},[487],[212,82243,82245],{"className":82244,"style":7060},[491],[212,82246,82247,82250],{"style":7063},[212,82248],{"className":82249,"style":500},[499],[212,82251,82253],{"className":82252},[504,505,506,507],[212,82254,82256],{"className":82255},[256,507],[212,82257,21948],{"className":82258},[256,507],[212,82260,310],{"className":82261},[343],[212,82263,314],{"className":82264},[256],[212,82266,317],{"className":82267},[350]," 只是「单位选择」。这也解释了为什么 GAN 中「选 JS 还是选 KL」在小偏差区几乎无差别，差别只在远离平衡或支撑不重叠时才显现。",[2509,82270,82272],{"id":82271},"_47-不等式网络","4.7 不等式网络",[24,82274,82275,82471,82977,83438],{},[11,82276,82277,79131,82280,82470],{},[1194,82278,82279],{},"命题 4.6（不等式网络）",[212,82281,82283,82321],{"className":82282,"translate":216},[215],[212,82284,82286],{"className":82285},[220],[222,82287,82288],{"xmlns":224},[226,82289,82290,82318],{},[229,82291,82292,82298,82300,82308,82310,82312,82314,82316],{},[7012,82293,82294,82296],{},[232,82295,34084],{},[312,82297,2661],{},[307,82299,320],{},[7751,82301,82302,82304,82306],{},[232,82303,34084],{},[1495,82305,42337],{},[312,82307,2661],{},[307,82309,320],{},[312,82311,314],{},[307,82313,5011],{},[232,82315,39491],{},[232,82317,39494],{},[236,82319,82320],{"encoding":238},"H^2=H^2_{\\text{Bhattacharyya}}=1-BC",[212,82322,82324,82368,82440,82458],{"className":82323,"ariaHidden":243},[242],[212,82325,82327,82330,82359,82362,82365],{"className":82326},[247],[212,82328],{"className":82329,"style":20228},[251],[212,82331,82333,82336],{"className":82332},[256],[212,82334,34084],{"className":82335,"style":34238},[256,257],[212,82337,82339],{"className":82338},[478],[212,82340,82342],{"className":82341},[482],[212,82343,82345],{"className":82344},[487],[212,82346,82348],{"className":82347,"style":20228},[491],[212,82349,82350,82353],{"style":7063},[212,82351],{"className":82352,"style":500},[499],[212,82354,82356],{"className":82355},[504,505,506,507],[212,82357,2661],{"className":82358},[256,507],[212,82360],{"className":82361,"style":355},[354],[212,82363,320],{"className":82364},[359],[212,82366],{"className":82367,"style":355},[354],[212,82369,82371,82374,82431,82434,82437],{"className":82370},[247],[212,82372],{"className":82373,"style":43085},[251],[212,82375,82377,82380],{"className":82376},[256],[212,82378,34084],{"className":82379,"style":34238},[256,257],[212,82381,82383],{"className":82382},[478],[212,82384,82386,82423],{"className":82385},[482,483],[212,82387,82389,82420],{"className":82388},[487],[212,82390,82392,82409],{"className":82391,"style":20228},[491],[212,82393,82394,82397],{"style":43109},[212,82395],{"className":82396,"style":500},[499],[212,82398,82400],{"className":82399},[504,505,506,507],[212,82401,82403],{"className":82402},[256,507],[212,82404,82406],{"className":82405},[256,4796,507],[212,82407,42337],{"className":82408},[256,507],[212,82410,82411,82414],{"style":7063},[212,82412],{"className":82413,"style":500},[499],[212,82415,82417],{"className":82416},[504,505,506,507],[212,82418,2661],{"className":82419},[256,507],[212,82421,515],{"className":82422},[514],[212,82424,82426],{"className":82425},[487],[212,82427,82429],{"className":82428,"style":43145},[491],[212,82430],{},[212,82432],{"className":82433,"style":355},[354],[212,82435,320],{"className":82436},[359],[212,82438],{"className":82439,"style":355},[354],[212,82441,82443,82446,82449,82452,82455],{"className":82442},[247],[212,82444],{"className":82445,"style":12778},[251],[212,82447,314],{"className":82448},[256],[212,82450],{"className":82451,"style":2785},[354],[212,82453,5011],{"className":82454},[2789],[212,82456],{"className":82457,"style":2785},[354],[212,82459,82461,82464,82467],{"className":82460},[247],[212,82462],{"className":82463,"style":861},[251],[212,82465,39491],{"className":82466,"style":39587},[256,257],[212,82468,39494],{"className":82469,"style":10982},[256,257],"，则对概率测度有",[212,82472,82474],{"className":82473,"translate":216},[377],[212,82475,82477,82598],{"className":82476,"translate":216},[215],[212,82478,82480],{"className":82479},[220],[222,82481,82482],{"xmlns":224,"display":386},[226,82483,82484,82595],{},[1441,82485,82486,82521],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,82487,82488,82494],{},[1450,82489,82490],{},[1453,82491,82492],{"scriptlevel":323,"displaystyle":243},[229,82493],{},[1450,82495,82496],{},[1453,82497,82498],{"scriptlevel":323,"displaystyle":243},[229,82499,82500,82502],{},[229,82501],{},[229,82503,82504,82506,82508,82511,82513,82515,82517,82519],{},[232,82505,403],{"mathvariant":406},[232,82507,12163],{"mathvariant":406},[232,82509,82510],{"mathvariant":406},"n",[232,82512,7759],{"mathvariant":406},[232,82514,7762],{"mathvariant":406},[232,82516,7765],{"mathvariant":406},[232,82518,16650],{"mathvariant":406},[307,82520,1214],{},[1447,82522,82523,82529],{},[1450,82524,82525],{},[1453,82526,82527],{"scriptlevel":323,"displaystyle":243},[229,82528],{},[1450,82530,82531],{},[1453,82532,82533],{"scriptlevel":323,"displaystyle":243},[229,82534,82535,82537,82539,82549,82551,82553,82555,82557,82559,82561,82593],{},[229,82536],{},[354,82538],{"width":3460},[392,82540,82541,82543],{},[232,82542,396],{},[229,82544,82545,82547],{},[232,82546,5590],{},[232,82548,35050],{},[307,82550,310],{"stretchy":309},[232,82552,403],{},[307,82554,748],{"separator":243},[232,82556,410],{},[307,82558,317],{"stretchy":309},[307,82560,10150],{},[34539,82562,82563],{},[229,82564,82565,82573,82583,82585,82587,82589,82591],{},[1453,82566,82567],{"scriptlevel":323,"displaystyle":309},[435,82568,82569,82571],{},[312,82570,314],{},[312,82572,2661],{},[392,82574,82575,82577],{},[232,82576,396],{},[229,82578,82579,82581],{},[232,82580,10894],{},[232,82582,22093],{},[307,82584,310],{"stretchy":309},[232,82586,403],{},[232,82588,407],{"mathvariant":406},[232,82590,410],{},[307,82592,317],{"stretchy":309},[307,82594,748],{"separator":243},[236,82596,82597],{"encoding":238},"\\begin{aligned}\n&\\mathrm{Pinsker:}\\\\\n&\\qquad D_{TV}(P,Q)\\le\n\\sqrt{\\tfrac12 D_{KL}(P\\|Q)},\n\\end{aligned}",[212,82599,82601],{"className":82600,"ariaHidden":243},[242],[212,82602,82604,82608],{"className":82603},[247],[212,82605],{"className":82606,"style":82607},[251],"height:3.34em;vertical-align:-1.42em;",[212,82609,82611],{"className":82610},[256],[212,82612,82614,82658],{"className":82613},[1441],[212,82615,82617],{"className":82616},[1558],[212,82618,82620,82649],{"className":82619},[482,483],[212,82621,82623,82646],{"className":82622},[487],[212,82624,82627,82637],{"className":82625,"style":82626},[491],"height:1.92em;",[212,82628,82630,82634],{"style":82629},"top:-4.3639em;",[212,82631],{"className":82632,"style":82633},[499],"height:3.2839em;",[212,82635],{"className":82636},[256],[212,82638,82640,82643],{"style":82639},"top:-2.42em;",[212,82641],{"className":82642,"style":82633},[499],[212,82644],{"className":82645},[256],[212,82647,515],{"className":82648},[514],[212,82650,82652],{"className":82651},[487],[212,82653,82656],{"className":82654,"style":82655},[491],"height:1.42em;",[212,82657],{},[212,82659,82661],{"className":82660},[1649],[212,82662,82664,82969],{"className":82663},[482,483],[212,82665,82667,82966],{"className":82666},[487],[212,82668,82670,82694],{"className":82669,"style":82626},[491],[212,82671,82672,82675],{"style":82629},[212,82673],{"className":82674,"style":82633},[499],[212,82676,82678,82681],{"className":82677},[256],[212,82679],{"className":82680},[256],[212,82682,82684,82688,82691],{"className":82683},[256],[212,82685,82687],{"className":82686},[256,32862],"Pinsker",[212,82689],{"className":82690,"style":355},[354],[212,82692,1214],{"className":82693},[359],[212,82695,82696,82699],{"style":82639},[212,82697],{"className":82698,"style":82633},[499],[212,82700,82702,82705,82708,82754,82757,82760,82763,82766,82769,82772,82775,82778,82781,82963],{"className":82701},[256],[212,82703],{"className":82704},[256],[212,82706],{"className":82707,"style":3832},[354],[212,82709,82711,82714],{"className":82710},[256],[212,82712,396],{"className":82713,"style":474},[256,257],[212,82715,82717],{"className":82716},[478],[212,82718,82720,82746],{"className":82719},[482,483],[212,82721,82723,82743],{"className":82722},[487],[212,82724,82726],{"className":82725,"style":576},[491],[212,82727,82728,82731],{"style":495},[212,82729],{"className":82730,"style":500},[499],[212,82732,82734],{"className":82733},[504,505,506,507],[212,82735,82737,82740],{"className":82736},[256,507],[212,82738,5590],{"className":82739,"style":531},[256,257,507],[212,82741,35050],{"className":82742,"style":2785},[256,257,507],[212,82744,515],{"className":82745},[514],[212,82747,82749],{"className":82748},[487],[212,82750,82752],{"className":82751,"style":8166},[491],[212,82753],{},[212,82755,310],{"className":82756},[343],[212,82758,403],{"className":82759,"style":531},[256,257],[212,82761,748],{"className":82762},[770],[212,82764],{"className":82765,"style":603},[354],[212,82767,410],{"className":82768},[256,257],[212,82770,317],{"className":82771},[350],[212,82773],{"className":82774,"style":355},[354],[212,82776,10150],{"className":82777},[359],[212,82779],{"className":82780,"style":355},[354],[212,82782,82784],{"className":82783},[256,34567],[212,82785,82787,82954],{"className":82786},[482,483],[212,82788,82790,82951],{"className":82789},[487],[212,82791,82794,82934],{"className":82792,"style":82793},[491],"height:1.2839em;",[212,82795,82798,82802],{"className":82796,"style":82797},[6505],"top:-3.8em;",[212,82799],{"className":82800,"style":82801},[499],"height:3.8em;",[212,82803,82805,82873,82919,82922,82925,82928,82931],{"className":82804,"style":41361},[256],[212,82806,82808,82811,82870],{"className":82807},[256],[212,82809],{"className":82810},[343,638],[212,82812,82814],{"className":82813},[435],[212,82815,82817,82862],{"className":82816},[482,483],[212,82818,82820,82859],{"className":82819},[487],[212,82821,82823,82837,82845],{"className":82822,"style":2722},[491],[212,82824,82825,82828],{"style":2725},[212,82826],{"className":82827,"style":658},[499],[212,82829,82831],{"className":82830},[504,505,506,507],[212,82832,82834],{"className":82833},[256,507],[212,82835,2661],{"className":82836},[256,507],[212,82838,82839,82842],{"style":670},[212,82840],{"className":82841,"style":658},[499],[212,82843],{"className":82844,"style":678},[677],[212,82846,82847,82850],{"style":2748},[212,82848],{"className":82849,"style":658},[499],[212,82851,82853],{"className":82852},[504,505,506,507],[212,82854,82856],{"className":82855},[256,507],[212,82857,314],{"className":82858},[256,507],[212,82860,515],{"className":82861},[514],[212,82863,82865],{"className":82864},[487],[212,82866,82868],{"className":82867,"style":2770},[491],[212,82869],{},[212,82871],{"className":82872},[350,638],[212,82874,82876,82879],{"className":82875},[256],[212,82877,396],{"className":82878,"style":474},[256,257],[212,82880,82882],{"className":82881},[478],[212,82883,82885,82911],{"className":82884},[482,483],[212,82886,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\\ge\\ \nD_{KL}\\big(\\mathrm{Bern}(\\alpha)\\,\\|\\,\n\\mathrm{Bern}(\\beta)\\big),\n\\qquad \\alpha=P(A),\\ 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2 步（二元问题的精确最小值）。"," 固定差 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TV 值），对 ",[212,84747,84749,84762],{"className":84748,"translate":216},[215],[212,84750,84752],{"className":84751},[220],[222,84753,84754],{"xmlns":224},[226,84755,84756,84760],{},[229,84757,84758],{},[232,84759,44954],{},[236,84761,49289],{"encoding":238},[212,84763,84765],{"className":84764,"ariaHidden":243},[242],[212,84766,84768,84771],{"className":84767},[247],[212,84769],{"className":84770,"style":2543},[251],[212,84772,44954],{"className":84773,"style":44984},[256,257]," 最小化二元 KL。取对称中心 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",[212,85042,85044,85066],{"className":85043,"translate":216},[215],[212,85045,85047],{"className":85046},[220],[222,85048,85049],{"xmlns":224},[226,85050,85051,85063],{},[229,85052,85053,85055,85057,85059,85061],{},[312,85054,314],{},[307,85056,5011],{},[232,85058,44954],{},[307,85060,320],{},[232,85062,84331],{},[236,85064,85065],{"encoding":238},"1-\\alpha=\\beta",[212,85067,85069,85087,85105],{"className":85068,"ariaHidden":243},[242],[212,85070,85072,85075,85078,85081,85084],{"className":85071},[247],[212,85073],{"className":85074,"style":12778},[251],[212,85076,314],{"className":85077},[256],[212,85079],{"className":85080,"style":2785},[354],[212,85082,5011],{"className":85083},[2789],[212,85085],{"className":85086,"style":2785},[354],[212,85088,85090,85093,85096,85099,85102],{"className":85089},[247],[212,85091],{"className":85092,"style":2543},[251],[212,85094,44954],{"className":85095,"style":44984},[256,257],[212,85097],{"className":85098,"style":355},[354],[212,85100,320],{"className":85101},[359],[212,85103],{"className":85104,"style":355},[354],[212,85106,85108,85111],{"className":85107},[247],[212,85109],{"className":85110,"style":252},[251],[212,85112,84331],{"className":85113,"style":84553},[256,257],[212,85115,85117,85139],{"className":85116,"translate":216},[215],[212,85118,85120],{"className":85119},[220],[222,85121,85122],{"xmlns":224},[226,85123,85124,85136],{},[229,85125,85126,85128,85130,85132,85134],{},[312,85127,314],{},[307,85129,5011],{},[232,85131,84331],{},[307,85133,320],{},[232,85135,44954],{},[236,85137,85138],{"encoding":238},"1-\\beta=\\alpha",[212,85140,85142,85160,85178],{"className":85141,"ariaHidden":243},[242],[212,85143,85145,85148,85151,85154,85157],{"className":85144},[247],[212,85146],{"className":85147,"style":12778},[251],[212,85149,314],{"className":85150},[256],[212,85152],{"className":85153,"style":2785},[354],[212,85155,5011],{"className":85156},[2789],[212,85158],{"className":85159,"style":2785},[354],[212,85161,85163,85166,85169,85172,85175],{"className":85162},[247],[212,85164],{"className":85165,"style":252},[251],[212,85167,84331],{"className":85168,"style":84553},[256,257],[212,85170],{"className":85171,"style":355},[354],[212,85173,320],{"className":85174},[359],[212,85176],{"className":85177,"style":355},[354],[212,85179,85181,85184],{"className":85180},[247],[212,85182],{"className":85183,"style":2543},[251],[212,85185,44954],{"className":85186,"style":44984},[256,257],"，算得",[212,85189,85191],{"className":85190,"translate":216},[377],[212,85192,85194,85450],{"className":85193,"translate":216},[215],[212,85195,85197],{"className":85196},[220],[222,85198,85199],{"xmlns":224,"display":386},[226,85200,85201,85447],{},[1441,85202,85203,85261,85311,85385],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,85204,85205,85211],{},[1450,85206,85207],{},[1453,85208,85209],{"scriptlevel":323,"displaystyle":243},[229,85210],{},[1450,85212,85213],{},[1453,85214,85215],{"scriptlevel":323,"displaystyle":243},[229,85216,85217,85219,85229,85231,85241,85243,85257,85259],{},[229,85218],{},[392,85220,85221,85223],{},[232,85222,396],{},[229,85224,85225,85227],{},[232,85226,10894],{},[232,85228,22093],{},[307,85230,310],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[229,85232,85233,85235,85237,85239],{},[232,85234,39491],{"mathvariant":406},[232,85236,7765],{"mathvariant":406},[232,85238,16650],{"mathvariant":406},[232,85240,82510],{"mathvariant":406},[307,85242,310],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[1453,85244,85245],{"scriptlevel":323,"displaystyle":309},[435,85246,85247,85255],{},[229,85248,85249,85251,85253],{},[312,85250,314],{},[307,85252,2668],{},[232,85254,15912],{},[312,85256,2661],{},[307,85258,317],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[307,85260,317],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[1447,85262,85263,85269],{},[1450,85264,85265],{},[1453,85266,85267],{"scriptlevel":323,"displaystyle":243},[229,85268],{},[1450,85270,85271],{},[1453,85272,85273],{"scriptlevel":323,"displaystyle":243},[229,85274,85275,85277,85279,85281,85291,85293,85307,85309],{},[229,85276],{},[354,85278],{"width":3460},[307,85280,407],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[229,85282,85283,85285,85287,85289],{},[232,85284,39491],{"mathvariant":406},[232,85286,7765],{"mathvariant":406},[232,85288,16650],{"mathvariant":406},[232,85290,82510],{"mathvariant":406},[307,85292,310],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[1453,85294,85295],{"scriptlevel":323,"displaystyle":309},[435,85296,85297,85305],{},[229,85298,85299,85301,85303],{},[312,85300,314],{},[307,85302,5011],{},[232,85304,15912],{},[312,85306,2661],{},[307,85308,317],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[307,85310,317],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[1447,85312,85313,85319],{},[1450,85314,85315],{},[1453,85316,85317],{"scriptlevel":323,"displaystyle":243},[229,85318],{},[1450,85320,85321],{},[1453,85322,85323],{"scriptlevel":323,"displaystyle":243},[229,85324,85325,85327,85329,85331,85333,85335,85343,85345,85347,85349,85351,85359,85361,85363,85365,85367,85369,85371,85373,85375,85377],{},[229,85326],{},[307,85328,320],{},[232,85330,44954],{},[232,85332,4298],{},[307,85334,4301],{},[1453,85336,85337],{"scriptlevel":323,"displaystyle":309},[435,85338,85339,85341],{},[232,85340,44954],{},[232,85342,84331],{},[307,85344,2668],{},[232,85346,84331],{},[232,85348,4298],{},[307,85350,4301],{},[1453,85352,85353],{"scriptlevel":323,"displaystyle":309},[435,85354,85355,85357],{},[232,85356,84331],{},[232,85358,44954],{},[307,85360,320],{},[307,85362,310],{"stretchy":309},[232,85364,44954],{},[307,85366,5011],{},[232,85368,84331],{},[307,85370,317],{"stretchy":309},[1495,85372,1497],{},[232,85374,4298],{},[307,85376,4301],{},[1453,85378,85379],{"scriptlevel":323,"displaystyle":309},[435,85380,85381,85383],{},[232,85382,44954],{},[232,85384,84331],{},[1447,85386,85387,85393],{},[1450,85388,85389],{},[1453,85390,85391],{"scriptlevel":323,"displaystyle":243},[229,85392],{},[1450,85394,85395],{},[1453,85396,85397],{"scriptlevel":323,"displaystyle":243},[229,85398,85399,85401,85403,85405,85407,85409,85411,85431,85433,85435,85437,85439,85441,85443,85445],{},[229,85400],{},[307,85402,320],{},[232,85404,15912],{},[1495,85406,1497],{},[232,85408,4298],{},[307,85410,4301],{},[1453,85412,85413],{"scriptlevel":323,"displaystyle":309},[435,85414,85415,85423],{},[229,85416,85417,85419,85421],{},[312,85418,314],{},[307,85420,2668],{},[232,85422,15912],{},[229,85424,85425,85427,85429],{},[312,85426,314],{},[307,85428,5011],{},[232,85430,15912],{},[307,85432,320],{},[307,85434,1214],{},[1495,85436,1497],{},[232,85438,38865],{},[307,85440,310],{"stretchy":309},[232,85442,15912],{},[307,85444,317],{"stretchy":309},[232,85446,4573],{"mathvariant":406},[236,85448,85449],{"encoding":238},"\\begin{aligned}\n&D_{KL}\\Big(\\mathrm{Bern}\n\\Big(\\tfrac{1+\\delta}2\\Big)\\Big)\\\\\n&\\qquad\\Big\\|\\mathrm{Bern}\n\\Big(\\tfrac{1-\\delta}2\\Big)\\Big)\\\\\n&=\\alpha\\log\\tfrac{\\alpha}{\\beta}\n+\\beta\\log\\tfrac{\\beta}{\\alpha}\n=(\\alpha-\\beta)\\,\\log\\tfrac{\\alpha}{\\beta}\\\\\n&=\\delta\\,\\log\\tfrac{1+\\delta}{1-\\delta}\n=:\\,h(\\delta).\n\\end{aligned}",[212,85451,85453],{"className":85452,"ariaHidden":243},[242],[212,85454,85456,85460],{"className":85455},[247],[212,85457],{"className":85458,"style":85459},[251],"height:7.1968em;vertical-align:-3.3484em;",[212,85461,85463],{"className":85462},[256],[212,85464,85466,85527],{"className":85465},[1441],[212,85467,85469],{"className":85468},[1558],[212,85470,85472,85518],{"className":85471},[482,483],[212,85473,85475,85515],{"className":85474},[487],[212,85476,85479,85488,85497,85506],{"className":85477,"style":85478},[491],"height:3.8484em;",[212,85480,85482,85485],{"style":85481},"top:-5.8484em;",[212,85483],{"className":85484,"style":17788},[499],[212,85486],{"className":85487},[256],[212,85489,85491,85494],{"style":85490},"top:-3.7484em;",[212,85492],{"className":85493,"style":17788},[499],[212,85495],{"className":85496},[256],[212,85498,85500,85503],{"style":85499},"top:-1.8661em;",[212,85501],{"className":85502,"style":17788},[499],[212,85504],{"className":85505},[256],[212,85507,85509,85512],{"style":85508},"top:-0.2049em;",[212,85510],{"className":85511,"style":17788},[499],[212,85513],{"className":85514},[256],[212,85516,515],{"className":85517},[514],[212,85519,85521],{"className":85520},[487],[212,85522,85525],{"className":85523,"style":85524},[491],"height:3.3484em;",[212,85526],{},[212,85528,85530],{"className":85529},[1649],[212,85531,85533,86307],{"className":85532},[482,483],[212,85534,85536,86304],{"className":85535},[487],[212,85537,85539,85700,85854,86160],{"className":85538,"style":85478},[491],[212,85540,85541,85544],{"style":85481},[212,85542],{"className":85543,"style":17788},[499],[212,85545,85547,85550,85596,85602,85608,85614,85688,85694],{"className":85546},[256],[212,85548],{"className":85549},[256],[212,85551,85553,85556],{"className":85552},[256],[212,85554,396],{"className":85555,"style":474},[256,257],[212,85557,85559],{"className":85558},[478],[212,85560,85562,85588],{"className":85561},[482,483],[212,85563,85565,85585],{"className":85564},[487],[212,85566,85568],{"className":85567,"style":576},[491],[212,85569,85570,85573],{"style":495},[212,85571],{"className":85572,"style":500},[499],[212,85574,85576],{"className":85575},[504,505,506,507],[212,85577,85579,85582],{"className":85578},[256,507],[212,85580,10894],{"className":85581,"style":10982},[256,257,507],[212,85583,22093],{"className":85584},[256,257,507],[212,85586,515],{"className":85587},[514],[212,85589,85591],{"className":85590},[487],[212,85592,85594],{"className":85593,"style":8166},[491],[212,85595],{},[212,85597,85599],{"className":85598},[256],[212,85600,310],{"className":85601},[616,3918],[212,85603,85605],{"className":85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时不平衡质量挤出 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时值为 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",[212,86685,86687,86714],{"className":86686,"translate":216},[215],[212,86688,86690],{"className":86689},[220],[222,86691,86692],{"xmlns":224},[226,86693,86694,86712],{},[229,86695,86696,86698,86700],{},[232,86697,44954],{},[307,86699,320],{},[435,86701,86702,86710],{},[229,86703,86704,86706,86708],{},[312,86705,314],{},[307,86707,2668],{},[232,86709,15912],{},[312,86711,2661],{},[236,86713,84805],{"encoding":238},[212,86715,86717,86735],{"className":86716,"ariaHidden":243},[242],[212,86718,86720,86723,86726,86729,86732],{"className":86719},[247],[212,86721],{"className":86722,"style":2543},[251],[212,86724,44954],{"className":86725,"style":44984},[256,257],[212,86727],{"className":86728,"style":355},[354],[212,86730,320],{"className":86731},[359],[212,86733],{"className":86734,"style":355},[354],[212,86736,86738,86741],{"className":86737},[247],[212,86739],{"className":86740,"style":84833},[251],[212,86742,86744,86747,86812],{"className":86743},[256],[212,86745],{"className":86746},[343,638],[212,86748,86750],{"className":86749},[435],[212,86751,86753,86804],{"className":86752},[482,483],[212,86754,86756,86801],{"className":86755},[487],[212,86757,86759,86773,86781],{"className":86758,"style":2885},[491],[212,86760,86761,86764],{"style":2725},[212,86762],{"className":86763,"style":658},[499],[212,86765,86767],{"className":86766},[504,505,506,507],[212,86768,86770],{"className":86769},[256,507],[212,86771,2661],{"className":86772},[256,507],[212,86774,86775,86778],{"style":670},[212,86776],{"className":86777,"style":658},[499],[212,86779],{"className":86780,"style":678},[677],[212,86782,86783,86786],{"style":2748},[212,86784],{"className":86785,"style":658},[499],[212,86787,86789],{"className":86788},[504,505,506,507],[212,86790,86792,86795,86798],{"className":86791},[256,507],[212,86793,314],{"className":86794},[256,507],[212,86796,2668],{"className":86797},[2789,507],[212,86799,15912],{"className":86800,"style":15961},[256,257,507],[212,86802,515],{"className":86803},[514],[212,86805,86807],{"className":86806},[487],[212,86808,86810],{"className":86809,"style":2770},[491],[212,86811],{},[212,86813],{"className":86814},[350,638],"，且是",[1194,86817,86818],{},"精确最小值","（Vajda 界）：",[212,86821,86823,86879],{"className":86822,"translate":216},[215],[212,86824,86826],{"className":86825},[220],[222,86827,86828],{"xmlns":224},[226,86829,86830,86876],{},[229,86831,86832,86842,86844,86846,86848,86850,86852,86854,86856,86858,86864,86866,86868,86870,86872,86874],{},[392,86833,86834,86836],{},[232,86835,396],{},[229,86837,86838,86840],{},[232,86839,10894],{},[232,86841,22093],{},[307,86843,310],{"stretchy":309},[232,86845,403],{},[232,86847,407],{"mathvariant":406},[232,86849,410],{},[307,86851,317],{"stretchy":309},[307,86853,7126],{},[232,86855,38865],{},[307,86857,310],{"stretchy":309},[229,86859,86860,86862],{},[232,86861,5590],{"mathvariant":406},[232,86863,35050],{"mathvariant":406},[307,86865,310],{"stretchy":309},[232,86867,403],{},[307,86869,748],{"separator":243},[232,86871,410],{},[307,86873,317],{"stretchy":309},[307,86875,317],{"stretchy":309},[236,86877,86878],{"encoding":238},"D_{KL}(P\\|Q)\\ge h(\\mathrm{TV}(P,Q))",[212,86880,86882,86958],{"className":86881,"ariaHidden":243},[242],[212,86883,86885,86888,86934,86937,86940,86943,86946,86949,86952,86955],{"className":86884},[247],[212,86886],{"className":86887,"style":336},[251],[212,86889,86891,86894],{"className":86890},[256],[212,86892,396],{"className":86893,"style":474},[256,257],[212,86895,86897],{"className":86896},[478],[212,86898,86900,86926],{"className":86899},[482,483],[212,86901,86903,86923],{"className":86902},[487],[212,86904,86906],{"className":86905,"style":576},[491],[212,86907,86908,86911],{"style":495},[212,86909],{"className":86910,"style":500},[499],[212,86912,86914],{"className":86913},[504,505,506,507],[212,86915,86917,86920],{"className":86916},[256,507],[212,86918,10894],{"className":86919,"style":10982},[256,257,507],[212,86921,22093],{"className":86922},[256,257,507],[212,86924,515],{"className":86925},[514],[212,86927,86929],{"className":86928},[487],[212,86930,86932],{"className":86931,"style":8166},[491],[212,86933],{},[212,86935,310],{"className":86936},[343],[212,86938,403],{"className":86939,"style":531},[256,257],[212,86941,407],{"className":86942},[256],[212,86944,410],{"className":86945},[256,257],[212,86947,317],{"className":86948},[350],[212,86950],{"className":86951,"style":355},[354],[212,86953,7126],{"className":86954},[359],[212,86956],{"className":86957,"style":355},[354],[212,86959,86961,86964,86967,86970,86977,86980,86983,86986,86989,86992],{"className":86960},[247],[212,86962],{"className":86963,"style":336},[251],[212,86965,38865],{"className":86966},[256,257],[212,86968,310],{"className":86969},[343],[212,86971,86973],{"className":86972},[256],[212,86974,86976],{"className":86975,"style":4355},[256,32862],"TV",[212,86978,310],{"className":86979},[343],[212,86981,403],{"className":86982,"style":531},[256,257],[212,86984,748],{"className":86985},[770],[212,86987],{"className":86988,"style":603},[354],[212,86990,410],{"className":86991},[256,257],[212,86993,19247],{"className":86994},[350],"，其中 ",[212,86997,86999,87045],{"className":86998,"translate":216},[215],[212,87000,87002],{"className":87001},[220],[222,87003,87004],{"xmlns":224},[226,87005,87006,87042],{},[229,87007,87008,87010,87012,87014,87016,87018,87020,87022,87024],{},[232,87009,38865],{},[307,87011,310],{"stretchy":309},[232,87013,15912],{},[307,87015,317],{"stretchy":309},[307,87017,320],{},[232,87019,15912],{},[232,87021,4298],{},[307,87023,4301],{},[435,87025,87026,87034],{},[229,87027,87028,87030,87032],{},[312,87029,314],{},[307,87031,2668],{},[232,87033,15912],{},[229,87035,87036,87038,87040],{},[312,87037,314],{},[307,87039,5011],{},[232,87041,15912],{},[236,87043,87044],{"encoding":238},"h(\\delta)=\\delta\\log\\frac{1+\\delta}{1-\\delta}",[212,87046,87048,87075],{"className":87047,"ariaHidden":243},[242],[212,87049,87051,87054,87057,87060,87063,87066,87069,87072],{"className":87050},[247],[212,87052],{"className":87053,"style":336},[251],[212,87055,38865],{"className":87056},[256,257],[212,87058,310],{"className":87059},[343],[212,87061,15912],{"className":87062,"style":15961},[256,257],[212,87064,317],{"className":87065},[350],[212,87067],{"className":87068,"style":355},[354],[212,87070,320],{"className":87071},[359],[212,87073],{"className":87074,"style":355},[354],[212,87076,87078,87081,87084,87087,87092,87095],{"className":87077},[247],[212,87079],{"className":87080,"style":16553},[251],[212,87082,15912],{"className":87083,"style":15961},[256,257],[212,87085],{"className":87086,"style":603},[354],[212,87088,4352,87090],{"className":87089},[1682],[212,87091,4356],{"style":4355},[212,87093],{"className":87094,"style":603},[354],[212,87096,87098,87101,87172],{"className":87097},[256],[212,87099],{"className":87100},[343,638],[212,87102,87104],{"className":87103},[435],[212,87105,87107,87164],{"className":87106},[482,483],[212,87108,87110,87161],{"className":87109},[487],[212,87111,87113,87133,87141],{"className":87112,"style":2885},[491],[212,87114,87115,87118],{"style":2725},[212,87116],{"className":87117,"style":658},[499],[212,87119,87121],{"className":87120},[504,505,506,507],[212,87122,87124,87127,87130],{"className":87123},[256,507],[212,87125,314],{"className":87126},[256,507],[212,87128,5011],{"className":87129},[2789,507],[212,87131,15912],{"className":87132,"style":15961},[256,257,507],[212,87134,87135,87138],{"style":670},[212,87136],{"className":87137,"style":658},[499],[212,87139],{"className":87140,"style":678},[677],[212,87142,87143,87146],{"style":2748},[212,87144],{"className":87145,"style":658},[499],[212,87147,87149],{"className":87148},[504,505,506,507],[212,87150,87152,87155,87158],{"className":87151},[256,507],[212,87153,314],{"className":87154},[256,507],[212,87156,2668],{"className":87157},[2789,507],[212,87159,15912],{"className":87160,"style":15961},[256,257,507],[212,87162,515],{"className":87163},[514],[212,87165,87167],{"className":87166},[487],[212,87168,87170],{"className":87169,"style":16629},[491],[212,87171],{},[212,87173],{"className":87174},[350,638],[212,87176,87178,87196],{"className":87177,"translate":216},[215],[212,87179,87181],{"className":87180},[220],[222,87182,87183],{"xmlns":224},[226,87184,87185,87193],{},[229,87186,87187,87189,87191],{},[232,87188,15912],{},[307,87190,1228],{},[312,87192,314],{},[236,87194,87195],{"encoding":238},"\\delta\\to1",[212,87197,87199,87217],{"className":87198,"ariaHidden":243},[242],[212,87200,87202,87205,87208,87211,87214],{"className":87201},[247],[212,87203],{"className":87204,"style":12797},[251],[212,87206,15912],{"className":87207,"style":15961},[256,257],[212,87209],{"className":87210,"style":355},[354],[212,87212,1228],{"className":87213},[359],[212,87215],{"className":87216,"style":355},[354],[212,87218,87220,87223],{"className":87219},[247],[212,87221],{"className":87222,"style":369},[251],[212,87224,314],{"className":87225},[256]," 时发散（与 KL 在支撑分离时为 ",[212,87228,87230,87243],{"className":87229,"translate":216},[215],[212,87231,87233],{"className":87232},[220],[222,87234,87235],{"xmlns":224},[226,87236,87237,87241],{},[229,87238,87239],{},[232,87240,1223],{"mathvariant":406},[236,87242,4068],{"encoding":238},[212,87244,87246],{"className":87245,"ariaHidden":243},[242],[212,87247,87249,87252],{"className":87248},[247],[212,87250],{"className":87251,"style":2543},[251],[212,87253,1223],{"className":87254},[256]," 一致）。",[11,87257,87258,87261],{},[1194,87259,87260],{},"第 3 步（初等放缩）。"," 由",[212,87263,87265],{"className":87264,"translate":216},[377],[212,87266,87268,87354],{"className":87267,"translate":216},[215],[212,87269,87271],{"className":87270},[220],[222,87272,87273],{"xmlns":224,"display":386},[226,87274,87275,87351],{},[229,87276,87277,87279,87281,87299,87301,87303,87343,87345,87347,87349],{},[232,87278,4298],{},[307,87280,4301],{},[435,87282,87283,87291],{},[229,87284,87285,87287,87289],{},[312,87286,314],{},[307,87288,2668],{},[232,87290,15912],{},[229,87292,87293,87295,87297],{},[312,87294,314],{},[307,87296,5011],{},[232,87298,15912],{},[307,87300,320],{},[312,87302,2661],{},[229,87304,87305,87307,87309,87311,87321,87323,87334,87336,87339,87341],{},[307,87306,310],{"fence":243},[232,87308,15912],{},[307,87310,2668],{},[435,87312,87313,87319],{},[7012,87314,87315,87317],{},[232,87316,15912],{},[312,87318,40935],{},[312,87320,40935],{},[307,87322,2668],{},[435,87324,87325,87332],{},[7012,87326,87327,87329],{},[232,87328,15912],{},[312,87330,87331],{},"5",[312,87333,87331],{},[307,87335,2668],{},[307,87337,87338],{},"⋯",[1495,87340,1497],{},[307,87342,317],{"fence":243},[307,87344,7126],{},[312,87346,2661],{},[232,87348,15912],{},[307,87350,748],{"separator":243},[236,87352,87353],{"encoding":238},"\\log\\frac{1+\\delta}{1-\\delta}\n=2\\left(\\delta+\\frac{\\delta^3}3\n+\\frac{\\delta^5}5+\\cdots\\right)\n\\ge 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Pinsker 不等式中的 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的系数 2）是最优的：取两分布仅在极小 ",[212,88632,88634,88648],{"className":88633,"translate":216},[215],[212,88635,88637],{"className":88636},[220],[222,88638,88639],{"xmlns":224},[226,88640,88641,88645],{},[229,88642,88643],{},[232,88644,38862],{},[236,88646,88647],{"encoding":238},"\\varepsilon",[212,88649,88651],{"className":88650,"ariaHidden":243},[242],[212,88652,88654,88657],{"className":88653},[247],[212,88655],{"className":88656,"style":2543},[251],[212,88658,38862],{"className":88659},[256,257]," 上偏离最优对称配置，可让 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2",[212,88697,88699,88761],{"className":88698,"ariaHidden":243},[242],[212,88700,88702,88705,88708,88711,88714,88717,88723,88752,88755,88758],{"className":88701},[247],[212,88703],{"className":88704,"style":20763},[251],[212,88706,38865],{"className":88707},[256,257],[212,88709,310],{"className":88710},[343],[212,88712,15912],{"className":88713,"style":15961},[256,257],[212,88715,317],{"className":88716},[350],[212,88718,88720],{"className":88719},[256],[212,88721,1138],{"className":88722},[616,9872],[212,88724,88726,88729],{"className":88725},[256],[212,88727,15912],{"className":88728,"style":15961},[256,257],[212,88730,88732],{"className":88731},[478],[212,88733,88735],{"className":88734},[482],[212,88736,88738],{"className":88737},[487],[212,88739,88741],{"className":88740,"style":20228},[491],[212,88742,88743,88746],{"style":7063},[212,88744],{"className":88745,"style":500},[499],[212,88747,88749],{"className":88748},[504,505,506,507],[212,88750,2661],{"className":88751},[256,507],[212,88753],{"className":88754,"style":355},[354],[212,88756,1228],{"className":88757},[359],[212,88759],{"className":88760,"style":355},[354],[212,88762,88764,88767],{"className":88763},[247],[212,88765],{"className":88766,"style":369},[251],[212,88768,2661],{"className":88769},[256],[212,88771,88773,88791],{"className":88772,"translate":216},[215],[212,88774,88776],{"className":88775},[220],[222,88777,88778],{"xmlns":224},[226,88779,88780,88788],{},[229,88781,88782,88784,88786],{},[232,88783,15912],{},[307,88785,1228],{},[312,88787,323],{},[236,88789,88790],{"encoding":238},"\\delta\\to0",[212,88792,88794,88812],{"className":88793,"ariaHidden":243},[242],[212,88795,88797,88800,88803,88806,88809],{"className":88796},[247],[212,88798],{"className":88799,"style":12797},[251],[212,88801,15912],{"className":88802,"style":15961},[256,257],[212,88804],{"className":88805,"style":355},[354],[212,88807,1228],{"className":88808},[359],[212,88810],{"className":88811,"style":355},[354],[212,88813,88815,88818],{"className":88814},[247],[212,88816],{"className":88817,"style":369},[251],[212,88819,323],{"className":88820},[256],"），故常数不能改进。",[11,88823,88824,88825,88894],{},"顺便指出：对一般 f-散度也有平行的\"固定 TV 时最小化 ",[212,88826,88828,88845],{"className":88827,"translate":216},[215],[212,88829,88831],{"className":88830},[220],[222,88832,88833],{"xmlns":224},[226,88834,88835,88843],{},[229,88836,88837],{},[392,88838,88839,88841],{},[232,88840,396],{},[232,88842,234],{},[236,88844,4220],{"encoding":238},[212,88846,88848],{"className":88847,"ariaHidden":243},[242],[212,88849,88851,88854],{"className":88850},[247],[212,88852],{"className":88853,"style":4230},[251],[212,88855,88857,88860],{"className":88856},[256],[212,88858,396],{"className":88859,"style":474},[256,257],[212,88861,88863],{"className":88862},[478],[212,88864,88866,88886],{"className":88865},[482,483],[212,88867,88869,88883],{"className":88868},[487],[212,88870,88872],{"className":88871,"style":492},[491],[212,88873,88874,88877],{"style":495},[212,88875],{"className":88876,"style":500},[499],[212,88878,88880],{"className":88879},[504,505,506,507],[212,88881,234],{"className":88882,"style":258},[256,257,507],[212,88884,515],{"className":88885},[514],[212,88887,88889],{"className":88888},[487],[212,88890,88892],{"className":88891,"style":522},[491],[212,88893],{},"\"函数（Fedotov–Harremoës 2003 给出完整刻画），即每个 f-散度都自带一个 TV 的下界函数；这是 4.7 末拓扑结论的定量基础。",[11,88896,88897,88900,88901,88929,88930,88933],{},[1194,88898,88899],{},"Bretagnolle–Huber 的推导。"," 由 Rényi 散度在阶数 ",[212,88902,88904,88917],{"className":88903,"translate":216},[215],[212,88905,88907],{"className":88906},[220],[222,88908,88909],{"xmlns":224},[226,88910,88911,88915],{},[229,88912,88913],{},[232,88914,44954],{},[236,88916,49289],{"encoding":238},[212,88918,88920],{"className":88919,"ariaHidden":243},[242],[212,88921,88923,88926],{"className":88922},[247],[212,88924],{"className":88925,"style":2543},[251],[212,88927,44954],{"className":88928,"style":44984},[256,257]," 上",[1194,88931,88932],{},"单调不减","（Hölder 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\\ge\\ D^{R}_{1\u002F2}(P\\|Q)=-2\\log BC 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Cauchy–Schwarz，",[212,90725,90727],{"className":90726,"translate":216},[377],[212,90728,90730,90956],{"className":90729,"translate":216},[215],[212,90731,90733],{"className":90732},[220],[222,90734,90735],{"xmlns":224,"display":386},[226,90736,90737,90953],{},[1441,90738,90739,90805,90873],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,90740,90741,90757],{},[1450,90742,90743],{},[1453,90744,90745],{"scriptlevel":323,"displaystyle":243},[229,90746,90747,90749,90751],{},[312,90748,2661],{},[1495,90750,1497],{},[229,90752,90753,90755],{},[232,90754,5590],{"mathvariant":406},[232,90756,35050],{"mathvariant":406},[1450,90758,90759],{},[1453,90760,90761],{"scriptlevel":323,"displaystyle":243},[229,90762,90763,90765,90767,90769,90771,90775,90777,90781,90783,90785,90787,90791,90793,90797,90799,90801,90803],{},[229,90764],{},[307,90766,320],{},[307,90768,1485],{},[232,90770,5006],{"mathvariant":406},[34539,90772,90773],{},[232,90774,11],{},[307,90776,5011],{},[34539,90778,90779],{},[232,90780,1141],{},[232,90782,5006],{"mathvariant":406},[1495,90784,16104],{},[232,90786,5006],{"mathvariant":406},[34539,90788,90789],{},[232,90790,11],{},[307,90792,2668],{},[34539,90794,90795],{},[232,90796,1141],{},[232,90798,5006],{"mathvariant":406},[1495,90800,1497],{},[232,90802,441],{},[232,90804,971],{},[1447,90806,90807,90813],{},[1450,90808,90809],{},[1453,90810,90811],{"scriptlevel":323,"displaystyle":243},[229,90812],{},[1450,90814,90815],{},[1453,90816,90817],{"scriptlevel":323,"displaystyle":243},[229,90818,90819,90821,90823,90847,90849],{},[229,90820],{},[307,90822,10150],{},[34539,90824,90825],{},[229,90826,90827,90829,90831,90835,90837,90841],{},[307,90828,1485],{},[307,90830,310],{"stretchy":309},[34539,90832,90833],{},[232,90834,11],{},[307,90836,5011],{},[34539,90838,90839],{},[232,90840,1141],{},[7012,90842,90843,90845],{},[307,90844,317],{"stretchy":309},[312,90846,2661],{},[307,90848,3497],{},[34539,90850,90851],{},[229,90852,90853,90855,90857,90861,90863,90867],{},[307,90854,1485],{},[307,90856,310],{"stretchy":309},[34539,90858,90859],{},[232,90860,11],{},[307,90862,2668],{},[34539,90864,90865],{},[232,90866,1141],{},[7012,90868,90869,90871],{},[307,90870,317],{"stretchy":309},[312,90872,2661],{},[1447,90874,90875,90881],{},[1450,90876,90877],{},[1453,90878,90879],{"scriptlevel":323,"displaystyle":243},[229,90880],{},[1450,90882,90883],{},[1453,90884,90885],{"scriptlevel":323,"displaystyle":243},[229,90886,90887,90889,90891,90903,90905,90923,90925,90951],{},[229,90888],{},[307,90890,320],{},[34539,90892,90893],{},[229,90894,90895,90897],{},[312,90896,2661],{},[7012,90898,90899,90901],{},[232,90900,34084],{},[312,90902,2661],{},[307,90904,3497],{},[34539,90906,90907],{},[229,90908,90909,90911,90913,90915,90917,90919,90921],{},[312,90910,2661],{},[307,90912,310],{"stretchy":309},[312,90914,314],{},[307,90916,2668],{},[232,90918,39491],{},[232,90920,39494],{},[307,90922,317],{"stretchy":309},[307,90924,320],{},[34539,90926,90927],{},[229,90928,90929,90931,90937,90939,90941,90943,90949],{},[312,90930,39189],{},[7012,90932,90933,90935],{},[232,90934,34084],{},[312,90936,2661],{},[307,90938,310],{"stretchy":309},[312,90940,2661],{},[307,90942,5011],{},[7012,90944,90945,90947],{},[232,90946,34084],{},[312,90948,2661],{},[307,90950,317],{"stretchy":309},[307,90952,748],{"separator":243},[236,90954,90955],{"encoding":238},"\\begin{aligned}\n2\\,\\mathrm{TV}\n&=\\int|\\sqrt p-\\sqrt q|\\;|\\sqrt p+\\sqrt q|\\,dx\\\\\n&\\le\\sqrt{\\int(\\sqrt p-\\sqrt q)^2}\n\\cdot\\sqrt{\\int(\\sqrt p+\\sqrt q)^2}\\\\\n&=\\sqrt{2H^2}\\cdot\\sqrt{2(1+BC)}\n=\\sqrt{4H^2(2-H^2)},\n\\end{aligned}",[212,90957,90959],{"className":90958,"ariaHidden":243},[242],[212,90960,90962,90966],{"className":90961},[247],[212,90963],{"className":90964,"style":90965},[251],"height:7.2262em;vertical-align:-3.3631em;",[212,90967,90969],{"className":90968},[256],[212,90970,90972,91037],{"className":90971},[1441],[212,90973,90975],{"className":90974},[1558],[212,90976,90978,91028],{"className":90977},[482,483],[212,90979,90981,91025],{"className":90980},[487],[212,90982,90985,91007,91016],{"className":90983,"style":90984},[491],"height:3.8631em;",[212,90986,90988,90992],{"style":90987},"top:-6.3858em;",[212,90989],{"className":90990,"style":90991},[499],"height:3.8828em;",[212,90993,90995,90998,91001],{"className":90994},[256],[212,90996,2661],{"className":90997},[256],[212,90999],{"className":91000,"style":603},[354],[212,91002,91004],{"className":91003},[256],[212,91005,86976],{"className":91006,"style":4355},[256,32862],[212,91008,91010,91013],{"style":91009},"top:-3.3408em;",[212,91011],{"className":91012,"style":90991},[499],[212,91014],{"className":91015},[256],[212,91017,91019,91022],{"style":91018},"top:-0.8797em;",[212,91020],{"className":91021,"style":90991},[499],[212,91023],{"className":91024},[256],[212,91026,515],{"className":91027},[514],[212,91029,91031],{"className":91030},[487],[212,91032,91035],{"className":91033,"style":91034},[491],"height:3.3631em;",[212,91036],{},[212,91038,91040],{"className":91039},[1649],[212,91041,91043,91997],{"className":91042},[482,483],[212,91044,91046,91994],{"className":91045},[487],[212,91047,91049,91293,91683],{"className":91048,"style":90984},[491],[212,91050,91051,91054],{"style":90987},[212,91052],{"className":91053,"style":90991},[499],[212,91055,91057,91060,91063,91066,91069,91072,91075,91078,91122,91125,91128,91131,91175,91178,91181,91184,91228,91231,91234,91237,91281,91284,91287,91290],{"className":91056},[256],[212,91058],{"className":91059},[256],[212,91061],{"className":91062,"style":355},[354],[212,91064,320],{"className":91065},[359],[212,91067],{"className":91068,"style":355},[354],[212,91070,1485],{"className":91071,"style":1685},[1682,1683,1684],[212,91073],{"className":91074,"style":603},[354],[212,91076,5006],{"className":91077},[256],[212,91079,91081],{"className":91080},[256,34567],[212,91082,91084,91114],{"className":91083},[482,483],[212,91085,91087,91111],{"className":91086},[487],[212,91088,91090,91099],{"className":91089,"style":7060},[491],[212,91091,91093,91096],{"className":91092,"style":12063},[6505],[212,91094],{"className":91095,"style":658},[499],[212,91097,11],{"className":91098,"style":34587},[256,257],[212,91100,91101,91104],{"style":41550},[212,91102],{"className":91103,"style":658},[499],[212,91105,91107],{"className":91106,"style":34644},[34643],[6521,91108,91109],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,91110],{"d":34651},[212,91112,515],{"className":91113},[514],[212,91115,91117],{"className":91116},[487],[212,91118,91120],{"className":91119,"style":41570},[491],[212,91121],{},[212,91123],{"className":91124,"style":2785},[354],[212,91126,5011],{"className":91127},[2789],[212,91129],{"className":91130,"style":2785},[354],[212,91132,91134],{"className":91133},[256,34567],[212,91135,91137,91167],{"className":91136},[482,483],[212,91138,91140,91164],{"className":91139},[487],[212,91141,91143,91152],{"className":91142,"style":7060},[491],[212,91144,91146,91149],{"className":91145,"style":12063},[6505],[212,91147],{"className":91148,"style":658},[499],[212,91150,1141],{"className":91151,"style":39299},[256,257],[212,91153,91154,91157],{"style":41550},[212,91155],{"className":91156,"style":658},[499],[212,91158,91160],{"className":91159,"style":34644},[34643],[6521,91161,91162],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,91163],{"d":34651},[212,91165,515],{"className":91166},[514],[212,91168,91170],{"className":91169},[487],[212,91171,91173],{"className":91172,"style":41570},[491],[212,91174],{},[212,91176,5006],{"className":91177},[256],[212,91179],{"className":91180,"style":355},[354],[212,91182,5006],{"className":91183},[256],[212,91185,91187],{"className":91186},[256,34567],[212,91188,91190,91220],{"className":91189},[482,483],[212,91191,91193,91217],{"className":91192},[487],[212,91194,91196,91205],{"className":91195,"style":7060},[491],[212,91197,91199,91202],{"className":91198,"style":12063},[6505],[212,91200],{"className":91201,"style":658},[499],[212,91203,11],{"className":91204,"style":34587},[256,257],[212,91206,91207,91210],{"style":41550},[212,91208],{"className":91209,"style":658},[499],[212,91211,91213],{"className":91212,"style":34644},[34643],[6521,91214,91215],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,91216],{"d":34651},[212,91218,515],{"className":91219},[514],[212,91221,91223],{"classNa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凸、",[212,92687,92689,92712],{"className":92688,"translate":216},[215],[212,92690,92692],{"className":92691},[220],[222,92693,92694],{"xmlns":224},[226,92695,92696,92710],{},[229,92697,92698,92700,92702,92704,92706,92708],{},[232,92699,234],{},[307,92701,310],{"stretchy":309},[312,92703,314],{},[307,92705,317],{"stretchy":309},[307,92707,320],{},[312,92709,323],{},[236,92711,326],{"encoding":238},[212,92713,92715,92742],{"className":92714,"ariaHidden":243},[242],[212,92716,92718,92721,92724,92727,92730,92733,92736,92739],{"className":92717},[247],[212,92719],{"className":92720,"style":336},[251],[212,92722,234],{"className":92723,"style":258},[256,257],[212,92725,310],{"className":92726},[343],[212,92728,314],{"className":92729},[256],[212,92731,317],{"className":92732},[350],[212,92734],{"className":92735,"style":355},[354],[212,92737,320],{"className":92738},[359],[212,92740],{"className":92741,"style":355},[354],[212,92743,92745,92748],{"className":92744},[247],[212,92746],{"className":92747,"style":369},[251],[212,92749,323],{"className":92750},[256]," 且在 ",[212,92753,92755,92777],{"className":92754,"translate":216},[215],[212,92756,92758],{"className":92757},[220],[222,92759,92760],{"xmlns":224},[226,92761,92762,92774],{},[229,92763,92764,92766,92768,92770,92772],{},[307,92765,310],{"stretchy":309},[312,92767,323],{},[307,92769,748],{"separator":243},[232,92771,1223],{"mathvariant":406},[307,92773,317],{"stretchy":309},[236,92775,92776],{"encoding":238},"(0,\\infty)",[212,92778,92780],{"className":92779,"ariaHidden":243},[242],[212,92781,92783,92786,92789,92792,92795,92798,92801],{"className":92782},[247],[212,92784],{"className":92785,"style":336},[251],[212,92787,310],{"className":92788},[343],[212,92790,323],{"className":92791},[256],[212,92793,748],{"className":92794},[770],[212,92796],{"className":92797,"style":603},[354],[212,92799,1223],{"className":92800},[256],[212,92802,317],{"className":92803},[350]," 上连续。",[11,92806,92807,6692,92810,93143,93144,93215,93216,5843,93323,93472,93473,93628,93629,93779,93780,93838,93839,93967,93968,94025,94026,94332],{},[1194,92808,92809],{},"(a)（\"下来\"方向，一般成立）",[212,92811,92813,92883],{"className":92812,"translate":216},[215],[212,92814,92816],{"className":92815},[220],[222,92817,92818],{"xmlns":224},[226,92819,92820,92880],{},[229,92821,92822,92828,92830,92836,92838,92840,92842,92844,92846,92848,92850,92852,92862,92864,92870,92872,92874,92876,92878],{},[392,92823,92824,92826],{},[232,92825,396],{},[232,92827,234],{},[307,92829,310],{"stretchy":309},[392,92831,92832,92834],{},[232,92833,403],{},[232,92835,82510],{},[232,92837,407],{"mathvariant":406},[232,92839,410],{},[307,92841,317],{"stretchy":309},[307,92843,1228],{},[312,92845,323],{},[1495,92847,4481],{},[307,92849,4484],{},[1495,92851,4481],{},[392,92853,92854,92856],{},[232,92855,396],{},[229,92857,92858,92860],{},[232,92859,5590],{},[232,92861,35050],{},[307,92863,310],{"stretchy":309},[392,92865,92866,92868],{},[232,92867,403],{},[232,92869,82510],{},[307,92871,748],{"separator":243},[232,92873,410],{},[307,92875,317],{"stretchy":309},[307,92877,1228],{},[312,92879,323],{},[236,92881,92882],{"encoding":238},"D_f(P_n\\|Q)\\to0\\ \\Longrightarrow\\ D_{TV}(P_n,Q)\\to0",[212,92884,92886,92993,93018,93134],{"className":92885,"ariaHidden":243},[242],[212,92887,92889,92892,92932,92935,92975,92978,92981,92984,92987,92990],{"className":92888},[247],[212,92890],{"className":92891,"style":467},[251],[212,92893,92895,92898],{"className":92894},[256],[212,92896,396],{"className":92897,"style":474},[256,257],[212,92899,92901],{"className":92900},[478],[212,92902,92904,92924],{"className":92903},[482,483],[212,92905,92907,92921],{"className":92906},[487],[212,92908,92910],{"className":92909,"style":492},[491],[212,92911,92912,92915],{"style":495},[212,92913],{"className":92914,"style":500},[499],[212,92916,92918],{"className":92917},[504,505,506,507],[212,92919,234],{"className":92920,"style":258},[256,257,507],[212,92922,515],{"className":92923},[514],[212,92925,92927],{"className":92926},[487],[212,92928,92930],{"className":92929,"style":522},[491],[212,92931],{},[212,92933,310],{"className":92934},[343],[212,92936,92938,92941],{"className":92937},[256],[212,92939,403],{"className":92940,"style":531},[256,257],[212,92942,92944],{"className":92943},[478],[212,92945,92947,92967],{"className":92946},[482,483],[212,92948,92950,92964],{"className":92949},[487],[212,92951,92953],{"className":92952,"style":45129},[491],[212,92954,92955,92958],{"style":11336},[212,92956],{"className":92957,"style":500},[499],[212,92959,92961],{"className":92960},[504,505,506,507],[212,92962,82510],{"className":92963},[256,257,507],[212,92965,515],{"className":92966},[514],[212,92968,92970],{"className":92969},[487],[212,92971,92973],{"className":92972,"style":8166},[491],[212,92974],{},[212,92976,407],{"className":92977},[256],[212,92979,410],{"className":92980},[256,257],[212,92982,317],{"className":92983},[350],[212,92985],{"className":92986,"style":355},[354],[212,92988,1228],{"className":92989},[359],[212,92991],{"className":92992,"style":355},[354],[212,92994,92996,93000,93003,93006,93009,93012,93015],{"className":92995},[247],[212,92997],{"className":92998,"style":92999},[251],"height:0.6684em;vertical-align:-0.024em;",[212,93001,323],{"className":93002},[256],[212,93004,4481],{"className":93005},[354],[212,93007],{"className":93008,"style":355},[354],[212,93010,4484],{"className":93011},[359],[212,93013,4481],{"className":93014},[354],[212,93016],{"className":93017,"style":355},[354],[212,93019,93021,93024,93070,93073,93113,93116,93119,93122,93125,93128,93131],{"className":93020},[247],[212,93022],{"className":93023,"style":336},[251],[212,93025,93027,93030],{"className":93026},[256],[212,93028,396],{"className":93029,"style":474},[256,257],[212,93031,93033],{"className":93032},[478],[212,93034,93036,93062],{"className":93035},[482,483],[212,93037,93039,93059],{"className":93038},[487],[212,93040,93042],{"className":93041,"style":576},[491],[212,93043,93044,93047],{"style":495},[212,93045],{"className":93046,"style":500},[499],[212,93048,93050],{"className":93049},[504,505,506,507],[212,93051,93053,93056],{"className":93052},[256,507],[212,93054,5590],{"className":93055,"style":531},[256,257,507],[212,93057,35050],{"className":93058,"style":2785},[256,257,507],[212,93060,515],{"className":93061},[514],[212,93063,93065],{"className":93064},[487],[212,93066,93068],{"className":93067,"style":8166},[491],[212,93069],{},[212,93071,310],{"className":93072},[343],[212,93074,93076,93079],{"className":93075},[256],[212,93077,403],{"className":93078,"style":531},[256,257],[212,93080,93082],{"className":93081},[478],[212,93083,93085,93105],{"className":93084},[482,483],[212,93086,93088,93102],{"className":93087},[487],[212,93089,93091],{"className":93090,"style":45129},[491],[212,93092,93093,93096],{"style":11336},[212,93094],{"className":93095,"style":500},[499],[212,93097,93099],{"className":93098},[504,505,506,507],[212,93100,82510],{"className":93101},[256,257,507],[212,93103,515],{"className":93104},[514],[212,93106,93108],{"className":93107},[487],[212,93109,93111],{"className":93110,"style":8166},[491],[212,93112],{},[212,93114,748],{"className":93115},[770],[212,93117],{"className":93118,"style":603},[354],[212,93120,410],{"className":93121},[256,257],[212,93123,317],{"className":93124},[350],[212,93126],{"className":93127,"style":355},[354],[212,93129,1228],{"className":93130},[359],[212,93132],{"className":93133,"style":355},[354],[212,93135,93137,93140],{"className":93136},[247],[212,93138],{"className":93139,"style":369},[251],[212,93141,323],{"className":93142},[256],"。每个适度正则的 f-散度都自带一个连续的 TV 下界函数 ",[212,93145,93147,93165],{"className":93146,"translate":216},[215],[212,93148,93150],{"className":93149},[220],[222,93151,93152],{"xmlns":224},[226,93153,93154,93162],{},[229,93155,93156],{},[392,93157,93158,93160],{},[232,93159,4356],{},[232,93161,234],{},[236,93163,93164],{"encoding":238},"g_f",[212,93166,93168],{"className":93167,"ariaHidden":243},[242],[212,93169,93171,93175],{"className":93170},[247],[212,93172],{"className":93173,"style":93174},[251],"height:0.7167em;vertical-align:-0.2861em;",[212,93176,93178,93181],{"className":93177},[256],[212,93179,4356],{"className":93180,"style":1178},[256,257],[212,93182,93184],{"className":93183},[478],[212,93185,93187,93207],{"className":93186},[482,483],[212,93188,93190,93204],{"className":93189},[487],[212,93191,93193],{"className":93192,"style":492},[491],[212,93194,93195,93198],{"style":19043},[212,93196],{"className":93197,"style":500},[499],[212,93199,93201],{"className":93200},[504,505,506,507],[212,93202,234],{"className":93203,"style":258},[256,257,507],[212,93205,515],{"className":93206},[514],[212,93208,93210],{"className":93209},[487],[212,93211,93213],{"className":93212,"style":522},[491],[212,93214],{},"（Vajda \u002F Fedotov–Harremoës），",[212,93217,93219,93247],{"className":93218,"translate":216},[215],[212,93220,93222],{"className":93221},[220],[222,93223,93224],{"xmlns":224},[226,93225,93226,93244],{},[229,93227,93228,93234,93236,93238,93240,93242],{},[392,93229,93230,93232],{},[232,93231,4356],{},[232,93233,234],{},[307,93235,310],{"stretchy":309},[312,93237,323],{},[307,93239,317],{"stretchy":309},[307,93241,320],{},[312,93243,323],{},[236,93245,93246],{"encoding":238},"g_f(0)=0",[212,93248,93250,93314],{"className":93249,"ariaHidden":243},[242],[212,93251,93253,93256,93296,93299,93302,93305,93308,93311],{"className":93252},[247],[212,93254],{"className":93255,"style":467},[251],[212,93257,93259,93262],{"className":93258},[256],[212,93260,4356],{"className":93261,"style":1178},[256,257],[212,93263,93265],{"className":93264},[478],[212,93266,93268,93288],{"className":93267},[482,483],[212,93269,93271,93285],{"className":93270},[487],[212,93272,93274],{"className":93273,"style":492},[491],[212,93275,93276,93279],{"style":19043},[212,93277],{"className":93278,"style":500},[499],[212,93280,93282],{"className":93281},[504,505,506,507],[212,93283,234],{"className":93284,"style":258},[256,257,507],[212,93286,515],{"className":93287},[514],[212,93289,93291],{"className":93290},[487],[212,93292,93294],{"className":93293,"style":522},[491],[212,93295],{},[212,93297,310],{"className":93298},[343],[212,93300,323],{"className":93301},[256],[212,93303,317],{"className":93304},[350],[212,93306],{"className":93307,"style":355},[354],[212,93309,320],{"className":93310},[359],[212,93312],{"className":93313,"style":355},[354],[212,93315,93317,93320],{"className":93316},[247],[212,93318],{"className":93319,"style":369},[251],[212,93321,323],{"className":93322},[256],[212,93324,93326,93366],{"className":93325,"translate":216},[215],[212,93327,93329],{"className":93328},[220],[222,93330,93331],{"xmlns":224},[226,93332,93333,93363],{},[229,93334,93335,93341,93343,93345,93347,93349,93351,93353,93355,93357,93359,93361],{},[392,93336,93337,93339],{},[232,93338,4356],{},[232,93340,234],{},[307,93342,310],{"stretchy":309},[232,93344,966],{},[307,93346,317],{"stretchy":309},[307,93348,3101],{},[312,93350,323],{},[1495,93352,4481],{},[307,93354,310],{"stretchy":309},[232,93356,966],{},[307,93358,3101],{},[312,93360,323],{},[307,93362,317],{"stretchy":309},[236,93364,93365],{"encoding":238},"g_f(t)>0\\ (t>0)",[212,93367,93369,93433,93460],{"className":93368,"ariaHidden":243},[242],[212,93370,93372,93375,93415,93418,93421,93424,93427,93430],{"className":93371},[247],[212,93373],{"className":93374,"style":467},[251],[212,93376,93378,93381],{"className":93377},[256],[212,93379,4356],{"className":93380,"style":1178},[256,257],[212,93382,93384],{"className":93383},[478],[212,93385,93387,93407],{"className":93386},[482,483],[212,93388,93390,93404],{"className":93389},[487],[212,93391,93393],{"className":93392,"style":492},[491],[212,93394,93395,93398],{"style":19043},[212,93396],{"className":93397,"style":500},[499],[212,93399,93401],{"className":93400},[504,505,506,507],[212,93402,234],{"className":93403,"style":258},[256,257,507],[212,93405,515],{"className":93406},[514],[212,93408,93410],{"className":93409},[487],[212,93411,93413],{"className":93412,"style":522},[491],[212,93414],{},[212,93416,310],{"className":93417},[343],[212,93419,966],{"className":93420},[256,257],[212,93422,317],{"className":93423},[350],[212,93425],{"className":93426,"style":355},[354],[212,93428,3101],{"className":93429},[359],[212,93431],{"className":93432,"style":355},[354],[212,93434,93436,93439,93442,93445,93448,93451,93454,93457],{"className":93435},[247],[212,93437],{"className":93438,"style":336},[251],[212,93440,323],{"className":93441},[256],[212,93443,4481],{"className":93444},[354],[212,93446,310],{"className":93447},[343],[212,93449,966],{"className":93450},[256,257],[212,93452],{"className":93453,"style":355},[354],[212,93455,3101],{"className":93456},[359],[212,93458],{"className":93459,"style":355},[354],[212,93461,93463,93466,93469],{"className":93462},[247],[212,93464],{"className":93465,"style":336},[251],[212,93467,323],{"className":93468},[256],[212,93470,317],{"className":93471},[350],"，使 ",[212,93474,93476,93512],{"className":93475,"translate":216},[215],[212,93477,93479],{"className":93478},[220],[222,93480,93481],{"xmlns":224},[226,93482,93483,93509],{},[229,93484,93485,93491,93493,93499,93501,93507],{},[392,93486,93487,93489],{},[232,93488,396],{},[232,93490,234],{},[307,93492,7126],{},[392,93494,93495,93497],{},[232,93496,4356],{},[232,93498,234],{},[307,93500,310],{"stretchy":309},[229,93502,93503,93505],{},[232,93504,5590],{"mathvariant":406},[232,93506,35050],{"mathvariant":406},[307,93508,317],{"stretchy":309},[236,93510,93511],{"encoding":238},"D_f\\ge g_f(\\mathrm{TV})",[212,93513,93515,93570],{"className":93514,"ariaHidden":243},[242],[212,93516,93518,93521,93561,93564,93567],{"className":93517},[247],[212,93519],{"className":93520,"style":4230},[251],[212,93522,93524,93527],{"className":93523},[256],[212,93525,396],{"className":93526,"style":474},[256,257],[212,93528,93530],{"className":93529},[478],[212,93531,93533,93553],{"className":93532},[482,483],[212,93534,93536,93550],{"className":93535},[487],[212,93537,93539],{"className":93538,"style":492},[491],[212,93540,93541,93544],{"style":495},[212,93542],{"className":93543,"style":500},[499],[212,93545,93547],{"className":93546},[504,505,506,507],[212,93548,234],{"className":93549,"style":258},[256,257,507],[212,93551,515],{"className":93552},[514],[212,93554,93556],{"className":93555},[487],[212,93557,93559],{"className":93558,"style":522},[491],[212,93560],{},[212,93562],{"className":93563,"style":355},[354],[212,93565,7126],{"className":93566},[359],[212,93568],{"className":93569,"style":355},[354],[212,93571,93573,93576,93616,93619,93625],{"className":93572},[247],[212,93574],{"className":93575,"style":467},[251],[212,93577,93579,93582],{"className":93578},[256],[212,93580,4356],{"className":93581,"style":1178},[256,257],[212,93583,93585],{"className":93584},[478],[212,93586,93588,93608],{"className":93587},[482,483],[212,93589,93591,93605],{"className":93590},[487],[212,93592,93594],{"className":93593,"style":492},[491],[212,93595,93596,93599],{"style":19043},[212,93597],{"className":93598,"style":500},[499],[212,93600,93602],{"className":93601},[504,505,506,507],[212,93603,234],{"className":93604,"style":258},[256,257,507],[212,93606,515],{"className":93607},[514],[212,93609,93611],{"className":93610},[487],[212,93612,93614],{"className":93613,"style":522},[491],[212,93615],{},[212,93617,310],{"className":93618},[343],[212,93620,93622],{"className":93621},[256],[212,93623,86976],{"className":93624,"style":4355},[256,32862],[212,93626,317],{"className":93627},[350],"；常用成员的具体形式：KL 给 ",[212,93630,93632,93670],{"className":93631,"translate":216},[215],[212,93633,93635],{"className":93634},[220],[222,93636,93637],{"xmlns":224},[226,93638,93639,93667],{},[229,93640,93641,93643,93645,93655,93657],{},[312,93642,2661],{},[1495,93644,1497],{},[7012,93646,93647,93653],{},[229,93648,93649,93651],{},[232,93650,5590],{"mathvariant":406},[232,93652,35050],{"mathvariant":406},[312,93654,2661],{},[307,93656,10150],{},[392,93658,93659,93661],{},[232,93660,396],{},[229,93662,93663,93665],{},[232,93664,10894],{},[232,93666,22093],{},[236,93668,93669],{"encoding":238},"2\\,\\mathrm{TV}^2\\le D_{KL}",[212,93671,93673,93727],{"className":93672,"ariaHidden":243},[242],[212,93674,93676,93680,93683,93686,93718,93721,93724],{"className":93675},[247],[212,93677],{"className":93678,"style":93679},[251],"height:1.0233em;vertical-align:-0.136em;",[212,93681,2661],{"className":93682},[256],[212,93684],{"className":93685,"style":603},[354],[212,93687,93689,93695],{"className":93688},[256],[212,93690,93692],{"className":93691},[256],[212,93693,86976],{"className":93694,"style":4355},[256,32862],[212,93696,93698],{"className":93697},[478],[212,93699,93701],{"className":93700},[482],[212,93702,93704],{"className":93703},[487],[212,93705,93707],{"className":93706,"style":88590},[491],[212,93708,93709,93712],{"style":88620},[212,93710],{"className":93711,"style":500},[499],[212,93713,93715],{"className":93714},[504,505,506,507],[212,93716,2661],{"className":93717},[256,507],[212,93719],{"className":93720,"style":355},[354],[212,93722,10150],{"className":93723},[359],[212,93725],{"className":93726,"style":355},[354],[212,93728,93730,93733],{"className":93729},[247],[212,93731],{"className":93732,"style":16161},[251],[212,93734,93736,93739],{"className":93735},[256],[212,93737,396],{"className":93738,"style":474},[256,257],[212,93740,93742],{"className":93741},[478],[212,93743,93745,93771],{"className":93744},[482,483],[212,93746,93748,93768],{"className":93747},[487],[212,93749,93751],{"className":93750,"style":576},[491],[212,93752,93753,93756],{"style":495},[212,93754],{"className":93755,"style":500},[499],[212,93757,93759],{"className":93758},[504,505,506,507],[212,93760,93762,93765],{"className":93761},[256,507],[212,93763,10894],{"className":93764,"style":10982},[256,257,507],[212,93766,22093],{"className":93767},[256,257,507],[212,93769,515],{"className":93770},[514],[212,93772,93774],{"className":93773},[487],[212,93775,93777],{"className":93776,"style":8166},[491],[212,93778],{},"（Pinsker），",[212,93781,93783,93800],{"className":93782,"translate":216},[215],[212,93784,93786],{"className":93785},[220],[222,93787,93788],{"xmlns":224},[226,93789,93790,93798],{},[229,93791,93792],{},[7012,93793,93794,93796],{},[232,93795,37649],{},[312,93797,2661],{},[236,93799,40594],{"encoding":238},[212,93801,93803],{"className":93802,"ariaHidden":243},[242],[212,93804,93806,93809],{"className":93805},[247],[212,93807],{"className":93808,"style":40604},[251],[212,93810,93812,93815],{"className":93811},[256],[212,93813,37649],{"className":93814},[256,257],[212,93816,93818],{"className":93817},[478],[212,93819,93821],{"className":93820},[482],[212,93822,93824],{"className":93823},[487],[212,93825,93827],{"className":93826,"style":20228},[491],[212,93828,93829,93832],{"style":7063},[212,93830],{"className":93831,"style":500},[499],[212,93833,93835],{"className":93834},[504,505,506,507],[212,93836,2661],{"className":93837},[256,507]," 给 ",[212,93840,93842,93876],{"className":93841,"translate":216},[215],[212,93843,93845],{"className":93844},[220],[222,93846,93847],{"xmlns":224},[226,93848,93849,93873],{},[229,93850,93851,93857,93859,93861,93863],{},[7012,93852,93853,93855],{},[232,93854,37649],{},[312,93856,2661],{},[307,93858,7126],{},[312,93860,39189],{},[1495,93862,1497],{},[7012,93864,93865,93871],{},[229,93866,93867,93869],{},[232,93868,5590],{"mathvariant":406},[232,93870,35050],{"mathvariant":406},[312,93872,2661],{},[236,93874,93875],{"encoding":238},"\\chi^2\\ge4\\,\\mathrm{TV}^2",[212,93877,93879,93923],{"className":93878,"ariaHidden":243},[242],[212,93880,93882,93885,93914,93917,93920],{"className":93881},[247],[212,93883],{"className":93884,"style":40604},[251],[212,93886,93888,93891],{"className":93887},[256],[212,93889,37649],{"className":93890},[256,257],[212,93892,93894],{"className":93893},[478],[212,93895,93897],{"className":93896},[482],[212,93898,93900],{"className":93899},[487],[212,93901,93903],{"className":93902,"style":20228},[491],[212,93904,93905,93908],{"style":7063},[212,93906],{"className":93907,"style":500},[499],[212,93909,93911],{"className":93910},[504,505,506,507],[212,93912,2661],{"className":93913},[256,507],[212,93915],{"className":93916,"style":355},[354],[212,93918,7126],{"className":93919},[359],[212,93921],{"className":93922,"style":355},[354],[212,93924,93926,93929,93932,93935],{"className":93925},[247],[212,93927],{"className":93928,"style":88590},[251],[212,93930,39189],{"className":93931},[256],[212,93933],{"className":93934,"style":603},[354],[212,93936,93938,93944],{"className":93937},[256],[212,93939,93941],{"className":93940},[256],[212,93942,86976],{"className":93943,"style":4355},[256,32862],[212,93945,93947],{"className":93946},[478],[212,93948,93950],{"className":93949},[482],[212,93951,93953],{"className":93952},[487],[212,93954,93956],{"className":93955,"style":88590},[491],[212,93957,93958,93961],{"style":88620},[212,93959],{"className":93960,"style":500},[499],[212,93962,93964],{"className":93963},[504,505,506,507],[212,93965,2661],{"className":93966},[256,507],"，Hellinger",[212,93969,93971,93988],{"className":93970,"translate":216},[215],[212,93972,93974],{"className":93973},[220],[222,93975,93976],{"xmlns":224},[226,93977,93978,93986],{},[229,93979,93980],{},[7012,93981,93982,93984],{},[229,93983],{},[312,93985,2661],{},[236,93987,44469],{"encoding":238},[212,93989,93991],{"className":93990,"ariaHidden":243},[242],[212,93992,93994,93997],{"className":93993},[247],[212,93995],{"className":93996,"style":20228},[251],[212,93998,94000,94002],{"className":93999},[256],[212,94001],{},[212,94003,94005],{"className":94004},[478],[212,94006,94008],{"className":94007},[482],[212,94009,94011],{"className":94010},[487],[212,94012,94014],{"className":94013,"style":20228},[491],[212,94015,94016,94019],{"style":7063},[212,94017],{"className":94018,"style":500},[499],[212,94020,94022],{"className":94021},[504,505,506,507],[212,94023,2661],{"className":94024},[256,507]," 经由 ",[212,94027,94029,94087],{"className":94028,"translate":216},[215],[212,94030,94032],{"className":94031},[220],[222,94033,94034],{"xmlns":224},[226,94035,94036,94084],{},[229,94037,94038,94044,94046,94070,94072],{},[229,94039,94040,94042],{},[232,94041,5590],{"mathvariant":406},[232,94043,35050],{"mathvariant":406},[307,94045,10150],{},[34539,94047,94048],{},[229,94049,94050,94056,94058,94060,94062,94068],{},[7012,94051,94052,94054],{},[232,94053,34084],{},[312,94055,2661],{},[307,94057,310],{"stretchy":309},[312,94059,2661],{},[307,94061,5011],{},[7012,94063,94064,94066],{},[232,94065,34084],{},[312,94067,2661],{},[307,94069,317],{"stretchy":309},[307,94071,10150],{},[34539,94073,94074],{},[229,94075,94076,94078],{},[312,94077,2661],{},[7012,94079,94080,94082],{},[232,94081,34084],{},[312,94083,2661],{},[236,94085,94086],{"encoding":238},"\\mathrm{TV}\\le\\sqrt{H^2(2-H^2)}\\le\\sqrt{2H^2}",[212,94088,94090,94111,94246],{"className":94089,"ariaHidden":243},[242],[212,94091,94093,94096,94102,94105,94108],{"className":94092},[247],[212,94094],{"className":94095,"style":88568},[251],[212,94097,94099],{"className":94098},[256],[212,94100,86976],{"className":94101,"style":4355},[256,32862],[212,94103],{"className":94104,"style":355},[354],[212,94106,10150],{"className":94107},[359],[212,94109],{"className":94110,"style":355},[354],[212,94112,94114,94117,94237,94240,94243],{"className":94113},[247],[212,94115],{"className":94116,"style":92085},[251],[212,94118,94120],{"className":94119},[256,34567],[212,94121,94123,94229],{"className":94122},[482,483],[212,94124,94126,94226],{"className":94125},[487],[212,94127,94129,94214],{"className":94128,"style":92098},[491],[212,94130,94132,94135],{"className":94131,"style":83750},[6505],[212,94133],{"className":94134,"style":15046},[499],[212,94136,94138,94167,94170,94173,94176,94179,94182,94211],{"className":94137,"style":41361},[256],[212,94139,94141,94144],{"className":94140},[256],[212,94142,34084],{"className":94143,"style":34238},[256,257],[212,94145,94147],{"className":94146},[478],[212,94148,94150],{"className":94149},[482],[212,94151,94153],{"className":94152},[487],[212,94154,94156],{"className":94155,"style":45232},[491],[212,94157,94158,94161],{"style":45235},[212,94159],{"className":94160,"style":500},[499],[212,94162,94164],{"className":94163},[504,505,506,507],[212,94165,2661],{"className":94166},[256,507],[212,94168,310],{"className":94169},[343],[212,94171,2661],{"className":94172},[256],[212,94174],{"className":94175,"style":2785},[354],[212,94177,5011],{"className":94178},[2789],[212,94180],{"className":94181,"style":2785},[354],[212,94183,94185,94188],{"className":94184},[256],[212,94186,34084],{"className":94187,"style":34238},[256,257],[212,94189,94191],{"className":94190},[478],[212,94192,94194],{"className":94193},[482],[212,94195,94197],{"className":94196},[487],[212,94198,94200],{"className":94199,"style":45232},[491],[212,94201,94202,94205],{"style":45235},[212,94203],{"className":94204,"style":500},[499],[212,94206,94208],{"className":94207},[504,505,506,507],[212,94209,2661],{"className":94210},[256,507],[212,94212,317],{"className":94213},[350],[212,94215,94216,94219],{"style":92186},[212,94217],{"className":94218,"style":15046},[499],[212,94220,94222],{"className":94221,"style":83842},[34643],[6521,94223,94224],{"xmlns":6523,"width":6524,"height":83845,"viewBox":83846,"preserveAspectRatio":6527},[6529,94225],{"d":83849},[212,94227,515],{"className":94228},[514],[212,94230,94232],{"className":94231},[487],[212,94233,94235],{"className":94234,"style":92206},[491],[212,94236],{},[212,94238],{"className":94239,"style":355},[354],[212,94241,10150],{"className":94242},[359],[212,94244],{"className":94245,"style":355},[354],[212,94247,94249,94253],{"className":94248},[247],[212,94250],{"className":94251,"style":94252},[251],"height:1.04em;vertical-align:-0.0849em;",[212,94254,94256],{"className":94255},[256,34567],[212,94257,94259,94323],{"className":94258},[482,483],[212,94260,94262,94320],{"className":94261},[487],[212,94263,94266,94307],{"className":94264,"style":94265},[491],"height:0.9551em;",[212,94267,94269,94272],{"className":94268,"style":12063},[6505],[212,94270],{"className":94271,"style":658},[499],[212,94273,94275,94278],{"className":94274,"style":34587},[256],[212,94276,2661],{"className":94277},[256],[212,94279,94281,94284],{"className":94280},[256],[212,94282,34084],{"className":94283,"style":34238},[256,257],[212,94285,94287],{"className":94286},[478],[212,94288,94290],{"className":94289},[482],[212,94291,94293],{"className":94292},[487],[212,94294,94296],{"className":94295,"style":45232},[491],[212,94297,94298,94301],{"style":45235},[212,94299],{"className":94300,"style":500},[499],[212,94302,94304],{"className":94303},[504,505,506,507],[212,94305,2661],{"className":94306},[256,507],[212,94308,94310,94313],{"style":94309},"top:-2.9151em;",[212,94311],{"className":94312,"style":658},[499],[212,94314,94316],{"className":94315,"style":34644},[34643],[6521,94317,94318],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,94319],{"d":34651},[212,94321,515],{"className":94322},[514],[212,94324,94326],{"className":94325},[487],[212,94327,94330],{"className":94328,"style":94329},[491],"height:0.0849em;",[212,94331],{},"，TV 本身平凡。",[11,94334,94335,6692,94338,94670,94671,94674,94675,94726,94727,2943,94780,95107,95108,5843,95290,95422,95423,95613,95614,95824],{},[1194,94336,94337],{},"(b)（\"上去\"方向，需要条件）",[212,94339,94341,94411],{"className":94340,"translate":216},[215],[212,94342,94344],{"className":94343},[220],[222,94345,94346],{"xmlns":224},[226,94347,94348,94408],{},[229,94349,94350,94360,94362,94368,94370,94372,94374,94376,94378,94380,94382,94384,94390,94392,94398,94400,94402,94404,94406],{},[392,94351,94352,94354],{},[232,94353,396],{},[229,94355,94356,94358],{},[232,94357,5590],{},[232,94359,35050],{},[307,94361,310],{"stretchy":309},[392,94363,94364,94366],{},[232,94365,403],{},[232,94367,82510],{},[307,94369,748],{"separator":243},[232,94371,410],{},[307,94373,317],{"stretchy":309},[307,94375,1228],{},[312,94377,323],{},[1495,94379,4481],{},[307,94381,4484],{},[1495,94383,4481],{},[392,94385,94386,94388],{},[232,94387,396],{},[232,94389,234],{},[307,94391,310],{"stretchy":309},[392,94393,94394,94396],{},[232,94395,403],{},[232,94397,82510],{},[232,94399,407],{"mathvariant":406},[232,94401,410],{},[307,94403,317],{"stretchy":309},[307,94405,1228],{},[312,94407,323],{},[236,94409,94410],{"encoding":238},"D_{TV}(P_n,Q)\\to0\\ \\Longrightarrow\\ 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一般",[1194,94672,94673],{},"不成立","。反例：在 ",[212,94676,94678,94699],{"className":94677,"translate":216},[215],[212,94679,94681],{"className":94680},[220],[222,94682,94683],{"xmlns":224},[226,94684,94685,94697],{},[229,94686,94687,94689,94691,94693,94695],{},[307,94688,427],{"stretchy":309},[312,94690,323],{},[307,94692,748],{"separator":243},[312,94694,314],{},[307,94696,454],{"stretchy":309},[236,94698,37014],{"encoding":238},[212,94700,94702],{"className":94701,"ariaHidden":243},[242],[212,94703,94705,94708,94711,94714,94717,94720,94723],{"className":94704},[247],[212,94706],{"className":94707,"style":336},[251],[212,94709,427],{"className":94710},[343],[212,94712,323],{"className":94713},[256],[212,94715,748],{"className":94716},[770],[212,94718],{"className":94719,"style":603},[354],[212,94721,314],{"className":94722},[256],[212,94724,454],{"className":94725},[350]," 上取 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",[212,95424,95426,95470],{"className":95425,"translate":216},[215],[212,95427,95429],{"className":95428},[220],[222,95430,95431],{"xmlns":224},[226,95432,95433,95467],{},[229,95434,95435,95441,95443,95449,95451,95453,95455,95457,95463,95465],{},[229,95436,95437,95439],{},[232,95438,5590],{"mathvariant":406},[232,95440,35050],{"mathvariant":406},[307,95442,310],{"stretchy":309},[392,95444,95445,95447],{},[232,95446,1141],{},[232,95448,82510],{},[307,95450,748],{"separator":243},[232,95452,11],{},[307,95454,317],{"stretchy":309},[307,95456,33159],{},[392,95458,95459,95461],{},[232,95460,15912],{},[232,95462,82510],{},[307,95464,1228],{},[312,95466,323],{},[236,95468,95469],{"encoding":238},"\\mathrm{TV}(q_n,p)\\approx\\delta_n\\to0",[212,95471,95473,95549,95604],{"className":95472,"ariaHidden":243},[242],[212,95474,95476,95479,95485,95488,95528,95531,95534,95537,95540,95543,95546],{"className":95475},[247],[212,95477],{"className":95478,"style":336},[251],[212,95480,95482],{"className":95481},[256],[212,95483,86976],{"className":95484,"style":4355},[256,32862],[212,95486,310],{"className":95487},[343],[212,95489,95491,95494],{"className":95490},[256],[212,95492,1141],{"className":95493,"style":1178},[256,257],[212,95495,95497],{"className":95496},[478],[212,95498,95500,95520],{"className":95499},[482,483],[212,95501,95503,95517],{"className":95502},[487],[212,95504,95506],{"className":95505,"style":45129},[491],[212,95507,95508,95511],{"style":19043},[212,95509],{"className":95510,"style":500},[499],[212,95512,95514],{"className":95513},[504,505,506,507],[212,95515,82510],{"className":95516},[256,257,507],[212,95518,515],{"className":95519},[514],[212,95521,95523],{"className":95522},[487],[212,95524,95526],{"className":95525,"style":8166},[491],[212,95527],{},[212,95529,748],{"className":95530},[770],[212,95532],{"className":95533,"style":603},[354],[212,95535,11],{"className":95536},[256,257],[212,95538,317],{"className":95539},[350],[212,95541],{"className":95542,"style":355},[354],[212,95544,33159],{"className":95545},[359],[212,95547],{"className":95548,"style":355},[354],[212,95550,95552,95555,95595,95598,95601],{"className":95551},[247],[212,95553],{"className":95554,"style":11674},[251],[212,95556,95558,95561],{"className":95557},[256],[212,95559,15912],{"className":95560,"style":15961},[256,257],[212,95562,95564],{"className":95563},[478],[212,95565,95567,95587],{"className":95566},[482,483],[212,95568,95570,95584],{"className":95569},[487],[212,95571,95573],{"className":95572,"style":45129},[491],[212,95574,95575,95578],{"style":94959},[212,95576],{"className":95577,"style":500},[499],[212,95579,95581],{"className":95580},[504,505,506,507],[212,95582,82510],{"className":95583},[256,257,507],[212,95585,515],{"className":95586},[514],[212,95588,95590],{"className":95589},[487],[212,95591,95593],{"className":95592,"style":8166},[491],[212,95594],{},[212,95596],{"className":95597,"style":355},[354],[212,95599,1228],{"className":95600},[359],[212,95602],{"className":95603,"style":355},[354],[212,95605,95607,95610],{"className":95606},[247],[212,95608],{"className":95609,"style":369},[251],[212,95611,323],{"className":95612},[256],"，但 ",[212,95615,95617,95666],{"className":95616,"translate":216},[215],[212,95618,95620],{"className":95619},[220],[222,95621,95622],{"xmlns":224},[226,95623,95624,95663],{},[229,95625,95626,95632,95634,95640,95642,95644,95646,95649,95655,95657,95659,95661],{},[229,95627,95628,95630],{},[232,95629,10894],{"mathvariant":406},[232,95631,22093],{"mathvariant":406},[307,95633,310],{"stretchy":309},[392,95635,95636,95638],{},[232,95637,1141],{},[232,95639,82510],{},[232,95641,407],{"mathvariant":406},[232,95643,11],{},[307,95645,317],{"stretchy":309},[307,95647,95648],{},"≳",[392,95650,95651,95653],{},[232,95652,15912],{},[232,95654,82510],{},[307,95656,3497],{},[232,95658,82510],{},[307,95660,1228],{},[232,95662,1223],{"mathvariant":406},[236,95664,95665],{"encoding":238},"\\mathrm{KL}(q_n\\|p)\\gtrsim \\delta_n\\cdot n\\to\\infty",[212,95667,95669,95742,95797,95815],{"className":95668,"ariaHidden":243},[242],[212,95670,95672,95675,95681,95684,95724,95727,95730,95733,95736,95739],{"className":95671},[247],[212,95673],{"className":95674,"style":336},[251],[212,95676,95678],{"className":95677},[256],[212,95679,32863],{"className":95680},[256,32862],[212,95682,310],{"className":95683},[343],[212,95685,95687,95690],{"className":95686},[256],[212,95688,1141],{"className":95689,"style":1178},[256,257],[212,95691,95693],{"className":95692},[478],[212,95694,95696,95716],{"className":95695},[482,483],[212,95697,95699,95713],{"className":95698},[487],[212,95700,95702],{"className":95701,"style":45129},[491],[212,95703,95704,95707],{"style":19043},[212,95705],{"className":95706,"style":500},[499],[212,95708,95710],{"className":95709},[504,505,506,507],[212,95711,82510],{"className":95712},[256,257,507],[212,95714,515],{"className":95715},[514],[212,95717,95719],{"className":95718},[487],[212,95720,95722],{"className":95721,"style":8166},[491],[212,95723],{},[212,95725,407],{"className":95726},[256],[212,95728,11],{"className":95729},[256,257],[212,95731,317],{"className":95732},[350],[212,95734],{"className":95735,"style":355},[354],[212,95737,95648],{"className":95738},[359,60002],[212,95740],{"className":95741,"style":355},[354],[212,95743,95745,95748,95788,95791,95794],{"className":95744},[247],[212,95746],{"className":95747,"style":11674},[251],[212,95749,95751,95754],{"className":95750},[256],[212,95752,15912],{"className":95753,"style":15961},[256,257],[212,95755,95757],{"className":95756},[478],[212,95758,95760,95780],{"className":95759},[482,483],[212,95761,95763,95777],{"className":95762},[487],[212,95764,95766],{"className":95765,"style":45129},[491],[212,95767,95768,95771],{"style":94959},[212,95769],{"className":95770,"style":500},[499],[212,95772,95774],{"className":95773},[504,505,506,507],[212,95775,82510],{"className":95776},[256,257,507],[212,95778,515],{"className":95779},[514],[212,95781,95783],{"className":95782},[487],[212,95784,95786],{"className":95785,"style":8166},[491],[212,95787],{},[212,95789],{"className":95790,"style":2785},[354],[212,95792,3497],{"className":95793},[2789],[212,95795],{"className":95796,"style":2785},[354],[212,95798,95800,95803,95806,95809,95812],{"className":95799},[247],[212,95801],{"className":95802,"style":2543},[251],[212,95804,82510],{"className":95805},[256,257],[212,95807],{"className":95808,"style":355},[354],[212,95810,1228],{"className":95811},[359],[212,95813],{"className":95814,"style":355},[354],[212,95816,95818,95821],{"className":95817},[247],[212,95819],{"className":95820,"style":2543},[251],[212,95822,1223],{"className":95823},[256],"。反例的机制很典型：TV 只控制\"总质量差\"，控制不了小测度集合上密度的巨大尖峰，而 KL 对小分母极其敏感——这正是 KL\u002Fχ² \"无界\"分歧的拓扑体现。",[11,95826,95827,95830,95831,95859,95860,60272,95926,95991,95992,23824],{},[1194,95828,95829],{},"(c)（有限字母表\u002F一致比值界下，全部等价）"," 若似然比一致有界（例如：",[212,95832,95834,95847],{"className":95833,"translate":216},[215],[212,95835,95837],{"className":95836},[220],[222,95838,95839],{"xmlns":224},[226,95840,95841,95845],{},[229,95842,95843],{},[232,95844,410],{},[236,95846,410],{"encoding":238},[212,95848,95850],{"className":95849,"ariaHidden":243},[242],[212,95851,95853,95856],{"className":95852},[247],[212,95854],{"className":95855,"style":763},[251],[212,95857,410],{"className":95858},[256,257]," 在有限字母表上且 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",[212,96959,96961,97005],{"className":96960,"translate":216},[215],[212,96962,96964],{"className":96963},[220],[222,96965,96966],{"xmlns":224},[226,96967,96968,97002],{},[229,96969,96970,96972,96974,96976,96978,96980,96988,96990,96992,97000],{},[232,96971,966],{},[307,96973,6107],{},[307,96975,427],{"stretchy":309},[312,96977,314],{},[232,96979,1138],{"mathvariant":406},[392,96981,96982,96984,96986],{},[232,96983,966],{},[232,96985,51807],{},[307,96987,4301],{},[307,96989,748],{"separator":243},[1495,96991,1497],{},[392,96993,96994,96996,96998],{},[232,96995,966],{},[232,96997,52586],{},[307,96999,4301],{},[307,97001,454],{"stretchy":309},[236,97003,97004],{"encoding":238},"t\\in[1\u002Ft_{\\min},\\,t_{\\max}]",[212,97006,97008,97026],{"className":97007,"ariaHidden":243},[242],[212,97009,97011,97014,97017,97020,97023],{"className":97010},[247],[212,97012],{"className":97013,"style":7464},[251],[212,97015,966],{"className":97016},[256,257],[212,97018],{"className":97019,"style":355},[354],[212,97021,6107],{"className":97022},[359],[212,97024],{"className":97025,"style":355},[354],[212,97027,97029,97032,97035,97038,97091,97094,97097,97100,97152],{"className":97028},[247],[212,97030],{"className":97031,"style":336},[251],[212,97033,427],{"className":97034},[343],[212,97036,8787],{"className":97037},[256],[212,97039,97041,97044],{"className":97040},[256],[212,97042,966],{"className":97043},[256,257],[212,97045,97047],{"className":97046},[478],[212,97048,97050,97083],{"className":97049},[482,483],[212,97051,97053,97080],{"className":97052},[487],[212,97054,97057],{"className":97055,"style":97056},[491],"height:0.3175em;",[212,97058,97059,97062],{"style":579},[212,97060],{"className":97061,"style":500},[499],[212,97063,97065],{"className":97064},[504,505,506,507],[212,97066,97068],{"className":97067},[256,507],[212,97069,97071,97074,97077],{"className":97070},[1682,507],[212,97072,26523],{"className":97073},[507],[212,97075,12163],{"className":97076},[507],[212,97078,82510],{"className":97079},[507],[212,97081,515],{"className":97082},[514],[212,97084,97086],{"className":97085},[487],[212,97087,97089],{"className":97088,"style":8166},[491],[212,97090],{},[212,97092,748],{"className":97093},[770],[212,97095],{"className":97096,"style":603},[354],[212,97098],{"className":97099,"style":603},[354],[212,97101,97103,97106],{"className":97102},[256],[212,97104,966],{"className":97105},[256,257],[212,97107,97109],{"className":97108},[478],[212,97110,97112,97144],{"className":97111},[482,483],[212,97113,97115,97141],{"className":97114},[487],[212,97116,97118],{"className":97117,"style":45129},[491],[212,97119,97120,97123],{"style":579},[212,97121],{"className":97122,"style":500},[499],[212,97124,97126],{"className":97125},[504,505,506,507],[212,97127,97129],{"className":97128},[256,507],[212,97130,97132,97135,97138],{"className":97131},[1682,507],[212,97133,26523],{"className":97134},[507],[212,97136,15],{"className":97137},[507],[212,97139,971],{"className":97140},[507],[212,97142,515],{"className":97143},[514],[212,97145,97147],{"className":97146},[487],[212,97148,97150],{"className":97149,"style":8166},[491],[212,97151],{},[212,97153,454],{"className":97154},[350]," 的一致 Lipschitz 性给出）。",[11,97157,97158,97159,97162],{},"也就是说，",[1194,97160,97161],{},"\"所有 f-散度诱导同一拓扑\"必须在有限\u002F紧设定或一致比值界下读","：此时它们都等价于全变差拓扑（也叫强拓扑），只是\"度量标尺\"不同；而在一般测度空间上，KL 型拓扑严格强于 TV 拓扑。这一分层对理解第 6 节 f-散度与 Wasserstein 的真正差异很重要：f-散度族的内部差异是\"强度\"差异，而它们与 Wasserstein 的差异是\"性质\"差异。",[2509,97164,97166],{"id":97165},"_48-一般不是度量","4.8 一般不是度量",[11,97168,97169],{},"f-散度一般不对称，也不满足三角不等式，因此通常不是距离度量。但某些特殊形式可以诱导出度量：",[10225,97171,97172,98683],{},[6863,97173,97174,97177,97178,97850,97852,97853,97881,97882,97955,97956,98216,98217,98622,98623,98682],{},[1194,97175,97176],{},"Hellinger 距离","是度量：",[212,97179,97181],{"className":97180,"translate":216},[377],[212,97182,97184,97288],{"className":97183,"translate":216},[215],[212,97185,97187],{"className":97186},[220],[222,97188,97189],{"xmlns":224,"display":386},[226,97190,97191,97285],{},[229,97192,97193,97199,97201,97203,97205,97207,97209,97211,97249,97251,97263,97265,97283],{},[392,97194,97195,97197],{},[232,97196,44760],{},[232,97198,34084],{},[307,97200,310],{"stretchy":309},[232,97202,403],{},[307,97204,748],{"separator":243},[232,97206,410],{},[307,97208,317],{"stretchy":309},[307,97210,320],{},[34539,97212,97213],{},[229,97214,97215,97223,97225,97227,97231,97233,97237,97243,97245,97247],{},[1453,97216,97217],{"scriptlevel":323,"displaystyle":309},[435,97218,97219,97221],{},[312,97220,314],{},[312,97222,2661],{},[307,97224,1485],{},[307,97226,310],{"stretchy":309},[34539,97228,97229],{},[232,97230,11],{},[307,97232,5011],{},[34539,97234,97235],{},[232,97236,1141],{},[7012,97238,97239,97241],{},[307,97240,317],{"stretchy":309},[312,97242,2661],{},[1495,97244,1497],{},[232,97246,441],{},[232,97248,971],{},[307,97250,320],{},[34539,97252,97253],{},[229,97254,97255,97257,97259,97261],{},[312,97256,314],{},[307,97258,5011],{},[232,97260,39491],{},[232,97262,39494],{},[307,97264,320],{},[34539,97266,97267],{},[229,97268,97269,97271,97273,97275],{},[312,97270,2661],{},[307,97272,5011],{},[312,97274,2661],{},[7751,97276,97277,97279,97281],{},[232,97278,34084],{},[1495,97280,42337],{},[312,97282,2661],{},[232,97284,4573],{"mathvariant":406},[236,97286,97287],{"encoding":238},"\\rho_H(P,Q)\n=\\sqrt{\\tfrac12\\int(\\sqrt p-\\sqrt q)^2\\,dx}\n=\\sqrt{1-BC}\n=\\sqrt{2-2H^2_{\\text{Bhattacharyya}}}.",[212,97289,97291,97364,97636,97717],{"className":97290,"ariaHidden":243},[242],[212,97292,97294,97297,97337,97340,97343,97346,97349,97352,97355,97358,97361],{"className":97293},[247],[212,97295],{"className":97296,"style":336},[251],[212,97298,97300,97303],{"className":97299},[256],[212,97301,44760],{"className":97302},[256,257],[212,97304,97306],{"className":97305},[478],[212,97307,97309,97329],{"className":97308},[482,483],[212,97310,97312,97326],{"className":97311},[487],[212,97313,97315],{"className":97314,"style":576},[491],[212,97316,97317,97320],{"style":579},[212,97318],{"className":97319,"style":500},[499],[212,97321,97323],{"className":97322},[504,505,506,507],[212,97324,34084],{"className":97325,"style":34238},[256,257,507],[212,97327,515],{"className":97328},[514],[212,97330,97332],{"className":97331},[487],[212,97333,97335],{"className":97334,"style":8166},[491],[212,97336],{},[212,97338,310],{"className":97339},[343],[212,97341,403],{"className":97342,"style":531},[256,257],[212,97344,748],{"className":97345},[770],[212,97347],{"className":97348,"style":603},[354],[212,97350,410],{"className":97351},[256,257],[212,97353,317],{"className":97354},[350],[212,97356],{"className":97357,"style":355},[354],[212,97359,320],{"className":97360},[359],[212,97362],{"className":97363,"style":355},[354],[212,97365,97367,97371,97627,97630,97633],{"className":97366},[247],[212,97368],{"className":97369,"style":97370},[251],"height:3.04em;vertical-align:-1.1572em;",[212,97372,97374],{"className":97373},[256,34567],[212,97375,97377,97619],{"className":97376},[482,483],[212,97378,97380,97616],{"className":97379},[487],[212,97381,97383,97604],{"className":97382,"style":91325},[491],[212,97384,97386,97389],{"className":97385,"style":91329},[6505],[212,97387],{"className":97388,"style":91333},[499],[212,97390,97392,97460,97463,97466,97469,97513,97516,97519,97522,97566,97595,97598,97601],{"className":97391,"style":41361},[256],[212,97393,97395,97398,97457],{"className":97394},[256],[212,97396],{"className":97397},[343,638],[212,97399,97401],{"className":97400},[435],[212,97402,97404,97449],{"className":97403},[482,483],[212,97405,97407,97446],{"className":97406},[487],[212,97408,97410,97424,97432],{"className":97409,"style":2722},[491],[212,97411,97412,97415],{"style":2725},[212,97413],{"className":97414,"style":658},[499],[212,97416,97418],{"className":97417},[504,505,506,507],[212,97419,97421],{"className":97420},[256,507],[212,97422,2661],{"className":97423},[256,507],[212,97425,97426,97429],{"style":670},[212,97427],{"className":97428,"style":658},[499],[212,97430],{"className":97431,"style":678},[677],[212,97433,97434,97437],{"style":2748},[212,97435],{"className":97436,"style":658},[499],[212,97438,97440],{"className":97439},[504,505,506,507],[212,97441,97443],{"className":97442},[256,507],[212,97444,314],{"className":97445},[256,507],[212,97447,515],{"className":97448},[514],[212,97450,97452],{"className":97451},[487],[212,97453,97455],{"className":97454,"style":2770},[491],[212,97456],{},[212,97458],{"className":97459},[350,638],[212,97461],{"className":97462,"style":603},[354],[212,97464,1485],{"className":97465,"style":1685},[1682,1683,1684],[212,97467,310],{"className":97468},[343],[212,97470,97472],{"className":97471},[256,34567],[212,97473,97475,97505],{"className":97474},[482,483],[212,97476,97478,97502],{"className":97477},[487],[212,97479,97481,97490],{"className":97480,"style":7060},[491],[212,97482,97484,97487],{"className":97483,"style":12063},[6505],[212,97485],{"className":97486,"style":658},[499],[212,97488,11],{"className":97489,"style":34587},[256,257],[212,97491,97492,97495],{"style":41550},[212,97493],{"className":97494,"style":658},[499],[212,97496,97498],{"className":97497,"style":34644},[34643],[6521,97499,97500],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,97501],{"d":34651},[212,97503,515],{"className":97504},[514],[212,97506,97508],{"className":97507},[487],[212,97509,97511],{"className":97510,"style":41570},[491],[212,97512],{},[212,97514],{"className":97515,"style":2785},[354],[212,97517,5011],{"className":97518},[2789],[212,97520],{"className":97521,"style":2785},[354],[212,97523,97525],{"className":97524},[256,34567],[212,97526,97528,97558],{"className":97527},[482,483],[212,97529,97531,97555],{"className":97530},[487],[212,97532,97534,97543],{"className":97533,"style":7060},[491],[212,97535,97537,97540],{"className":97536,"style":12063},[6505],[212,97538],{"className":97539,"style":658},[499],[212,97541,1141],{"className":97542,"style":39299},[256,257],[212,97544,97545,97548],{"style":41550},[212,97546],{"className":97547,"style":658},[499],[212,97549,97551],{"className":97550,"style":34644},[34643],[6521,97552,97553],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,97554],{"d":34651},[212,97556,515],{"className":97557},[51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就是单位球面上的欧氏距离——度量公理（对称、三角不等式）由 ",[212,98624,98626,98644],{"className":98625,"translate":216},[215],[212,98627,98629],{"className":98628},[220],[222,98630,98631],{"xmlns":224},[226,98632,98633,98641],{},[229,98634,98635],{},[7012,98636,98637,98639],{},[232,98638,22093],{},[312,98640,2661],{},[236,98642,98643],{"encoding":238},"L^2",[212,98645,98647],{"className":98646,"ariaHidden":243},[242],[212,98648,98650,98653],{"className":98649},[247],[212,98651],{"className":98652,"style":20228},[251],[212,98654,98656,98659],{"className":98655},[256],[212,98657,22093],{"className":98658},[256,257],[212,98660,98662],{"className":98661},[478],[212,98663,98665],{"className":98664},[482],[212,98666,98668],{"className":98667},[487],[212,98669,98671],{"className":98670,"style":20228},[491],[212,98672,98673,98676],{"style":7063},[212,98674],{"className":98675,"style":500},[499],[212,98677,98679],{"className":98678},[504,505,506,507],[212,98680,2661],{"className":98681},[256,507]," 距离直接继承，非退化由\"开平方是单射\"保证；",[6863,98684,98685,99001,99002,99081],{},[1194,98686,98687,98825,98826,99000],{},[212,98688,98690,98720],{"className":98689,"translate":216},[215],[212,98691,98693],{"className":98692},[220],[222,98694,98695],{"xmlns":224},[226,98696,98697,98717],{},[229,98698,98699],{},[34539,98700,98701],{},[229,98702,98703,98705,98707],{},[312,98704,2661],{},[1495,98706,1497],{},[392,98708,98709,98711],{},[232,98710,396],{},[229,98712,98713,98715],{},[232,98714,23943],{},[232,98716,25937],{},[236,98718,98719],{"encoding":238},"\\sqrt{2\\,D_{JS}}",[212,98721,98723],{"className":98722,"ariaHidden":243},[242],[212,98724,98726,98729],{"className":98725},[247],[212,98727],{"className":98728,"style":34563},[251],[212,98730,98732],{"className":98731},[256,34567],[212,98733,98735,98817],{"className":98734},[482,483],[212,98736,98738,98814],{"className":98737},[487],[212,98739,98741,98802],{"className":98740,"style":34577},[491],[212,98742,98744,98747],{"className":98743,"style":12063},[6505],[212,98745],{"className":98746,"style":658},[499],[212,98748,98750,98753,98756],{"className":98749,"style":34587},[256],[212,98751,2661],{"className":98752},[256],[212,98754],{"className":98755,"style":603},[354],[212,98757,98759,98762],{"className":98758},[256],[212,98760,396],{"className":98761,"style":474},[256,257],[212,98763,98765],{"className":98764},[478],[212,98766,98768,98794],{"className":98767},[482,483],[212,98769,98771,98791],{"className":98770},[487],[212,98772,98774],{"className":98773,"style":576},[491],[212,98775,98776,98779],{"style":495},[212,98777],{"className":98778,"style":500},[499],[212,98780,98782],{"className":98781},[504,505,506,507],[212,98783,98785,98788],{"className":98784},[256,507],[212,98786,23943],{"className":98787,"style":24353},[256,257,507],[212,98789,25937],{"className":98790,"style":26061},[256,257,507],[212,98792,515],{"className":98793},[514],[212,98795,98797],{"className":98796},[487],[212,98798,98800],{"className":98799,"style":8166},[491],[212,98801],{},[212,98803,98804,98807],{"style":34636},[212,98805],{"className":98806,"style":658},[499],[212,98808,98810],{"className":98809,"style":34644},[34643],[6521,98811,98812],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,98813],{"d":34651},[212,98815,515],{"className":98816},[514],[212,98818,98820],{"className":98819},[487],[212,98821,98823],{"className":98822,"style":34661},[491],[212,98824],{},"（等价地 ",[212,98827,98829,98857],{"className":98828,"translate":216},[215],[212,98830,98832],{"className":98831},[220],[222,98833,98834],{"xmlns":224},[226,98835,98836,98854],{},[229,98837,98838],{},[34539,98839,98840],{},[392,98841,98842,98844],{},[232,98843,396],{},[392,98845,98846,98848],{},[232,98847,234],{},[229,98849,98850,98852],{},[232,98851,23943],{},[232,98853,25937],{},[236,98855,98856],{"encoding":238},"\\sqrt{D_{f_{JS}}}",[212,98858,98860],{"className":98859,"ariaHidden":243},[242],[212,98861,98863,98867],{"className":98862},[247],[212,98864],{"className":98865,"style":98866},[251],"height:1.24em;vertical-align:-0.3564em;",[212,98868,98870],{"className":98869},[256,34567],[212,98871,98873,98991],{"className":98872},[482,483],[212,98874,98876,98988],{"className":98875},[487],[212,98877,98880,98975],{"className":98878,"style":98879},[491],"height:0.8836em;",[212,98881,98883,98886],{"className":98882,"style":83750},[6505],[212,98884],{"className":98885,"style":15046},[499],[212,98887,98889],{"className":98888,"style":41361},[256],[212,98890,98892,98895],{"className":98891},[256],[212,98893,396],{"className":98894,"style":474},[256,257],[212,98896,98898],{"className":98897},[478],[212,98899,98901,98967],{"className":98900},[482,483],[212,98902,98904,98964],{"className":98903},[487],[212,98905,98907],{"className":98906,"style":492},[491],[212,98908,98909,98912],{"style":495},[212,98910],{"className":98911,"style":500},[499],[212,98913,98915],{"className":98914},[504,505,506,507],[212,98916,98918],{"className":98917},[256,507],[212,98919,98921,98924],{"className":98920},[256,507],[212,98922,234],{"className":98923,"style":258},[256,257,507],[212,98925,98927],{"className":98926},[478],[212,98928,98930,98956],{"className":98929},[482,483],[212,98931,98933,98953],{"className":98932},[487],[212,98934,98936],{"className":98935,"style":6296},[491],[212,98937,98938,98941],{"style":30402},[212,98939],{"className":98940,"style":30406},[499],[212,98942,98944],{"className":98943},[504,30410,9872,507],[212,98945,98947,98950],{"className":98946},[256,507],[212,98948,23943],{"className":98949,"style":24353},[256,257,507],[212,98951,25937],{"className":98952,"style":26061},[256,257,507],[212,98954,515],{"className":98955},[514],[212,98957,98959],{"className":98958},[487],[212,98960,98962],{"className":98961,"style":30429},[491],[212,98963],{},[212,98965,515],{"className":98966},[514],[212,98968,98970],{"className":98969},[487],[212,98971,98973],{"className":98972,"style":522},[491],[212,98974],{},[212,98976,98978,98981],{"style":98977},"top:-2.8436em;",[212,98979],{"className":98980,"style":15046},[499],[212,98982,98984],{"className":98983,"style":83842},[34643],[6521,98985,98986],{"xmlns":6523,"width":6524,"height":83845,"viewBox":83846,"preserveAspectRatio":6527},[6529,98987],{"d":83849},[212,98989,515],{"className":98990},[514],[212,98992,98994],{"className":98993},[487],[212,98995,98998],{"className":98996,"style":98997},[491],"height:0.3564em;",[212,98999],{}," 规范化后）是度量","（Endres–Schindelin 的结论），其证明用到了 ",[212,99003,99005,99026],{"className":99004,"translate":216},[215],[212,99006,99008],{"className":99007},[220],[222,99009,99010],{"xmlns":224},[226,99011,99012,99024],{},[229,99013,99014],{},[392,99015,99016,99018],{},[232,99017,234],{},[229,99019,99020,99022],{},[232,99021,23943],{},[232,99023,25937],{},[236,99025,30955],{"encoding":238},[212,99027,99029],{"className":99028,"ariaHidden":243},[242],[212,99030,99032,99035],{"className":99031},[247],[212,99033],{"className":99034,"style":252},[251],[212,99036,99038,99041],{"className":99037},[256],[212,99039,234],{"className":99040,"style":258},[256,257],[212,99042,99044],{"className":99043},[478],[212,99045,99047,99073],{"className":99046},[482,483],[212,99048,99050,99070],{"className":99049},[487],[212,99051,99053],{"className":99052,"style":576},[491],[212,99054,99055,99058],{"style":27709},[212,99056],{"className":99057,"style":500},[499],[212,99059,99061],{"className":99060},[504,505,506,507],[212,99062,99064,99067],{"className":99063},[256,507],[212,99065,23943],{"className":99066,"style":24353},[256,257,507],[212,99068,25937],{"className":99069,"style":26061},[256,257,507],[212,99071,515],{"className":99072},[514],[212,99074,99076],{"className":99075},[487],[212,99077,99079],{"className":99078,"style":8166},[491],[212,99080],{}," 对应生成元的\"负定型\"性质。",[11,99083,99084,99085,99201,99202,99282,99283,99311,99312,99340],{},"反过来，不对称显然排除度量；即使对称，",[212,99086,99088,99108],{"className":99087,"translate":216},[215],[212,99089,99091],{"className":99090},[220],[222,99092,99093],{"xmlns":224},[226,99094,99095,99105],{},[229,99096,99097],{},[34539,99098,99099],{},[392,99100,99101,99103],{},[232,99102,396],{},[232,99104,234],{},[236,99106,99107],{"encoding":238},"\\sqrt{D_f}",[212,99109,99111],{"className":99110,"ariaHidden":243},[242],[212,99112,99114,99117],{"className":99113},[247],[212,99115],{"className":99116,"style":98866},[251],[212,99118,99120],{"className":99119},[256,34567],[212,99121,99123,99193],{"className":99122},[482,483],[212,99124,99126,99190],{"className":99125},[487],[212,99127,99129,99178],{"className":99128,"style":98879},[491],[212,99130,99132,99135],{"className":99131,"style":83750},[6505],[212,99133],{"className":99134,"style":15046},[499],[212,99136,99138],{"className":99137,"style":41361},[256],[212,99139,99141,99144],{"className":99140},[256],[212,99142,396],{"className":99143,"style":474},[256,257],[212,99145,99147],{"className":99146},[478],[212,99148,99150,99170],{"className":99149},[482,483],[212,99151,99153,99167],{"className":99152},[487],[212,99154,99156],{"className":99155,"style":492},[491],[212,99157,99158,99161],{"style":495},[212,99159],{"className":99160,"style":500},[499],[212,99162,99164],{"className":99163},[504,505,506,507],[212,99165,234],{"className":99166,"style":258},[256,257,507],[212,99168,515],{"className":99169},[514],[212,99171,99173],{"className":99172},[487],[212,99174,99176],{"className":99175,"style":522},[491],[212,99177],{},[212,99179,99180,99183],{"style":98977},[212,99181],{"className":99182,"style":15046},[499],[212,99184,99186],{"className":99185,"style":83842},[34643],[6521,99187,99188],{"xmlns":6523,"width":6524,"height":83845,"viewBox":83846,"preserveAspectRatio":6527},[6529,99189],{"d":83849},[212,99191,515],{"className":99192},[514],[212,99194,99196],{"className":99195},[487],[212,99197,99199],{"className":99198,"style":98997},[491],[212,99200],{}," 也不自动是度量。例如全变差 ",[212,99203,99205,99227],{"className":99204,"translate":216},[215],[212,99206,99208],{"className":99207},[220],[222,99209,99210],{"xmlns":224},[226,99211,99212,99224],{},[229,99213,99214],{},[392,99215,99216,99218],{},[232,99217,396],{},[229,99219,99220,99222],{},[232,99221,5590],{},[232,99223,35050],{},[236,99225,99226],{"encoding":238},"D_{TV}",[212,99228,99230],{"className":99229,"ariaHidden":243},[242],[212,99231,99233,99236],{"className":99232},[247],[212,99234],{"className":99235,"style":16161},[251],[212,99237,99239,99242],{"className":99238},[256],[212,99240,396],{"className":99241,"style":474},[256,257],[212,99243,99245],{"className":99244},[478],[212,99246,99248,99274],{"className":99247},[482,483],[212,99249,99251,99271],{"className":99250},[487],[212,99252,99254],{"className":99253,"style":576},[491],[212,99255,99256,99259],{"style":495},[212,99257],{"className":99258,"style":500},[499],[212,99260,99262],{"className":99261},[504,505,506,507],[212,99263,99265,99268],{"className":99264},[256,507],[212,99266,5590],{"className":99267,"style":531},[256,257,507],[212,99269,35050],{"className":99270,"style":2785},[256,257,507],[212,99272,515],{"className":99273},[514],[212,99275,99277],{"className":99276},[487],[212,99278,99280],{"className":99279,"style":8166},[491],[212,99281],{}," 本身就是度量，但若取某凸积 ",[212,99284,99286,99299],{"className":99285,"translate":216},[215],[212,99287,99289],{"className":99288},[220],[222,99290,99291],{"xmlns":224},[226,99292,99293,99297],{},[229,99294,99295],{},[232,99296,234],{},[236,99298,234],{"encoding":238},[212,99300,99302],{"className":99301,"ariaHidden":243},[242],[212,99303,99305,99308],{"className":99304},[247],[212,99306],{"className":99307,"style":252},[251],[212,99309,234],{"className":99310,"style":258},[256,257]," 的散度再做开方，三角不等式可能失效——这依赖 ",[212,99313,99315,99328],{"className":99314,"translate":216},[215],[212,99316,99318],{"className":99317},[220],[222,99319,99320],{"xmlns":224},[226,99321,99322,99326],{},[229,99323,99324],{},[232,99325,234],{},[236,99327,234],{"encoding":238},[212,99329,99331],{"className":99330,"ariaHidden":243},[242],[212,99332,99334,99337],{"className":99333},[247],[212,99335],{"className":99336,"style":252},[251],[212,99338,234],{"className":99339,"style":258},[256,257]," 是否落在\"负定（negative type）\"函数类中；不是自动成立的。",[11,99342,99343,99346,99347,99349,99350,99400,99401,99429,99430,99509],{},[1194,99344,99345],{},"与度量的对照结论："," f-散度的正确身份是",[1194,99348,52702],{},"（divergence）：非负、在 ",[212,99351,99353,99370],{"className":99352,"translate":216},[215],[212,99354,99356],{"className":99355},[220],[222,99357,99358],{"xmlns":224},[226,99359,99360,99368],{},[229,99361,99362,99364,99366],{},[232,99363,403],{},[307,99365,320],{},[232,99367,410],{},[236,99369,10469],{"encoding":238},[212,99371,99373,99391],{"className":99372,"ariaHidden":243},[242],[212,99374,99376,99379,99382,99385,99388],{"className":99375},[247],[212,99377],{"className":99378,"style":861},[251],[212,99380,403],{"className":99381,"style":531},[256,257],[212,99383],{"className":99384,"style":355},[354],[212,99386,320],{"className":99387},[359],[212,99389],{"className":99390,"style":355},[354],[212,99392,99394,99397],{"className":99393},[247],[212,99395],{"className":99396,"style":763},[251],[212,99398,410],{"className":99399},[256,257]," 处取零，但不要求对称与三角不等式。当我们需要真距离时（例如做收敛分析、中心化、 ",[212,99402,99404,99417],{"className":99403,"translate":216},[215],[212,99405,99407],{"className":99406},[220],[222,99408,99409],{"xmlns":224},[226,99410,99411,99415],{},[229,99412,99413],{},[232,99414,7762],{},[236,99416,7762],{"encoding":238},[212,99418,99420],{"className":99419,"ariaHidden":243},[242],[212,99421,99423,99426],{"className":99422},[247],[212,99424],{"className":99425,"style":12797},[251],[212,99427,7762],{"className":99428,"style":8465},[256,257],"-中心聚类），就从 f-散度族里挑那些 ",[212,99431,99433,99449],{"className":99432,"translate":216},[215],[212,99434,99436],{"className":99435},[220],[222,99437,99438],{"xmlns":224},[226,99439,99440,99446],{},[229,99441,99442],{},[34539,99443,99444],{},[307,99445,3497],{"lspace":1445,"rspace":1445},[236,99447,99448],{"encoding":238},"\\sqrt{\\cdot}",[212,99450,99452],{"className":99451,"ariaHidden":243},[242],[212,99453,99455,99459],{"className":99454},[247],[212,99456],{"className":99457,"style":99458},[251],"height:1.04em;vertical-align:-0.2328em;",[212,99460,99462],{"className":99461},[256,34567],[212,99463,99465,99500],{"className":99464},[482,483],[212,99466,99468,99497],{"className":99467},[487],[212,99469,99472,99484],{"className":99470,"style":99471},[491],"height:0.8072em;",[212,99473,99475,99478],{"className":99474,"style":12063},[6505],[212,99476],{"className":99477,"style":658},[499],[212,99479,99481],{"className":99480,"style":34587},[256],[212,99482,3497],{"className":99483},[256],[212,99485,99487,99490],{"style":99486},"top:-2.7672em;",[212,99488],{"className":99489,"style":658},[499],[212,99491,99493],{"className":99492,"style":34644},[34643],[6521,99494,99495],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,99496],{"d":34651},[212,99498,515],{"className":99499},[514],[212,99501,99503],{"className":99502},[487],[212,99504,99507],{"className":99505,"style":99506},[491],"height:0.2328em;",[212,99508],{}," 后成为度量的成员（Hellinger、JS、TV），或干脆换成真正的度量类（第 6 节的 IPM）。",[725,99511,99513],{"id":99512},"_5-变分表示与-f-gan","5. 变分表示与 f-GAN",[2509,99515,99517],{"id":99516},"_51-可训练目标","5.1 可训练目标",[11,99519,99520],{},"4.4 节给出精确对偶：",[212,99522,99524],{"className":99523,"translate":216},[377],[212,99525,99527,99621],{"className":99526,"translate":216},[215],[212,99528,99530],{"className":99529},[220],[222,99531,99532],{"xmlns":224,"display":386},[226,99533,99534,99618],{},[229,99535,99536,99542,99544,99546,99548,99550,99552,99554,99564,99566,99572,99574,99576,99578,99580,99582,99584,99586,99592,99594,99600,99602,99604,99606,99608,99610,99612,99614,99616],{},[392,99537,99538,99540],{},[232,99539,396],{},[232,99541,234],{},[307,99543,310],{"stretchy":309},[232,99545,403],{},[232,99547,407],{"mathvariant":406},[232,99549,410],{},[307,99551,317],{"stretchy":309},[307,99553,320],{},[6214,99555,99556,99562],{},[229,99557,99558,99560],{},[232,99559,35632],{},[307,99561,4301],{},[232,99563,4356],{},[307,99565,3096],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[392,99567,99568,99570],{},[232,99569,420],{"mathvariant":419},[232,99571,403],{},[307,99573,427],{"stretchy":309},[232,99575,4356],{},[307,99577,310],{"stretchy":309},[232,99579,795],{},[307,99581,317],{"stretchy":309},[307,99583,454],{"stretchy":309},[307,99585,5011],{},[392,99587,99588,99590],{},[232,99589,420],{"mathvariant":419},[232,99591,410],{},[307,99593,427],{"stretchy":309},[7012,99595,99596,99598],{},[232,99597,234],{},[307,99599,7771],{},[307,99601,310],{"stretchy":309},[232,99603,4356],{},[307,99605,310],{"stretchy":309},[232,99607,795],{},[307,99609,317],{"stretchy":309},[307,99611,317],{"stretchy":309},[307,99613,454],{"stretchy":309},[307,99615,3106],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[232,99617,4573],{"mathvariant":406},[236,99619,99620],{"encoding":238},"D_f(P\\|Q)\n=\\sup_{g}\\Big\\{\\mathbb E_P[g(X)]\n-\\mathbb E_Q[f^*(g(X))]\\Big\\}.",[212,99622,99624,99694,99821],{"className":99623,"ariaHidden":243},[242],[212,99625,99627,99630,99670,99673,99676,99679,99682,99685,99688,99691],{"className":99626},[247],[212,99628],{"className":99629,"style":467},[251],[212,99631,99633,99636],{"className":99632},[256],[212,99634,396],{"className":99635,"style":474},[256,257],[212,99637,99639],{"className":99638},[478],[212,99640,99642,99662],{"className":99641},[482,483],[212,99643,99645,99659],{"className":99644},[487],[212,99646,99648],{"className":99647,"style":492},[491],[212,99649,99650,99653],{"style":495},[212,99651],{"className":99652,"style":500},[499],[212,99654,99656],{"className":99655},[504,505,506,507],[212,99657,234],{"className":99658,"style":258},[256,257,507],[212,99660,515],{"className":99661},[514],[212,99663,99665],{"className":99664},[487],[212,99666,99668],{"className":99667,"style":522},[491],[212,99669],{},[212,99671,310],{"className":99672},[343],[212,99674,403],{"className":99675,"style":531},[256,257],[212,99677,407],{"className":99678},[256],[212,99680,410],{"className":99681},[256,257],[212,99683,317],{"className":99684},[350],[212,99686],{"className":99687,"style":355},[354],[212,99689,320],{"className":99690},[359],[212,99692],{"className":99693,"style":355},[354],[212,99695,99697,99701,99748,99751,99757,99797,99800,99803,99806,99809,99812,99815,99818],{"className":99696},[247],[212,99698],{"className":99699,"style":99700},[251],"height:2.1805em;vertical-align:-1.0305em;",[212,99702,99704],{"className":99703},[1682,13916],[212,99705,99707,99740],{"className":99706},[482,483],[212,99708,99710,99737],{"className":99709},[487],[212,99711,99713,99727],{"className":99712,"style":2543},[491],[212,99714,99715,99718],{"style":61400},[212,99716],{"className":99717,"style":658},[499],[212,99719,99721],{"className":99720},[504,505,506,507],[212,99722,99724],{"className":99723},[256,507],[212,99725,4356],{"className":99726,"style":1178},[256,257,507],[212,99728,99729,99732],{"style":12063},[212,99730],{"className":99731,"style":658},[499],[212,99733,99734],{},[212,99735,35632],{"className":99736},[1682],[212,99738,515],{"className":99739},[514],[212,99741,99743],{"className":99742},[487],[212,99744,99746],{"className":99745,"style":61432},[491],[212,99747],{},[212,99749],{"className":99750,"style":603},[354],[212,99752,99754],{"className":99753},[256],[212,99755,3096],{"className":99756},[616,3918],[212,99758,99760,99763],{"className":99759},[256],[212,99761,420],{"className":99762},[256,563],[212,99764,99766],{"className":99765},[478],[212,99767,99769,99789],{"className":99768},[482,483],[212,99770,99772,99786],{"className":99771},[487],[212,99773,99775],{"className":99774,"style":576},[491],[212,99776,99777,99780],{"style":579},[212,99778],{"className":99779,"style":500},[499],[212,99781,99783],{"className":99782},[504,505,506,507],[212,99784,403],{"className":99785,"style":531},[256,257,507],[212,99787,515],{"className":99788},[514],[212,99790,99792],{"className":99791},[487],[212,99793,99795],{"className":99794,"style":8166},[491],[212,99796],{},[212,99798,427],{"className":99799},[343],[212,99801,4356],{"className":99802,"style":1178},[256,257],[212,99804,310],{"className":99805},[343],[212,99807,795],{"className":99808,"style":9085},[256,257],[212,99810,20590],{"className":99811},[350],[212,99813],{"className":99814,"style":2785},[354],[212,99816,5011],{"className":99817},[2789],[212,99819],{"className":99820,"style":2785},[354],[212,99822,99824,99827,99867,99870,99899,99902,99905,99908,99911,99915,99921],{"className":99823},[247],[212,99825],{"className":99826,"style":68327},[251],[212,99828,99830,99833],{"className":99829},[256],[212,99831,420],{"className":99832},[256,563],[212,99834,99836],{"className":99835},[478],[212,99837,99839,99859],{"className":99838},[482,483],[212,99840,99842,99856],{"className":99841},[487],[212,99843,99845],{"className":99844,"style":576},[491],[212,99846,99847,99850],{"style":579},[212,99848],{"className":99849,"style":500},[499],[212,99851,99853],{"className":99852},[504,505,506,507],[212,99854,410],{"className":99855},[256,257,507],[212,99857,515],{"className":99858},[514],[212,99860,99862],{"className":99861},[487],[212,99863,99865],{"className":99864,"style":522},[491],[212,99866],{},[212,99868,427],{"className":99869},[343],[212,99871,99873,99876],{"className":99872},[256],[212,99874,234],{"className":99875,"style":258},[256,257],[212,99877,99879],{"className":99878},[478],[212,99880,99882],{"className":99881},[482],[212,99883,99885],{"className":99884},[487],[212,99886,99888],{"className":99887,"style":8446},[491],[212,99889,99890,99893],{"style":8475},[212,99891],{"className":99892,"style":500},[499],[212,99894,99896],{"className":99895},[504,505,506,507],[212,99897,7771],{"className":99898},[2789,507],[212,99900,310],{"className":99901},[343],[212,99903,4356],{"className":99904,"style":1178},[256,257],[212,99906,310],{"className":99907},[343],[212,99909,795],{"clas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是数据分布、",[212,99956,99958,99971],{"className":99957,"translate":216},[215],[212,99959,99961],{"className":99960},[220],[222,99962,99963],{"xmlns":224},[226,99964,99965,99969],{},[229,99966,99967],{},[232,99968,410],{},[236,99970,410],{"encoding":238},[212,99972,99974],{"className":99973,"ariaHidden":243},[242],[212,99975,99977,99980],{"className":99976},[247],[212,99978],{"className":99979,"style":763},[251],[212,99981,410],{"className":99982},[256,257]," 是生成分布时，右端可直接用两批样本做蒙特卡洛估计，得到 ",[212,99985,99987,100004],{"className":99986,"translate":216},[215],[212,99988,99990],{"className":99989},[220],[222,99991,99992],{"xmlns":224},[226,99993,99994,100002],{},[229,99995,99996],{},[392,99997,99998,100000],{},[232,99999,396],{},[232,100001,234],{},[236,100003,4220],{"encoding":238},[212,100005,100007],{"className":100006,"ariaHidden":243},[242],[212,100008,100010,100013],{"className":100009},[247],[212,100011],{"className":100012,"style":4230},[251],[212,100014,100016,100019],{"className":100015},[256],[212,100017,396],{"className":100018,"style":474},[256,257],[212,100020,100022],{"className":100021},[478],[212,100023,100025,100045],{"className":100024},[482,483],[212,100026,100028,100042],{"className":100027},[487],[212,100029,100031],{"className":100030,"style":492},[491],[212,100032,100033,100036],{"style":495},[212,100034],{"className":100035,"style":500},[499],[212,100037,100039],{"className":100038},[504,505,506,507],[212,100040,234],{"className":100041,"style":258},[256,257,507],[212,100043,515],{"className":100044},[514],[212,100046,100048],{"className":100047},[487],[212,100049,100051],{"className":100050,"style":522},[491],[212,100052],{}," 的一个",[1194,100055,100056],{},"下界","，并用一个网络 ",[212,100059,100061,100080],{"className":100060,"translate":216},[215],[212,100062,100064],{"className":100063},[220],[222,100065,100066],{"xmlns":224},[226,100067,100068,100077],{},[229,100069,100070],{},[392,100071,100072,100074],{},[232,100073,4356],{},[232,100075,100076],{},"ω",[236,100078,100079],{"encoding":238},"g_\\omega",[212,100081,100083],{"className":100082,"ariaHidden":243},[242],[212,100084,100086,100089],{"className":100085},[247],[212,100087],{"className":100088,"style":2474},[251],[212,100090,100092,100095],{"className":100091},[256],[212,100093,4356],{"className":100094,"style":1178},[256,257],[212,100096,100098],{"className":100097},[478],[212,100099,100101,100121],{"className":100100},[482,483],[212,100102,100104,100118],{"className":100103},[487],[212,100105,100107],{"className":100106,"style":45129},[491],[212,100108,100109,100112],{"style":19043},[212,100110],{"className":100111,"style":500},[499],[212,100113,100115],{"className":100114},[504,505,506,507],[212,100116,100076],{"className":100117,"style":1178},[256,257,507],[212,100119,515],{"className":100120},[514],[212,100122,100124],{"className":100123},[487],[212,100125,100127],{"className":100126,"style":8166},[491],[212,100128],{}," 逼近最优解。于是",[212,100131,100133],{"className":100132,"translate":216},[377],[212,100134,100136,100266],{"className":100135,"translate":216},[215],[212,100137,100139],{"className":100138},[220],[222,100140,100141],{"xmlns":224,"display":386},[226,100142,100143,100263],{},[229,100144,100145,100156,100158,100160,100162,100164,100166,100172,100174,100176,100182,100196,100202,100204,100210,100212,100214,100220,100235,100241,100243,100249,100251,100257,100259,100261],{},[392,100146,100147,100154],{},[12011,100148,100149,100151],{"accent":243},[232,100150,396],{},[307,100152,100153],{"stretchy":243},"^",[232,100155,234],{},[307,100157,310],{"stretchy":309},[232,100159,403],{},[232,100161,407],{"mathvariant":406},[232,100163,410],{},[307,100165,34075],{"separator":243},[392,100167,100168,100170],{},[232,100169,4356],{},[232,100171,100076],{},[307,100173,317],{"stretchy":309},[307,100175,320],{},[435,100177,100178,100180],{},[312,100179,314],{},[232,100181,82510],{},[48519,100183,100184,100186,100194],{},[307,100185,13661],{},[229,100187,100188,100190,100192],{},[232,100189,12163],{},[307,100191,320],{},[312,100193,314],{},[232,100195,82510],{},[392,100197,100198,100200],{},[232,100199,4356],{},[232,100201,100076],{},[307,100203,310],{"stretchy":309},[392,100205,100206,100208],{},[232,100207,971],{},[232,100209,12163],{},[307,100211,317],{"stretchy":309},[307,100213,5011],{},[435,100215,100216,100218],{},[312,100217,314],{},[232,100219,26523],{},[48519,100221,100222,100224,100233],{},[307,100223,13661],{},[229,100225,100226,100229,100231],{},[232,100227,100228],{},"j",[307,100230,320],{},[312,100232,314],{},[232,100234,26523],{},[7012,100236,100237,100239],{},[232,100238,234],{},[307,100240,7771],{},[307,100242,310],{"stretchy":309},[392,100244,100245,100247],{},[232,100246,4356],{},[232,100248,100076],{},[307,100250,310],{"stretchy":309},[392,100252,100253,100255],{},[232,100254,40437],{},[232,100256,100228],{},[307,100258,317],{"stretchy":309},[307,100260,317],{"stretchy":309},[232,100262,4573],{"mathvariant":406},[236,100264,100265],{"encoding":238},"\\widehat D_f(P\\|Q;g_\\omega)\n=\\frac1n\\sum_{i=1}^n g_\\omega(x_i)\n-\\frac1m\\sum_{j=1}^m f^*(g_\\omega(y_j)).",[212,100267,100269,100422,100658],{"className":100268,"ariaHidden":243},[242],[212,100270,100272,100276,100352,100355,100358,100361,100364,100367,100370,100410,100413,100416,100419],{"className":100271},[247],[212,100273],{"className":100274,"style":100275},[251],"height:1.2094em;vertical-align:-0.2861em;",[212,100277,100279,100318],{"className":100278},[256],[212,100280,100282],{"className":100281},[256,12051],[212,100283,100285],{"className":100284},[482],[212,100286,100288],{"className":100287},[487],[212,100289,100292,100300],{"className":100290,"style":100291},[491],"height:0.9233em;",[212,100293,100294,100297],{"style":12063},[212,100295],{"className":100296,"style":658},[499],[212,100298,396],{"className":100299,"style":474},[256,257],[212,100301,100304,100307],{"className":100302,"style":100303},[6505],"width:calc(100% - 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的最优解为",[212,101642,101644],{"className":101643,"translate":216},[377],[212,101645,101647,101711],{"className":101646,"translate":216},[215],[212,101648,101650],{"className":101649},[220],[222,101651,101652],{"xmlns":224,"display":386},[226,101653,101654,101708],{},[229,101655,101656,101662,101664,101666,101668,101670,101676,101678,101706],{},[7012,101657,101658,101660],{},[232,101659,4356],{},[307,101661,7771],{},[307,101663,310],{"stretchy":309},[232,101665,971],{},[307,101667,317],{"stretchy":309},[307,101669,320],{},[7012,101671,101672,101674],{},[232,101673,234],{},[307,101675,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[1495,101677,1502],{},[229,101679,101680,101682,101704],{},[307,101681,310],{"fence":243},[435,101683,101684,101694],{},[229,101685,101686,101688,101690,101692],{},[232,101687,11],{},[307,101689,310],{"stretchy":309},[232,101691,971],{},[307,101693,317],{"stretchy":309},[229,101695,101696,101698,101700,101702],{},[232,101697,1141],{},[307,101699,310],{"stretchy":309},[232,101701,971],{},[307,101703,317],{"stretchy":309},[307,101705,317],{"fence":243},[307,101707,748],{"separator":243},[236,101709,101710],{"encoding":238},"g^*(x)=f'\\!\\left(\\frac{p(x)}{q(x)}\\right),",[212,101712,101714,101767],{"className":101713,"ariaHidden":243},[242],[212,101715,101717,101720,101749,101752,101755,101758,101761,101764],{"className":101716},[247],[212,101718],{"className":101719,"style":336},[251],[212,101721,101723,101726],{"className":101722},[256],[212,101724,4356],{"className":101725,"style":1178},[256,257],[212,101727,101729],{"className":101728},[478],[212,101730,101732],{"className":101731},[482],[212,101733,101735],{"className":101734},[487],[212,101736,101738],{"className":101737,"style":8446},[491],[212,101739,101740,101743],{"style":8475},[212,101741],{"className":101742,"style":500},[499],[212,101744,101746],{"className":101745},[504,505,506,507],[212,101747,7771],{"className":101748},[2789,507],[212,101750,310],{"className":101751},[343],[212,101753,971],{"className":101754},[256,257],[212,101756,317],{"className":101757},[350],[212,101759],{"className":101760,"style":355},[354],[212,101762,320],{"className":101763},[359],[212,101765],{"className":101766,"style":355},[354],[212,101768,101770,101773,101805,101808,101811,101906,101909],{"className":101769},[247],[212,101771],{"className":101772,"style":556},[251],[212,101774,101776,101779],{"className":101775},[256],[212,101777,234],{"className":101778,"style":258},[256,257],[212,101780,101782],{"className":101781},[478],[212,101783,101785],{"className":101784},[482],[212,101786,101788],{"className":101787},[487],[212,101789,101791],{"className":101790,"style":29171},[491],[212,101792,101793,101796],{"style":8475},[212,101794],{"className":101795,"style":500},[499],[212,101797,101799],{"className":101798},[504,505,506,507],[212,101800,101802],{"className":101801},[256,507],[212,101803,7018],{"className":101804},[256,507],[212,101806],{"className":101807,"style":1710},[354],[212,101809],{"className":101810,"style":603},[354],[212,101812,101814,101820,101900],{"className":101813},[607],[212,101815,101817],{"className":101816,"style":612},[343,611],[212,101818,310],{"className":101819},[616,506],[212,101821,101823,101826,101897],{"className":101822},[256],[212,101824],{"className":101825},[343,638],[212,101827,101829],{"className":101828},[435],[212,101830,101832,101889],{"className":101831},[482,483],[212,101833,101835,101886],{"className":101834},[487],[212,101836,101838,101858,101866],{"className":101837,"style":1741},[491],[212,101839,101840,101843],{"style":654},[212,101841],{"className":101842,"style":658},[499],[212,101844,101846,101849,101852,101855],{"className":101845},[256],[212,101847,1141],{"className":101848,"style":1178},[256,257],[212,101850,310],{"className":101851},[343],[212,101853,971],{"className":101854},[256,257],[212,101856,317],{"className":101857},[350],[212,101859,101860,101863],{"style":670},[212,101861],{"className":101862,"style":658},[499],[212,101864],{"className":101865,"style":678},[677],[212,101867,101868,101871],{"style":681},[212,101869],{"className":101870,"style":658},[499],[212,101872,101874,101877,101880,101883],{"className":101873},[256],[212,101875,11],{"className":101876},[256,257],[212,101878,310],{"className":101879},[343],[212,101881,971],{"className":101882},[256,257],[212,101884,317],{"className":101885},[350],[212,101887,515],{"className":101888},[514],[212,101890,101892],{"className":101891},[487],[212,101893,101895],{"className":101894,"style":1799},[491],[212,101896],{},[212,101898],{"className":101899},[350,638],[212,101901,101903],{"className":101902,"style":612},[350,611],[212,101904,317],{"className":101905},[616,506],[212,101907],{"className":101908,"style":603},[354],[212,101910,748],{"className":101911},[770],[11,101913,101914,101915,101977],{},"即判别器学到的量是似然比经 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之后的取值。",[11,101979,101980,101982,101983,102027,102028,102191,102192,102235],{},[1194,101981,55672],{}," 目标对 ",[212,101984,101986,102006],{"className":101985,"translate":216},[215],[212,101987,101989],{"className":101988},[220],[222,101990,101991],{"xmlns":224},[226,101992,101993,102003],{},[229,101994,101995,101997,101999,102001],{},[232,101996,4356],{},[307,101998,310],{"stretchy":309},[232,102000,971],{},[307,102002,317],{"stretchy":309},[236,102004,102005],{"encoding":238},"g(x)",[212,102007,102009],{"className":102008,"ariaHidden":243},[242],[212,102010,102012,102015,102018,102021,102024],{"className":102011},[247],[212,102013],{"className":102014,"style":336},[251],[212,102016,4356],{"className":102017,"style":1178},[256,257],[212,102019,310],{"className":102020},[343],[212,102022,971],{"className":102023},[256,257],[212,102025,317],{"className":102026},[350]," 的逐点依赖是 ",[212,102029,102031,102087],{"className":102030,"translate":216},[215],[212,102032,102034],{"className":102033},[220],[222,102035,102036],{"xmlns":224},[226,102037,102038,102084],{},[229,102039,102040,102042,102044,102046,102048,102050,102052,102054,102056,102058,102060,102062,102064,102066,102072,102074,102076,102078,102080,102082],{},[232,102041,11],{},[307,102043,310],{"stretchy":309},[232,102045,971],{},[307,102047,317],{"stretchy":309},[232,102049,4356],{},[307,102051,310],{"stretchy":309},[232,102053,971],{},[307,102055,317],{"stretchy":309},[307,102057,5011],{},[232,102059,1141],{},[307,102061,310],{"stretchy":309},[232,102063,971],{},[307,102065,317],{"stretchy":309},[7012,102067,102068,102070],{},[232,102069,234],{},[307,102071,7771],{},[307,102073,310],{"stretchy":309},[232,102075,4356],{},[307,102077,310],{"stretchy":309},[232,102079,971],{},[307,102081,317],{"stretchy":309},[307,102083,317],{"stretchy":309},[236,102085,102086],{"encoding":238},"p(x)g(x)-q(x)f^*(g(x))",[212,102088,102090,102129],{"className":102089,"ariaHidden":243},[242],[212,102091,102093,102096,102099,102102,102105,102108,102111,102114,102117,102120,102123,102126],{"className":102092},[247],[212,102094],{"className":102095,"style":336},[251],[212,102097,11],{"className":102098},[256,257],[212,102100,310],{"className":102101},[343],[212,102103,971],{"className":102104},[256,257],[212,102106,317],{"className":102107},[350],[212,102109,4356],{"className":102110,"style":1178},[256,257],[212,102112,310],{"className":102113},[343],[212,102115,971],{"className":102116},[256,257],[212,102118,317],{"className":102119},[350],[212,102121],{"className":102122,"style":2785},[354],[212,102124,5011],{"className":102125},[2789],[212,102127],{"className":102128,"style":2785},[354],[212,102130,102132,102135,102138,102141,102144,102147,102176,102179,102182,102185,102188],{"className":102131},[247],[212,102133],{"className":102134,"style":336},[251],[212,102136,1141],{"className":102137,"style":1178},[256,257],[212,102139,310],{"className":102140},[343],[212,102142,971],{"className":102143},[256,257],[212,102145,317],{"className":102146},[350],[212,102148,102150,102153],{"className":102149},[256],[212,102151,234],{"className":102152,"style":258},[256,257],[212,102154,102156],{"className":102155},[478],[212,102157,102159],{"className":102158},[482],[212,102160,102162],{"className":102161},[487],[212,102163,102165],{"className":102164,"style":8697},[491],[212,102166,102167,102170],{"style":7063},[212,102168],{"className":102169,"style":500},[499],[212,102171,102173],{"className":102172},[504,505,506,507],[212,102174,7771],{"className":102175},[2789,507],[212,102177,310],{"className":102178},[343],[212,102180,4356],{"className":102181,"style":1178},[256,257],[212,102183,310],{"className":102184},[343],[212,102186,971],{"className":102187},[256,257],[212,102189,19247],{"className":102190},[350],"，对 ",[212,102193,102195,102214],{"className":102194,"translate":216},[215],[212,102196,102198],{"className":102197},[220],[222,102199,102200],{"xmlns":224},[226,102201,102202,102212],{},[229,102203,102204,102206,102208,102210],{},[232,102205,4356],{},[307,102207,310],{"stretchy":309},[232,102209,971],{},[307,102211,317],{"stretchy":309},[236,102213,102005],{"encoding":238},[212,102215,102217],{"className":102216,"ariaHidden":243},[242],[212,102218,102220,102223,102226,102229,102232],{"className":102219},[247],[212,102221],{"className":102222,"style":336},[251],[212,102224,4356],{"className":102225,"style":1178},[256,257],[212,102227,310],{"className":102228},[343],[212,102230,971],{"className":102231},[256,257],[212,102233,317],{"className":102234},[350]," 求导：",[212,102237,102239],{"className":102238,"translate":216},[377],[212,102240,102242,102362],{"className":102241,"translate":216},[215],[212,102243,102245],{"className":102244},[220],[222,102246,102247],{"xmlns":224,"display":386},[226,102248,102249,102359],{},[229,102250,102251,102253,102255,102257,102259,102261,102263,102265,102267,102269,102271,102281,102283,102285,102287,102289,102291,102293,102295,102297,102299,102301,102303,102313,102315,102321,102323,102325,102327,102329,102331,102353,102355,102357],{},[232,102252,11],{},[307,102254,310],{"stretchy":309},[232,102256,971],{},[307,102258,317],{"stretchy":309},[307,102260,5011],{},[232,102262,1141],{},[307,102264,310],{"stretchy":309},[232,102266,971],{},[307,102268,317],{"stretchy":309},[1495,102270,1497],{},[7012,102272,102273,102275],{},[232,102274,234],{},[229,102276,102277,102279],{},[307,102278,7771],{},[307,102280,7018],{"mathvariant":406},[307,102282,310],{"stretchy":309},[232,102284,4356],{},[307,102286,310],{"stretchy":309},[232,102288,971],{},[307,102290,317],{"stretchy":309},[307,102292,317],{"stretchy":309},[307,102294,320],{},[312,102296,323],{},[1495,102298,4481],{},[307,102300,4484],{},[1495,102302,4481],{},[7012,102304,102305,102307],{},[232,102306,234],{},[229,102308,102309,102311],{},[307,102310,7771],{},[307,102312,7018],{"mathvariant":406},[307,102314,310],{"stretchy":309},[7012,102316,102317,102319],{},[232,102318,4356],{},[307,102320,7771],{},[307,102322,310],{"stretchy":309},[232,102324,971],{},[307,102326,317],{"stretchy":309},[307,102328,317],{"stretchy":309},[307,102330,320],{},[435,102332,102333,102343],{},[229,102334,102335,102337,102339,102341],{},[232,102336,11],{},[307,102338,310],{"stretchy":309},[232,102340,971],{},[307,102342,317],{"stretchy":309},[229,102344,102345,102347,102349,102351],{},[232,102346,1141],{},[307,102348,310],{"stretchy":309},[232,102350,971],{},[307,102352,317],{"stretchy":309},[307,102354,320],{},[232,102356,966],{},[232,102358,4573],{"mathvariant":406},[236,102360,102361],{"encoding":238},"p(x)-q(x)\\,f^{*\\prime}(g(x))=0\n\\ \\Longrightarrow\\\nf^{*\\prime}(g^*(x))=\\frac{p(x)}{q(x)}=t .",[212,102363,102365,102392,102473,102497,102588,102684],{"className":102364,"ariaHidden":243},[242],[212,102366,102368,102371,102374,102377,102380,102383,102386,102389],{"className":102367},[247],[212,102369],{"className":102370,"style":336},[251],[212,102372,11],{"className":102373},[256,257],[212,102375,310],{"className":102376},[343],[212,102378,971],{"className":102379},[256,257],[212,102381,317],{"className":102382},[350],[212,102384],{"className":102385,"style":2785},[354],[212,102387,5011],{"className":102388},[2789],[212,102390],{"className":102391,"style":2785},[354],[212,102393,102395,102399,102402,102405,102408,102411,102414,102449,102452,102455,102458,102461,102464,102467,102470],{"className":102394},[247],[212,102396],{"className":102397,"style":102398},[251],"height:1.0519em;vertical-align:-0.25em;",[212,102400,1141],{"className":102401,"style":1178},[256,257],[212,102403,310],{"className":102404},[343],[212,102406,971],{"className":102407},[256,257],[212,102409,317],{"className":102410},[350],[212,102412],{"className":102413,"style":603},[354],[212,102415,102417,102420],{"className":102416},[256],[212,102418,234],{"className":102419,"style":258},[256,257],[212,102421,102423],{"className":102422},[478],[212,102424,102426],{"className":102425},[482],[212,102427,102429],{"className":102428},[487],[212,102430,102432],{"className":102431,"style":29171},[491],[212,102433,102434,102437],{"style":8475},[212,102435],{"className":102436,"style":500},[499],[212,102438,102440],{"className":102439},[504,505,506,507],[212,102441,102443,102446],{"className":102442},[256,507],[212,102444,7771],{"className":102445},[256,507],[212,102447,7018],{"className":102448},[256,507],[212,102450,310],{"className":102451},[343],[212,102453,4356],{"className":102454,"style":1178},[256,257],[212,102456,310],{"className":102457},[343],[212,102459,971],{"className":102460},[256,257],[212,102462,19247],{"className":102463},[350],[212,102465],{"className":102466,"style":355},[354],[212,102468,320],{"className":102469},[359],[212,102471],{"className":102472,"style":355},[354],[212,102474,102476,102479,102482,102485,102488,102491,102494],{"className":102475},[247],[212,102477],{"className":102478,"style":92999},[251],[212,102480,323],{"className":102481},[256],[212,102483,4481],{"className":102484},[354],[212,102486],{"className":102487,"style":355},[354],[212,102489,4484],{"className":102490},[359],[212,102492,4481],{"className":102493},[354],[212,102495],{"className":102496,"style":355},[354],[212,102498,102500,102503,102538,102541,102570,102573,102576,102579,102582,102585],{"className":102499},[247],[212,102501],{"className":102502,"style":102398},[251],[212,102504,102506,102509],{"className":102505},[256],[212,102507,234],{"className":102508,"style":258},[256,257],[212,102510,102512],{"className":102511},[478],[212,102513,102515],{"className":102514},[482],[212,102516,102518],{"className":102517},[487],[212,102519,102521],{"className":102520,"style":29171},[491],[212,102522,102523,102526],{"style":8475},[212,102524],{"className":102525,"style":500},[499],[212,102527,102529],{"className":102528},[504,505,506,507],[212,102530,102532,102535],{"className":102531},[256,507],[212,102533,7771],{"className":102534},[256,507],[212,102536,7018],{"className":102537},[256,507],[212,102539,310],{"className":102540},[343],[212,102542,102544,102547],{"className":102543},[256],[212,102545,4356],{"className":102546,"style":1178},[256,257],[212,102548,102550],{"className":102549},[478],[212,102551,102553],{"className":102552},[482],[212,102554,102556],{"className":102555},[487],[212,102557,102559],{"className":102558,"style":8446},[491],[212,102560,102561,102564],{"style":8475},[212,102562],{"className":102563,"style":500},[499],[212,102565,102567],{"className":102566},[504,505,506,507],[212,102568,7771],{"className":102569},[2789,507],[212,102571,310],{"className":102572},[343],[212,102574,971],{"className":102575},[256,257],[212,102577,19247],{"className":102578},[350],[212,102580],{"className":102581,"style":355},[354],[212,102583,320],{"className":102584},[359],[212,102586],{"className":102587,"style":355},[354],[212,102589,102591,102595,102675,102678,102681],{"className":102590},[247],[212,102592],{"className":102593,"style":102594},[251],"height:2.363em;vertical-align:-0.936em;",[212,102596,102598,102601,102672],{"className":102597},[256],[212,102599],{"className":102600},[343,638],[212,102602,102604],{"className":102603},[435],[212,102605,102607,102664],{"className":102606},[482,483],[212,102608,102610,102661],{"className":102609},[487],[212,102611,102613,102633,102641],{"className":102612,"style":1741},[491],[212,102614,102615,102618],{"style":654},[212,102616],{"className":102617,"style":658},[499],[212,102619,102621,102624,102627,102630],{"className":102620},[256],[212,102622,1141],{"className":102623,"style":1178},[256,257],[212,102625,310],{"className":102626},[343],[212,102628,971],{"className":102629},[256,257],[212,102631,317],{"className":102632},[350],[212,102634,102635,102638],{"style":670},[212,102636],{"className":102637,"style":658},[499],[212,102639],{"className":102640,"style":678},[677],[212,102642,102643,102646],{"style":681},[212,102644],{"className":102645,"style":658},[499],[212,102647,102649,102652,102655,102658],{"className":102648},[256],[212,102650,11],{"className":102651},[256,257],[212,102653,310],{"className":102654},[343],[212,102656,971],{"className":102657},[256,257],[212,102659,317],{"className":102660},[350],[212,102662,515],{"className":102663},[514],[212,102665,102667],{"className":102666},[487],[212,102668,102670],{"className":102669,"style":1799},[491],[212,102671],{},[212,102673],{"className":102674},[350,638],[212,102676],{"className":102677,"style":355},[354],[212,102679,320],{"className":102680},[359],[212,102682],{"className":102683,"style":355},[354],[212,102685,102687,102690,102693],{"className":102686},[247],[212,102688],{"className":102689,"style":5541},[251],[212,102691,966],{"className":102692},[256,257],[212,102694,4573],{"className":102695},[256],[11,102697,34292,102698,102905,102906,103062,103063,103121,103122,103216,103217,103220,103221,103290,103291,103372,103373,103401],{},[212,102699,102701,102747],{"className":102700,"translate":216},[215],[212,102702,102704],{"className":102703},[220],[222,102705,102706],{"xmlns":224},[226,102707,102708,102744],{},[229,102709,102710,102712,102718,102724,102726,102728,102734],{},[307,102711,310],{"stretchy":309},[7012,102713,102714,102716],{},[232,102715,234],{},[307,102717,7771],{},[7012,102719,102720,102722],{},[307,102721,317],{"stretchy":309},[307,102723,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,102725,320],{},[307,102727,310],{"stretchy":309},[7012,102729,102730,102732],{},[232,102731,234],{},[307,102733,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[7012,102735,102736,102738],{},[307,102737,317],{"stretchy":309},[229,102739,102740,102742],{},[307,102741,5011],{},[312,102743,314],{},[236,102745,102746],{"encoding":238},"(f^*)'=(f')^{-1}",[212,102748,102750,102829],{"className":102749,"ariaHidden":243},[242],[212,102751,102753,102756,102759,102788,102820,102823,102826],{"className":102752},[247],[212,102754],{"className":102755,"style":7041},[251],[212,102757,310],{"className":102758},[343],[212,102760,102762,102765],{"className":102761},[256],[212,102763,234],{"className":102764,"style":258},[256,257],[212,102766,102768],{"className":102767},[478],[212,102769,102771],{"className":102770},[482],[212,102772,102774],{"className":102773},[487],[212,102775,102777],{"className":102776,"style":8697},[491],[212,102778,102779,102782],{"style":7063},[212,102780],{"className":102781,"style":500},[499],[212,102783,102785],{"className":102784},[504,505,506,507],[212,102786,7771],{"className":102787},[2789,507],[212,102789,102791,102794],{"className":102790},[350],[212,102792,317],{"className":102793},[350],[212,102795,102797],{"className":102796},[478],[212,102798,102800],{"className":102799},[482],[212,102801,102803],{"className":102802},[487],[212,102804,102806],{"className":102805,"style":7060},[491],[212,102807,102808,102811],{"style":7063},[212,102809],{"className":102810,"style":500},[499],[212,102812,102814],{"className":102813},[504,505,506,507],[212,102815,102817],{"className":102816},[256,507],[212,102818,7018],{"className":102819},[256,507],[212,102821],{"className":102822,"style":355},[354],[212,102824,320],{"className":102825},[359],[212,102827],{"className":102828,"style":355},[354],[212,102830,102832,102835,102838,102870],{"className":102831},[247],[212,102833],{"className":102834,"style":20203},[251],[212,102836,310],{"className":102837},[343],[212,102839,102841,102844],{"className":102840},[256],[212,102842,234],{"className":102843,"style":258},[256,257],[212,102845,102847],{"className":102846},[478],[212,102848,102850],{"className":102849},[482],[212,102851,102853],{"className":102852},[487],[212,102854,102856],{"className":102855,"style":7060},[491],[212,102857,102858,102861],{"style":7063},[212,102859],{"className":102860,"style":500},[499],[212,102862,102864],{"className":102863},[504,505,506,507],[212,102865,102867],{"className":102866},[256,507],[212,102868,7018],{"className":102869},[256,507],[212,102871,102873,102876],{"className":102872},[350],[212,102874,317],{"className":102875},[350],[212,102877,102879],{"className":102878},[478],[212,102880,102882],{"className":102881},[482],[212,102883,102885],{"className":102884},[487],[212,102886,102888],{"className":102887,"style":20228},[491],[212,102889,102890,102893],{"style":7063},[212,102891],{"className":102892,"style":500},[499],[212,102894,102896],{"className":102895},[504,505,506,507],[212,102897,102899,102902],{"className":102898},[256,507],[212,102900,5011],{"className":102901},[256,507],[212,102903,314],{"className":102904},[256,507],"（Fenchel 的互逆关系），即得 ",[212,102907,102909,102953],{"className":102908,"translate":216},[215],[212,102910,102912],{"className":102911},[220],[222,102913,102914],{"xmlns":224},[226,102915,102916,102950],{},[229,102917,102918,102924,102926,102928,102930,102932,102938,102940,102942,102944,102946,102948],{},[7012,102919,102920,102922],{},[232,102921,4356],{},[307,102923,7771],{},[307,102925,310],{"stretchy":309},[232,102927,971],{},[307,102929,317],{"stretchy":309},[307,102931,320],{},[7012,102933,102934,102936],{},[232,102935,234],{},[307,102937,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,102939,310],{"stretchy":309},[232,102941,966],{},[307,102943,310],{"stretchy":309},[232,102945,971],{},[307,102947,317],{"stretchy":309},[307,102949,317],{"stretchy":309},[236,102951,102952],{"encoding":238},"g^*(x)=f'(t(x))",[212,102954,102956,103009],{"className":102955,"ariaHidden":243},[242],[212,102957,102959,102962,102991,102994,102997,103000,103003,103006],{"className":102958},[247],[212,102960],{"className":102961,"style":336},[251],[212,102963,102965,102968],{"className":102964},[256],[212,102966,4356],{"className":102967,"style":1178},[256,257],[212,102969,102971],{"className":102970},[478],[212,102972,102974],{"className":102973},[482],[212,102975,102977],{"className":102976},[487],[212,102978,102980],{"className":102979,"style":8697},[491],[212,102981,102982,102985],{"style":7063},[212,102983],{"className":102984,"style":500},[499],[212,102986,102988],{"className":102987},[504,505,506,507],[212,102989,7771],{"className":102990},[2789,507],[212,102992,310],{"className":102993},[343],[212,102995,971],{"className":102996},[256,257],[212,102998,317],{"className":102999},[350],[212,103001],{"className":103002,"style":355},[354],[212,103004,320],{"className":103005},[359],[212,103007],{"className":103008,"style":355},[354],[212,103010,103012,103015,103047,103050,103053,103056,103059],{"className":103011},[247],[212,103013],{"className":103014,"style":7041},[251],[212,103016,103018,103021],{"className":103017},[256],[212,103019,234],{"className":103020,"style":258},[256,257],[212,103022,103024],{"className":103023},[478],[212,103025,103027],{"className":103026},[482],[212,103028,103030],{"className":103029},[487],[212,103031,103033],{"className":103032,"style":7060},[491],[212,103034,103035,103038],{"style":7063},[212,103036],{"className":103037,"style":500},[499],[212,103039,103041],{"className":103040},[504,505,506,507],[212,103042,103044],{"className":103043},[256,507],[212,103045,7018],{"className":103046},[256,507],[212,103048,310],{"className":103049},[343],[212,103051,966],{"className":103052},[256,257],[212,103054,310],{"className":103055},[343],[212,103057,971],{"className":103058},[256,257],[212,103060,19247],{"className":103061},[350],"。把 ",[212,103064,103066,103083],{"className":103065,"translate":216},[215],[212,103067,103069],{"className":103068},[220],[222,103070,103071],{"xmlns":224},[226,103072,103073,103081],{},[229,103074,103075],{},[7012,103076,103077,103079],{},[232,103078,4356],{},[307,103080,7771],{},[236,103082,64215],{"encoding":238},[212,103084,103086],{"className":103085,"ariaHidden":243},[242],[212,103087,103089,103092],{"className":103088},[247],[212,103090],{"className":103091,"style":64225},[251],[212,103093,103095,103098],{"className":103094},[256],[212,103096,4356],{"className":103097,"style":1178},[256,257],[212,103099,103101],{"className":103100},[478],[212,103102,103104],{"className":103103},[482],[212,103105,103107],{"className":103106},[487],[212,103108,103110],{"className":103109,"style":8697},[491],[212,103111,103112,103115],{"style":7063},[212,103113],{"className":103114,"style":500},[499],[212,103116,103118],{"className":103117},[504,505,506,507],[212,103119,7771],{"className":103120},[2789,507]," 代回即得 ",[212,103123,103125,103152],{"className":103124,"translate":216},[215],[212,103126,103128],{"className":103127},[220],[222,103129,103130],{"xmlns":224},[226,103131,103132,103150],{},[229,103133,103134,103140,103142,103144,103146,103148],{},[392,103135,103136,103138],{},[232,103137,396],{},[232,103139,234],{},[307,103141,310],{"stretchy":309},[232,103143,403],{},[232,103145,407],{"mathvariant":406},[232,103147,410],{},[307,103149,317],{"stretchy":309},[236,103151,5437],{"encoding":238},[212,103153,103155],{"className":103154,"ariaHidden":243},[242],[212,103156,103158,103161,103201,103204,103207,103210,103213],{"className":103157},[247],[212,103159],{"className":103160,"style":467},[251],[212,103162,103164,103167],{"className":103163},[256],[212,103165,396],{"className":103166,"style":474},[256,257],[212,103168,103170],{"className":103169},[478],[212,103171,103173,103193],{"className":103172},[482,483],[212,103174,103176,103190],{"className":103175},[487],[212,103177,103179],{"className":103178,"style":492},[491],[212,103180,103181,103184],{"style":495},[212,103182],{"className":103183,"style":500},[499],[212,103185,103187],{"className":103186},[504,505,506,507],[212,103188,234],{"className":103189,"style":258},[256,257,507],[212,103191,515],{"className":103192},[514],[212,103194,103196],{"className":103195},[487],[212,103197,103199],{"className":103198,"style":522},[491],[212,103200],{},[212,103202,310],{"className":103203},[343],[212,103205,403],{"className":103206,"style":531},[256,257],[212,103208,407],{"className":103209},[256],[212,103211,410],{"className":103212},[256,257],[212,103214,317],{"className":103215},[350],"（这正是定理 4.1 所给的最优解）。",[1194,103218,103219],{},"实践含义："," 判别器网络 ",[212,103222,103224,103241],{"className":103223,"translate":216},[215],[212,103225,103227],{"className":103226},[220],[222,103228,103229],{"xmlns":224},[226,103230,103231,103239],{},[229,103232,103233],{},[392,103234,103235,103237],{},[232,103236,4356],{},[232,103238,100076],{},[236,103240,100079],{"encoding":238},[212,103242,103244],{"className":103243,"ariaHidden":243},[242],[212,103245,103247,103250],{"className":103246},[247],[212,103248],{"className":103249,"style":2474},[251],[212,103251,103253,103256],{"className":103252},[256],[212,103254,4356],{"className":103255,"style":1178},[256,257],[212,103257,103259],{"className":103258},[478],[212,103260,103262,103282],{"className":103261},[482,483],[212,103263,103265,103279],{"className":103264},[487],[212,103266,103268],{"className":103267,"style":45129},[491],[212,103269,103270,103273],{"style":19043},[212,103271],{"className":103272,"style":500},[499],[212,103274,103276],{"className":103275},[504,505,506,507],[212,103277,100076],{"className":103278,"style":1178},[256,257,507],[212,103280,515],{"className":103281},[514],[212,103283,103285],{"className":103284},[487],[212,103286,103288],{"className":103287,"style":8166},[491],[212,103289],{}," 学的是 ",[212,103292,103294,103319],{"className":103293,"translate":216},[215],[212,103295,103297],{"className":103296},[220],[222,103298,103299],{"xmlns":224},[226,103300,103301,103316],{},[229,103302,103303,103309,103311,103314],{},[7012,103304,103305,103307],{},[232,103306,234],{},[307,103308,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,103310,310],{"stretchy":309},[1495,103312,103313],{},"似然比",[307,103315,317],{"stretchy":309},[236,103317,103318],{"encoding":238},"f'(\\text{似然比})",[212,103320,103322],{"className":103321,"ariaHidden":243},[242],[212,103323,103325,103328,103360,103363,103369],{"className":103324},[247],[212,103326],{"className":103327,"style":7041},[251],[212,103329,103331,103334],{"className":103330},[256],[212,103332,234],{"className":103333,"style":258},[256,257],[212,103335,103337],{"className":103336},[478],[212,103338,103340],{"className":103339},[482],[212,103341,103343],{"className":103342},[487],[212,103344,103346],{"className":103345,"style":7060},[491],[212,103347,103348,103351],{"style":7063},[212,103349],{"className":103350,"style":500},[499],[212,103352,103354],{"className":103353},[504,505,506,507],[212,103355,103357],{"className":103356},[256,507],[212,103358,7018],{"className":103359},[256,507],[212,103361,310],{"className":103362},[343],[212,103364,103366],{"className":103365},[256,4796],[212,103367,103313],{"className":103368},[256,4800],[212,103370,317],{"className":103371},[350],"，而不是似然比本身；不同 ",[212,103374,103376,103389],{"className":103375,"translate":216},[215],[212,103377,103379],{"className":103378},[220],[222,103380,103381],{"xmlns":224},[226,103382,103383,103387],{},[229,103384,103385],{},[232,103386,234],{},[236,103388,234],{"encoding":238},[212,103390,103392],{"className":103391,"ariaHidden":243},[242],[212,103393,103395,103398],{"className":103394},[247],[212,103396],{"className":103397,"style":252},[251],[212,103399,234],{"className":103400,"style":258},[256,257]," 等价于对似然比做了不同的单调「整形」，因此决定了梯度的尺度与饱和方式。",[2509,103403,103405],{"id":103404},"_53-各散度的-gan-目标","5.3 各散度的 GAN 目标",[11,103407,103408,103409,9598],{},"取上表的 ",[212,103410,103412,103429],{"className":103411,"translate":216},[215],[212,103413,103415],{"className":103414},[220],[222,103416,103417],{"xmlns":224},[226,103418,103419,103427],{},[229,103420,103421],{},[7012,103422,103423,103425],{},[232,103424,234],{},[307,103426,7771],{},[236,103428,60918],{"encoding":238},[212,103430,103432],{"className":103431,"ariaHidden":243},[242],[212,103433,103435,103438],{"className":103434},[247],[212,103436],{"className":103437,"style":252},[251],[212,103439,103441,103444],{"className":103440},[256],[212,103442,234],{"className":103443,"style":258},[256,257],[212,103445,103447],{"className":103446},[478],[212,103448,103450],{"className":103449},[482],[212,103451,103453],{"className":103452},[487],[212,103454,103456],{"className":103455,"style":8697},[491],[212,103457,103458,103461],{"style":7063},[212,103459],{"className":103460,"style":500},[499],[212,103462,103464],{"className":103463},[504,505,506,507],[212,103465,7771],{"className":103466},[2789,507],[10225,103468,103469],{},[6863,103470,103471,15995,103473,45807],{},[1194,103472,32863],{},[212,103474,103476,103508],{"className":103475,"translate":216},[215],[212,103477,103479],{"className":103478},[220],[222,103480,103481],{"xmlns":224},[226,103482,103483,103505],{},[229,103484,103485,103491,103493],{},[7012,103486,103487,103489],{},[232,103488,234],{},[307,103490,7771],{},[307,103492,320],{},[7012,103494,103495,103497],{},[232,103496,7765],{},[229,103498,103499,103501,103503],{},[232,103500,40437],{},[307,103502,5011],{},[312,103504,314],{},[236,103506,103507],{"encoding":238},"f^*=e^{y-1}",[212,103509,103511,103555],{"className":103510,"ariaHidden":243},[242],[212,103512,103514,103517,103546,103549,103552],{"className":103513},[247],[212,103515],{"className":103516,"style":252},[251],[212,103518,103520,103523],{"className":103519},[256],[212,103521,234],{"className":103522,"style":258},[256,257],[212,103524,103526],{"className":103525},[478],[212,103527,103529],{"className":103528},[482],[212,103530,103532],{"className":103531},[487],[212,103533,103535],{"className":103534,"style":8697},[491],[212,103536,103537,103540],{"style":7063},[212,103538],{"className":103539,"style":500},[499],[212,103541,103543],{"className":103542},[504,505,506,507],[212,103544,7771],{"className":103545},[2789,507],[212,103547],{"className":103548,"style":355},[354],[212,103550,320],{"className":103551},[359],[212,103553],{"className":103554,"style":355},[354],[212,103556,103558,103561],{"className":103557},[247],[212,103559],{"className":103560,"style":20228},[251],[212,103562,103564,103567],{"className":103563},[256],[212,103565,7765],{"className":103566},[256,257],[212,103568,103570],{"className":103569},[478],[212,103571,103573],{"className":103572},[482],[212,103574,103576],{"className":103575},[487],[212,103577,103579],{"className":103578,"style":20228},[491],[212,103580,103581,103584],{"style":7063},[212,103582],{"className":103583,"style":500},[499],[212,103585,103587],{"className":103586},[504,505,506,507],[212,103588,103590,103593,103596],{"className":103589},[256,507],[212,103591,40437],{"className":103592,"style":1178},[256,257,507],[212,103594,5011],{"className":103595},[2789,507],[212,103597,314],{"className":103598},[256,507],[212,103600,103602],{"className":103601,"translate":216},[377],[212,103603,103605,103691],{"className":103604,"translate":216},[215],[212,103606,103608],{"className":103607},[220],[222,103609,103610],{"xmlns":224,"display":386},[226,103611,103612,103688],{},[229,103613,103614,103624,103626,103628,103630,103632,103634,103636,103646,103648,103654,103656,103658,103660,103662,103668,103670,103682,103684,103686],{},[392,103615,103616,103618],{},[232,103617,396],{},[229,103619,103620,103622],{},[232,103621,10894],{},[232,103623,22093],{},[307,103625,310],{"stretchy":309},[232,103627,403],{},[232,103629,407],{"mathvariant":406},[232,103631,410],{},[307,103633,317],{"stretchy":309},[307,103635,320],{},[6214,103637,103638,103644],{},[229,103639,103640,103642],{},[232,103641,35632],{},[307,103643,4301],{},[232,103645,4356],{},[307,103647,3096],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[392,103649,103650,103652],{},[232,103651,420],{"mathvariant":419},[232,103653,403],{},[307,103655,427],{"stretchy":309},[232,103657,4356],{},[307,103659,454],{"stretchy":309},[307,103661,5011],{},[392,103663,103664,103666],{},[232,103665,420],{"mathvariant":419},[232,103667,410],{},[307,103669,427],{"stretchy":309},[7012,103671,103672,103674],{},[232,103673,7765],{},[229,103675,103676,103678,103680],{},[232,103677,4356],{},[307,103679,5011],{},[312,103681,314],{},[307,103683,454],{"stretchy":309},[307,103685,3106],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[232,103687,4573],{"mathvariant":406},[236,103689,103690],{"encoding":238},"D_{KL}(P\\|Q)\n=\\sup_g\\Big\\{\\mathbb E_P[g]\n-\\mathbb E_Q[e^{g-1}]\\Big\\}.",[212,103692,103694,103770,103887],{"className":103693,"ariaHidden":243},[242],[212,103695,103697,103700,103746,103749,103752,103755,103758,103761,103764,103767],{"className":103696},[247],[212,103698],{"className":103699,"style":336},[251],[212,103701,103703,103706],{"className":103702},[256],[212,103704,396],{"className":103705,"style":474},[256,257],[212,103707,103709],{"className":103708},[478],[212,103710,103712,103738],{"className":103711},[482,483],[212,103713,103715,103735],{"className":103714},[487],[212,103716,103718],{"className":103717,"style":576},[491],[212,103719,103720,103723],{"style":495},[212,103721],{"className":103722,"style":500},[499],[212,103724,103726],{"className":103725},[504,505,506,507],[212,103727,103729,103732],{"className":103728},[256,507],[212,103730,10894],{"className":103731,"style":10982},[256,257,507],[212,103733,22093],{"className":103734},[256,257,507],[212,103736,515],{"className":103737},[514],[212,103739,103741],{"className":103740},[487],[212,103742,103744],{"className":103743,"style":8166},[491],[212,103745],{},[212,103747,310],{"className":103748},[343],[212,103750,403],{"className":103751,"style":531},[256,257],[212,103753,407],{"className":103754},[256],[212,103756,410],{"className":103757},[256,257],[212,103759,317],{"className":103760},[350],[212,103762],{"className":103763,"style":355},[354],[212,103765,320],{"className":103766},[359],[212,103768],{"className":103769,"style":355},[354],[212,103771,103773,103776,103820,103823,103829,103869,103872,103875,103878,103881,103884],{"className":103772},[247],[212,103774],{"className":103775,"style":99700},[251],[212,103777,103779],{"className":103778},[1682,13916],[212,103780,103782,103812],{"className":103781},[482,483],[212,103783,103785,103809],{"className":103784},[487],[212,103786,103788,103799],{"className":103787,"style":2543},[491],[212,103789,103790,103793],{"style":61400},[212,103791],{"className":103792,"style":658},[499],[212,103794,103796],{"className":103795},[504,505,506,507],[212,103797,4356],{"className":103798,"style":1178},[256,257,507],[212,103800,103801,103804],{"style":12063},[212,103802],{"className":103803,"style":658},[499],[212,103805,103806],{},[212,103807,35632],{"className":103808},[1682],[212,103810,515],{"className":103811},[514],[212,103813,103815],{"className":103814},[487],[212,103816,103818],{"className":103817,"style":61432},[491],[212,103819],{},[212,103821],{"className":103822,"style":603},[354],[212,103824,103826],{"className":103825},[256],[212,103827,3096],{"className":103828},[616,3918],[212,103830,103832,103835],{"className":103831},[256],[212,103833,420],{"className":103834},[256,563],[212,103836,103838],{"className":103837},[478],[212,103839,103841,103861],{"className":103840},[482,483],[212,103842,103844,103858],{"className":103843},[487],[212,103845,103847],{"className":103846,"style":576},[491],[212,103848,103849,103852],{"style":579},[212,103850],{"className":103851,"style":500},[499],[212,103853,103855],{"className":103854},[504,505,506,507],[212,103856,403],{"className":103857,"style":531},[256,257,507],[212,103859,515],{"className":103860},[514],[212,103862,103864],{"className":103863},[487],[212,103865,103867],{"className":103866,"style":8166},[491],[212,103868],{},[212,103870,427],{"className":103871},[343],[212,103873,4356],{"className":103874,"style":1178},[256,257],[212,103876,454],{"className":103877},[350],[212,103879],{"className":103880,"style":2785},[354],[212,103882,5011],{"className":103883},[2789],[212,103885],{"className":103886,"style":2785},[354],[212,103888,103890,103893,103933,103936,103974,103977,103983],{"className":103889},[247],[212,103891],{"className":103892,"style":68327},[251],[212,103894,103896,103899],{"className":103895},[256],[212,103897,420],{"className":103898},[256,563],[212,103900,103902],{"className":103901},[478],[212,103903,103905,103925],{"className":103904},[482,483],[212,103906,103908,103922],{"className":103907},[487],[212,103909,103911],{"className":103910,"style":576},[491],[212,103912,103913,103916],{"style":579},[212,103914],{"className":103915,"style":500},[499],[212,103917,103919],{"className":103918},[504,505,506,507],[212,103920,410],{"className":103921},[256,257,507],[212,103923,515],{"className":103924},[514],[212,103926,103928],{"className":103927},[487],[212,103929,103931],{"className":103930,"style":522},[491],[212,103932],{},[212,103934,427],{"className":103935},[343],[212,103937,103939,103942],{"className":103938},[256],[212,103940,7765],{"className":103941},[256,257],[212,103943,103945],{"className":103944},[478],[212,103946,103948],{"className":103947},[482],[212,103949,103951],{"className":103950},[487],[212,103952,103954],{"className":103953,"style":19935},[491],[212,103955,103956,103959],{"style":8475},[212,103957],{"className":103958,"style":500},[499],[212,103960,103962],{"className":103961},[504,505,506,507],[212,103963,103965,103968,103971],{"className":103964},[256,507],[212,10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Donsker–Varadhan 下界是 ",[212,103990,103992,104038],{"className":103991,"translate":216},[215],[212,103993,103995],{"className":103994},[220],[222,103996,103997],{"xmlns":224},[226,103998,103999,104035],{},[229,104000,104001,104007,104009,104011,104013,104015,104017,104019,104025,104027,104033],{},[392,104002,104003,104005],{},[232,104004,420],{"mathvariant":419},[232,104006,403],{},[307,104008,427],{"stretchy":309},[232,104010,4356],{},[307,104012,454],{"stretchy":309},[307,104014,5011],{},[232,104016,4298],{},[307,104018,4301],{},[392,104020,104021,104023],{},[232,104022,420],{"mathvariant":419},[232,104024,410],{},[307,104026,427],{"stretchy":309},[7012,104028,104029,104031],{},[232,104030,7765],{},[232,104032,4356],{},[307,104034,454],{"stretchy":309},[236,104036,104037],{"encoding":238},"\\mathbb E_P[g]-\\log\\mathbb E_Q[e^{g}]",[212,104039,104041,104105],{"className":104040,"ariaHidden":243},[242],[212,104042,104044,104047,104087,104090,104093,104096,104099,104102],{"className":104043},[247],[212,104045],{"className":104046,"style":336},[251],[212,104048,104050,104053],{"className":104049},[256],[212,104051,420],{"className":104052},[256,563],[212,104054,104056],{"className":104055},[478],[212,104057,104059,104079],{"className":104058},[482,483],[212,104060,104062,104076],{"className":104061},[487],[212,104063,104065],{"className":104064,"style":576},[491],[212,104066,104067,104070],{"style":579},[212,104068],{"className":104069,"style":500},[499],[212,104071,104073],{"className":104072},[504,505,506,507],[212,104074,403],{"className":104075,"style":531},[256,257,507],[212,104077,515],{"className":104078},[514],[212,104080,104082],{"className":104081},[487],[212,104083,104085],{"className":104084,"style":8166},[491],[212,104086],{},[212,104088,427],{"className":104089},[343],[212,104091,4356],{"className":104092,"style":1178},[256,257],[212,104094,454],{"className":104095},[350],[212,104097],{"className":104098,"style":2785},[354],[212,104100,5011],{"className":104101},[2789],[212,104103],{"className":104104,"style":2785},[354],[212,104106,104108,104111,104116,104119,104159,104162,104194],{"className":104107},[247],[212,104109],{"className":104110,"style":467},[251],[212,104112,4352,104114],{"className":104113},[1682],[212,104115,4356],{"style":4355},[212,104117],{"className":104118,"style":603},[354],[212,104120,104122,104125],{"className":104121},[256],[212,104123,420],{"className":104124},[256,563],[212,104126,104128],{"className":104127},[478],[212,104129,104131,104151],{"className":104130},[482,483],[212,104132,104134,104148],{"className":104133},[487],[212,104135,104137],{"className":104136,"style":576},[491],[212,104138,104139,104142],{"style":579},[212,104140],{"className":104141,"style":500},[499],[212,104143,104145],{"className":104144},[504,505,506,507],[212,104146,410],{"className":104147},[256,257,507],[212,104149,515],{"className":104150},[514],[212,104152,104154],{"className":104153},[487],[212,104155,104157],{"className":104156,"style":522},[491],[212,104158],{},[212,104160,427],{"className":104161},[343],[212,104163,104165,104168],{"className":104164},[256],[212,104166,7765],{"className":104167},[256,257],[212,104169,104171],{"className":104170},[478],[212,104172,104174],{"className":104173},[482],[212,104175,104177],{"className":104176},[487],[212,104178,104180],{"className":104179,"style":50552},[491],[212,104181,104182,104185],{"style":7063},[212,104183],{"className":104184,"style":500},[499],[212,104186,104188],{"className":104187},[504,505,506,507],[212,104189,104191],{"className":104190},[256,507],[212,104192,4356],{"className":104193,"style":1178},[256,257,507],[212,104195,454],{"className":104196},[350],"，二者同源但第二项不同：",[212,104199,104201,104224],{"className":104200,"translate":216},[215],[212,104202,104204],{"className":104203},[220],[222,104205,104206],{"xmlns":224},[226,104207,104208,104222],{},[229,104209,104210],{},[7012,104211,104212,104214],{},[232,104213,7765],{},[229,104215,104216,104218,104220],{},[232,104217,40437],{},[307,104219,5011],{},[312,104221,314],{},[236,104223,65112],{"encoding":238},[212,104225,104227],{"className":104226,"ariaHidden":243},[242],[212,104228,104230,104233],{"className":104229},[247],[212,104231],{"className":104232,"style":20228},[251],[212,104234,104236,104239],{"className":104235},[256],[212,104237,7765],{"className":104238},[256,257],[212,104240,104242],{"className":104241},[478],[212,104243,104245],{"className":104244},[482],[212,104246,104248],{"className":104247},[487],[212,104249,104251],{"className":104250,"style":20228},[491],[212,104252,104253,104256],{"style":7063},[212,104254],{"className":104255,"style":500},[499],[212,104257,104259],{"className":104258},[504,505,506,507],[212,104260,104262,104265,104268],{"className":104261},[256,507],[212,104263,40437],{"className":104264,"style":1178},[256,257,507],[212,104266,5011],{"className":104267},[2789,507],[212,104269,314],{"className":104270},[256,507]," 是把 ",[212,104273,104275,104290],{"className":104274,"translate":216},[215],[212,104276,104278],{"className":104277},[220],[222,104279,104280],{"xmlns":224},[226,104281,104282,104288],{},[229,104283,104284,104286],{},[232,104285,4298],{},[307,104287,4301],{},[236,104289,21783],{"encoding":238},[212,104291,104293],{"className":104292,"ariaHidden":243},[242],[212,104294,104296,104299],{"className":104295},[247],[212,104297],{"className":104298,"style":252},[251],[212,104300,4352,104302],{"className":104301},[1682],[212,104303,4356],{"style":4355}," 移到最外层并做 ",[212,104306,104308,104321],{"className":104307,"translate":216},[215],[212,104309,104311],{"className":104310},[220],[222,104312,104313],{"xmlns":224},[226,104314,104315,104319],{},[229,104316,104317],{},[232,104318,234],{},[236,104320,234],{"encoding":238},[212,104322,104324],{"className":104323,"ariaHidden":243},[242],[212,104325,104327,104330],{"className":104326},[247],[212,104328],{"className":104329,"style":252},[251],[212,104331,234],{"className":104332,"style":258},[256,257],"-散度对偶后的结果。）",[10225,104335,104336,104562,104955,105386],{},[6863,104337,104338,104341,104342,49371,104375,104403,104404,104459,104460,104510,104511,104561],{},[1194,104339,104340],{},"反向 KL \u002F α-GAN","：把 α 从 ",[212,104343,104345,104360],{"className":104344,"translate":216},[215],[212,104346,104348],{"className":104347},[220],[222,104349,104350],{"xmlns":224},[226,104351,104352,104358],{},[229,104353,104354,104356],{},[307,104355,5011],{},[312,104357,314],{},[236,104359,49355],{"encoding":238},[212,104361,104363],{"className":104362,"ariaHidden":243},[242],[212,104364,104366,104369,104372],{"className":104365},[247],[212,104367],{"className":104368,"style":12778},[251],[212,104370,5011],{"className":104371},[256],[212,104373,314],{"className":104374},[256],[212,104376,104378,104391],{"className":104377,"translate":216},[215],[212,104379,104381],{"className":104380},[220],[222,104382,104383],{"xmlns":224},[226,104384,104385,104389],{},[229,104386,104387],{},[312,104388,314],{},[236,104390,314],{"encoding":238},[212,104392,104394],{"className":104393,"ariaHidden":243},[242],[212,104395,104397,104400],{"className":104396},[247],[212,104398],{"className":104399,"style":369},[251],[212,104401,314],{"className":104402},[256],"，散度从反向 KL（",[212,104405,104407,104426],{"className":104406,"translate":216},[215],[212,104408,104410],{"className":104409},[220],[222,104411,104412],{"xmlns":224},[226,104413,104414,104424],{},[229,104415,104416,104418,104420,104422],{},[232,104417,44954],{},[307,104419,1228],{},[307,104421,5011],{},[312,104423,314],{},[236,104425,49238],{"encoding":238},[212,104427,104429,104447],{"className":104428,"ariaHidden":243},[242],[212,104430,104432,104435,104438,104441,104444],{"className":104431},[247],[212,104433],{"className":104434,"style":2543},[251],[212,104436,44954],{"className":104437,"style":44984},[256,257],[212,104439],{"className":104440,"style":355},[354],[212,104442,1228],{"className":104443},[359],[212,104445],{"className":104446,"style":355},[354],[212,104448,104450,104453,104456],{"className":104449},[247],[212,104451],{"className":104452,"style":12778},[251],[212,104454,5011],{"className":104455},[256],[212,104457,314],{"className":104458},[256],"，zero-forcing、模式崩塌倾向）经 Hellinger 型对称散度（",[212,104461,104463,104480],{"className":104462,"translate":216},[215],[212,104464,104466],{"className":104465},[220],[222,104467,104468],{"xmlns":224},[226,104469,104470,104478],{},[229,104471,104472,104474,104476],{},[232,104473,44954],{},[307,104475,320],{},[312,104477,323],{},[236,104479,46687],{"encoding":238},[212,104481,104483,104501],{"className":104482,"ariaHidden":243},[242],[212,104484,104486,104489,104492,104495,104498],{"className":104485},[247],[212,104487],{"className":104488,"style":2543},[251],[212,104490,44954],{"className":104491,"style":44984},[256,257],[212,104493],{"className":104494,"style":355},[354],[212,104496,320],{"className":104497},[359],[212,104499],{"className":104500,"style":355},[354],[212,104502,104504,104507],{"className":104503},[247],[212,104505],{"className":104506,"style":369},[251],[212,104508,323],{"className":104509},[256],"）过渡到正向 KL（",[212,104512,104514,104531],{"className":104513,"translate":216},[215],[212,104515,104517],{"className":104516},[220],[222,104518,104519],{"xmlns":224},[226,104520,104521,104529],{},[229,104522,104523,104525,104527],{},[232,104524,44954],{},[307,104526,1228],{},[312,104528,314],{},[236,104530,47414],{"encoding":238},[212,104532,104534,104552],{"className":104533,"ariaHidden":243},[242],[212,104535,104537,104540,104543,104546,104549],{"className":104536},[247],[212,104538],{"className":104539,"style":2543},[251],[212,104541,44954],{"className":104542,"style":44984},[256,257],[212,104544],{"className":104545,"style":355},[354],[212,104547,1228],{"className":104548},[359],[212,104550],{"className":104551,"style":355},[354],[212,104553,104555,104558],{"className":104554},[247],[212,104556],{"className":104557,"style":369},[251],[212,104559,314],{"className":104560},[256],"，zero-avoiding、模式覆盖倾向），可以在\"崩塌—覆盖\"之间连续调节（见 3.6 节的两端极限）。",[6863,104563,104564,9598,104566,2943,104810,104950,104951,104954],{},[1194,104565,53323],{},[212,104567,104569,104619],{"className":104568,"translate":216},[215],[212,104570,104572],{"className":104571},[220],[222,104573,104574],{"xmlns":224},[226,104575,104576,104616],{},[229,104577,104578,104584,104586,104588,104594,104596,104598,104600,104602,104604,104614],{},[7012,104579,104580,104582],{},[232,104581,234],{},[307,104583,7771],{},[307,104585,320],{},[307,104587,5011],{},[435,104589,104590,104592],{},[312,104591,314],{},[312,104593,2661],{},[232,104595,4298],{},[307,104597,4301],{},[307,104599,310],{"stretchy":309},[312,104601,2661],{},[307,104603,5011],{},[7012,104605,104606,104608],{},[232,104607,7765],{},[229,104609,104610,104612],{},[312,104611,2661],{},[232,104613,40437],{},[307,104615,317],{"stretchy":309},[236,104617,104618],{"encoding":238},"f^*=-\\frac12\\log(2-e^{2y})",[212,104620,104622,104666,104766],{"className":104621,"ariaHidden":243},[242],[212,104623,104625,104628,104657,104660,104663],{"className":104624},[247],[212,104626],{"className":104627,"style":252},[251],[212,104629,104631,104634],{"className":104630},[256],[212,104632,234],{"className":104633,"style":258},[256,257],[212,104635,104637],{"className":104636},[478],[212,104638,104640],{"className":104639},[482],[212,104641,104643],{"className":104642},[487],[212,104644,104646],{"className":104645,"style":8697},[491],[212,104647,104648,104651],{"style":7063},[212,104649],{"className":104650,"style":500},[499],[212,104652,104654],{"className":104653},[504,505,506,507],[212,104655,7771],{"className":104656},[2789,507],[212,104658],{"className":104659,"style":355},[354],[212,104661,320],{"className":104662},[359],[212,104664],{"className":104665,"style":355},[354],[212,104667,104669,104672,104675,104743,104746,104751,104754,104757,104760,104763],{"className":104668},[247],[212,104670],{"className":104671,"style":2703},[251],[212,104673,5011],{"className":104674},[256],[212,104676,104678,104681,104740],{"className":104677},[256],[212,104679],{"className":104680},[343,638],[212,104682,104684],{"className":104683},[435],[212,104685,104687,104732],{"className":104686},[482,483],[212,104688,104690,104729],{"className":104689},[487],[212,104691,104693,104707,104715],{"className":104692,"style":2722},[491],[212,104694,104695,104698],{"style":2725},[212,104696],{"className":104697,"style":658},[499],[212,104699,104701],{"className":104700},[504,505,506,507],[212,104702,104704],{"className":104703},[256,507],[212,104705,2661],{"className":104706},[256,507],[212,104708,104709,104712],{"style":670},[212,104710],{"className":104711,"style":658},[499],[212,104713],{"className":104714,"style":678},[677],[212,104716,104717,104720],{"style":2748},[212,104718],{"className":104719,"style":658},[499],[212,104721,104723],{"className":104722},[504,505,506,507],[212,104724,104726],{"className":104725},[256,507],[212,104727,314],{"className":104728},[256,507],[212,104730,515],{"className":104731},[514],[212,104733,104735],{"className":104734},[487],[212,104736,104738],{"className":104737,"style":2770},[491],[212,104739],{},[212,104741],{"className":104742},[350,638],[212,104744],{"className":104745,"style":603},[354],[212,104747,4352,104749],{"className":104748},[1682],[212,104750,4356],{"style":4355},[212,104752,310],{"className":104753},[343],[212,104755,2661],{"className":104756},[256],[212,104758],{"className":104759,"style":2785},[354],[212,104761,5011],{"className":104762},[2789],[212,104764],{"className":104765,"style":2785},[354],[212,104767,104769,104772,104807],{"className":104768},[247],[212,104770],{"className":104771,"style":20203},[251],[212,104773,104775,104778],{"className":104774},[256],[212,104776,7765],{"className":104777},[256,257],[212,104779,104781],{"className":104780},[478],[212,104782,104784],{"className":104783},[482],[212,104785,104787],{"className":104786},[487],[212,104788,104790],{"className":104789,"style":20228},[491],[212,104791,104792,104795],{"style":7063},[212,104793],{"className":104794,"style":500},[499],[212,104796,104798],{"className":104797},[504,505,506,507],[212,104799,104801,104804],{"className":104800},[256,507],[212,104802,2661],{"className":104803},[256,507],[212,104805,40437],{"className":104806,"style":1178},[256,257,507],[212,104808,317],{"className":104809},[350],[212,104811,104813,104840],{"className":104812,"translate":216},[215],[212,104814,104816],{"className":104815},[220],[222,104817,104818],{"xmlns":224},[226,104819,104820,104838],{},[229,104821,104822,104824,104826],{},[232,104823,40437],{},[307,104825,7449],{},[435,104827,104828,104836],{},[229,104829,104830,104832,104834],{},[232,104831,4298],{},[307,104833,4301],{},[312,104835,2661],{},[312,104837,2661],{},[236,104839,65953],{"encoding":238},[212,104841,104843,104861],{"className":104842,"ariaHidden":243},[242],[212,104844,104846,104849,104852,104855,104858],{"className":104845},[247],[212,104847],{"className":104848,"style":31892},[251],[212,104850,40437],{"className":104851,"style":1178},[256,257],[212,104853],{"className":104854,"style":355},[354],[212,104856,7449],{"className":104857},[359],[212,104859],{"className":104860,"style":355},[354],[212,104862,104864,104867],{"className":104863},[247],[212,104865],{"className":104866,"style":65981},[251],[212,104868,104870,104873,104947],{"className":104869},[256],[212,104871],{"className":104872},[343,638],[212,104874,104876],{"className":104875},[435],[212,104877,104879,104939],{"className":104878},[482,483],[212,104880,104882,104936],{"className":104881},[487],[212,104883,104885,104899,104907],{"className":104884,"style":3023},[491],[212,104886,104887,104890],{"style":2725},[212,104888],{"className":104889,"style":658},[499],[212,104891,104893],{"className":104892},[504,505,506,507],[212,104894,104896],{"className":104895},[256,507],[212,104897,2661],{"className":104898},[256,507],[212,104900,104901,104904],{"style":670},[212,104902],{"className":104903,"style":658},[499],[212,104905],{"className":104906,"style":678},[677],[212,104908,104909,104912],{"style":3051},[212,104910],{"className":104911,"style":658},[499],[212,104913,104915],{"className":104914},[504,505,506,507],[212,104916,104918,104930,104933],{"className":104917},[256,507],[212,104919,104921,104924,104927],{"className":104920},[1682,507],[212,104922,47857],{"className":104923},[507],[212,104925,47861],{"className":104926},[507],[212,104928,4356],{"className":104929,"style":4355},[507],[212,104931],{"className":104932,"style":42566},[354,507],[212,104934,2661],{"className":104935},[256,507],[212,104937,515],{"className":104938},[514],[212,104940,104942],{"className":104941},[487],[212,104943,104945],{"className":104944,"style":2770},[491],[212,104946],{},[212,104948],{"className":104949},[350,638],"。代回即",[1194,104952,104953],{},"原始 GAN 的对抗目标","（见 5.4）。",[6863,104956,104957,9598,105018,105158,105159,105381,105382,105385],{},[1194,104958,104959,105017],{},[212,104960,104962,104979],{"className":104961,"translate":216},[215],[212,104963,104965],{"className":104964},[220],[222,104966,104967],{"xmlns":224},[226,104968,104969,104977],{},[229,104970,104971],{},[7012,104972,104973,104975],{},[232,104974,37649],{},[312,104976,2661],{},[236,104978,40594],{"encoding":238},[212,104980,104982],{"className":104981,"ariaHidden":243},[242],[212,104983,104985,104988],{"className":104984},[247],[212,104986],{"className":104987,"style":40604},[251],[212,104989,104991,104994],{"className":104990},[256],[212,104992,37649],{"className":104993},[256,257],[212,104995,104997],{"className":104996},[478],[212,104998,105000],{"className":104999},[482],[212,105001,105003],{"className":105002},[487],[212,105004,105006],{"className":105005,"style":20228},[491],[212,105007,105008,105011],{"style":7063},[212,105009],{"className":105010,"style":500},[499],[212,105012,105014],{"className":105013},[504,505,506,507],[212,105015,2661],{"className":105016},[256,507],"（LSGAN）",[212,105019,105021,105055],{"className":105020,"translate":216},[215],[212,105022,105024],{"className":105023},[220],[222,105025,105026],{"xmlns":224},[226,105027,105028,105052],{},[229,105029,105030,105036,105038,105040,105042,105048,105050],{},[7012,105031,105032,105034],{},[232,105033,234],{},[307,105035,7771],{},[307,105037,320],{},[232,105039,40437],{},[307,105041,2668],{},[7012,105043,105044,105046],{},[232,105045,40437],{},[312,105047,2661],{},[232,105049,1138],{"mathvariant":406},[312,105051,39189],{},[236,105053,105054],{"encoding":238},"f^*=y+y^2\u002F4",[212,105056,105058,105102,105120],{"className":105057,"ariaHidden":243},[242],[212,105059,105061,105064,105093,105096,105099],{"className":105060},[247],[212,105062],{"className":105063,"style":252},[251],[212,105065,105067,105070],{"className":105066},[256],[212,105068,234],{"className":105069,"style":258},[256,257],[212,105071,105073],{"className":105072},[478],[212,105074,105076],{"className":105075},[482],[212,105077,105079],{"className":105078},[487],[212,105080,105082],{"className":105081,"style":8697},[491],[212,105083,105084,105087],{"style":7063},[212,105085],{"className":105086,"style":500},[499],[212,105088,105090],{"className":105089},[504,505,506,507],[212,105091,7771],{"className":105092},[2789,507],[212,105094],{"className":105095,"style":355},[354],[212,105097,320],{"className":105098},[359],[212,105100],{"className":105101,"style":355},[354],[212,105103,105105,105108,105111,105114,105117],{"className":105104},[247],[212,105106],{"className":105107,"style":40521},[251],[212,105109,40437],{"className":105110,"style":1178},[256,257],[212,105112],{"className":105113,"style":2785},[354],[212,105115,2668],{"className":105116},[2789],[212,105118],{"className":105119,"style":2785},[354],[212,105121,105123,105126,105155],{"className":105122},[247],[212,105124],{"className":105125,"style":20203},[251],[212,105127,105129,105132],{"className":105128},[256],[212,105130,40437],{"className":105131,"style":1178},[256,257],[212,105133,105135],{"className":105134},[478],[212,105136,105138],{"className":105137},[482],[212,105139,105141],{"className":105140},[487],[212,105142,105144],{"className":105143,"style":20228},[491],[212,105145,105146,105149],{"style":7063},[212,105147],{"className":105148,"style":500},[499],[212,105150,105152],{"className":105151},[504,505,506,507],[212,105153,2661],{"className":105154},[256,507],[212,105156,40572],{"className":105157},[256],"，目标变为 ",[212,105160,105162,105212],{"className":105161,"translate":216},[215],[212,105163,105165],{"className":105164},[220],[222,105166,105167],{"xmlns":224},[226,105168,105169,105209],{},[229,105170,105171,105177,105179,105181,105183,105185,105191,105193,105195,105197,105203,105205,105207],{},[392,105172,105173,105175],{},[232,105174,420],{"mathvariant":419},[232,105176,403],{},[307,105178,427],{"stretchy":309},[232,105180,4356],{},[307,105182,454],{"stretchy":309},[307,105184,5011],{},[392,105186,105187,105189],{},[232,105188,420],{"mathvariant":419},[232,105190,410],{},[307,105192,427],{"stretchy":309},[232,105194,4356],{},[307,105196,2668],{},[7012,105198,105199,105201],{},[232,105200,4356],{},[312,105202,2661],{},[232,105204,1138],{"mathvariant":406},[312,105206,39189],{},[307,105208,454],{"stretchy":309},[236,105210,105211],{"encoding":238},"\\mathbb E_P[g]-\\mathbb E_Q[g+g^2\u002F4]",[212,105213,105215,105279,105340],{"className":105214,"ariaHidden":243},[242],[212,105216,105218,105221,105261,105264,105267,105270,105273,105276],{"className":105217},[247],[212,105219],{"className":105220,"style":336},[251],[212,105222,105224,105227],{"className":105223},[256],[212,105225,420],{"className":105226},[256,563],[212,105228,105230],{"className":105229},[478],[212,105231,105233,105253],{"className":105232},[482,483],[212,105234,105236,105250],{"className":105235},[487],[212,105237,105239],{"className":105238,"style":576},[491],[212,105240,105241,105244],{"style":579},[212,105242],{"className":105243,"style":500},[499],[212,105245,105247],{"className":105246},[504,505,506,507],[212,105248,403],{"className":105249,"style":531},[256,257,507],[212,105251,515],{"className":105252},[514],[212,105254,105256],{"className":105255},[487],[212,105257,105259],{"className":105258,"style":8166},[491],[212,105260],{},[212,105262,427],{"className":105263},[343],[212,105265,4356],{"className":105266,"style":1178},[256,257],[212,105268,454],{"className":105269},[350],[212,105271],{"className":105272,"style":2785},[354],[212,105274,5011],{"className":105275},[2789],[212,105277],{"className":105278,"style":2785},[354],[212,105280,105282,105285,105325,105328,105331,105334,105337],{"className":105281},[247],[212,105283],{"className":105284,"style":467},[251],[212,105286,105288,105291],{"className":105287},[256],[212,105289,420],{"className":105290},[256,563],[212,105292,105294],{"className":105293},[478],[212,105295,105297,105317],{"className":105296},[482,483],[212,105298,105300,105314],{"className":105299},[487],[212,105301,105303],{"className":105302,"style":576},[491],[212,105304,105305,105308],{"style":579},[212,105306],{"className":105307,"style":500},[499],[212,105309,105311],{"className":105310},[504,505,506,507],[212,105312,410],{"className":105313},[256,257,507],[212,105315,515],{"className":105316},[514],[212,105318,105320],{"className":105319},[487],[212,105321,105323],{"className":105322,"style":522},[491],[212,105324],{},[212,105326,427],{"className":105327},[343],[212,105329,4356],{"className":105330,"style":1178},[256,257],[212,105332],{"className":105333,"style":2785},[354],[212,105335,2668],{"className":105336},[2789],[212,105338],{"className":105339,"style":2785},[354],[212,105341,105343,105346,105375,105378],{"className":105342},[247],[212,105344],{"className":105345,"style":20203},[251],[212,105347,105349,105352],{"className":105348},[256],[212,105350,4356],{"className":105351,"style":1178},[256,257],[212,105353,105355],{"className":105354},[478],[212,105356,105358],{"className":105357},[482],[212,105359,105361],{"className":105360},[487],[212,105362,105364],{"className":105363,"style":20228},[491],[212,105365,105366,105369],{"style":7063},[212,105367],{"className":105368,"style":500},[499],[212,105370,105372],{"className":105371},[504,505,506,507],[212,105373,2661],{"className":105374},[256,507],[212,105376,40572],{"className":105377},[256],[212,105379,454],{"className":105380},[350],"，即对判别器输出做",[1194,105383,105384],{},"最小二乘","回归，梯度不会像 sigmoid 那样饱和。",[6863,105387,105388,9598,105391,2943,105514,10378],{},[1194,105389,105390],{},"Hellinger²",[212,105392,105394,105428],{"className":105393,"translate":216},[215],[212,105395,105397],{"className":105396},[220],[222,105398,105399],{"xmlns":224},[226,105400,105401,105425],{},[229,105402,105403,105409,105411,105413,105415,105417,105419,105421,105423],{},[7012,105404,105405,105407],{},[232,105406,234],{},[307,105408,7771],{},[307,105410,320],{},[232,105412,40437],{},[232,105414,1138],{"mathvariant":406},[307,105416,310],{"stretchy":309},[312,105418,314],{},[307,105420,5011],{},[232,105422,40437],{},[307,105424,317],{"stretchy":309},[236,105426,105427],{"encoding":238},"f^*=y\u002F(1-y)",[212,105429,105431,105475,105502],{"className":105430,"ariaHidden":243},[242],[212,105432,105434,105437,105466,105469,105472],{"className":105433},[247],[212,105435],{"className":105436,"style":252},[251],[212,105438,105440,105443],{"className":105439},[256],[212,105441,234],{"className":105442,"style":258},[256,257],[212,105444,105446],{"className":105445},[478],[212,105447,105449],{"className":105448},[482],[212,105450,105452],{"className":105451},[487],[212,105453,105455],{"className":105454,"style":8697},[491],[212,105456,105457,105460],{"style":7063},[212,105458],{"className":105459,"style":500},[499],[212,105461,105463],{"className":105462},[504,505,506,507],[212,105464,7771],{"className":105465},[2789,507],[212,105467],{"className":105468,"style":355},[354],[212,105470,320],{"className":105471},[359],[212,105473],{"className":105474,"style":355},[354],[212,105476,105478,105481,105484,105487,105490,105493,105496,105499],{"className":105477},[247],[212,105479],{"className":105480,"style":336},[251],[212,105482,40437],{"className":105483,"style":1178},[256,257],[212,105485,1138],{"className":105486},[256],[212,105488,310],{"className":105489},[343],[212,105491,314],{"className":105492},[256],[212,105494],{"className":105495,"style":2785},[354],[212,105497,5011],{"className":105498},[2789],[212,105500],{"className":105501,"style":2785},[354],[212,105503,105505,105508,105511],{"className":105504},[247],[212,105506],{"className":105507,"style":336},[251],[212,105509,40437],{"className":105510,"style":1178},[256,257],[212,105512,317],{"className":105513},[350],[212,105515,105517,105534],{"className":105516,"translate":216},[215],[212,105518,105520],{"className":105519},[220],[222,105521,105522],{"xmlns":224},[226,105523,105524,105532],{},[229,105525,105526,105528,105530],{},[232,105527,40437],{},[307,105529,7449],{},[312,105531,314],{},[236,105533,66983],{"encoding":238},[212,105535,105537,105555],{"className":105536,"ariaHidden":243},[242],[212,105538,105540,105543,105546,105549,105552],{"className":105539},[247],[212,105541],{"className":105542,"style":31892},[251],[212,105544,40437],{"className":105545,"style":1178},[256,257],[212,105547],{"className":105548,"style":355},[354],[212,105550,7449],{"className":105551},[359],[212,105553],{"className":105554,"style":355},[354],[212,105556,105558,105561],{"className":105557},[247],[212,105559],{"className":105560,"style":369},[251],[212,105562,314],{"className":105563},[256],[2509,105565,105567],{"id":105566},"_54-原始-gan-与-js-散度","5.4 原始 GAN 与 JS 散度",[11,105569,105570,105571,105753],{},"原始 GAN 的判别器输出经 sigmoid 得 ",[212,105572,105574,105626],{"className":105573,"translate":216},[215],[212,105575,105577],{"className":105576},[220],[222,105578,105579],{"xmlns":224},[226,105580,105581,105623],{},[229,105582,105583,105585,105587,105589,105591,105593,105595,105597,105599,105605,105607,105609,105611,105613,105615,105617,105619,105621],{},[232,105584,2530],{},[307,105586,310],{"stretchy":309},[232,105588,396],{},[307,105590,310],{"stretchy":309},[232,105592,971],{},[307,105594,317],{"stretchy":309},[307,105596,317],{"stretchy":309},[307,105598,320],{},[392,105600,105601,105603],{},[232,105602,396],{},[232,105604,7759],{},[307,105606,310],{"stretchy":309},[232,105608,971],{},[307,105610,317],{"stretchy":309},[307,105612,6107],{},[307,105614,310],{"stretchy":309},[312,105616,323],{},[307,105618,748],{"separator":243},[312,105620,314],{},[307,105622,317],{"stretchy":309},[236,105624,105625],{"encoding":238},"\\sigma(D(x))=D_{s}(x)\\in(0,1)",[212,105627,105629,105662,105729],{"className":105628,"ariaHidden":243},[242],[212,105630,105632,105635,105638,105641,105644,105647,105650,105653,105656,105659],{"className":105631},[247],[212,105633],{"className":105634,"style":336},[251],[212,105636,2530],{"className":105637,"style":1178},[256,257],[212,105639,310],{"className":105640},[343],[212,105642,396],{"className":105643,"style":474},[256,257],[212,105645,310],{"className":105646},[343],[212,105648,971],{"className":105649},[256,257],[212,105651,19247],{"className":105652},[350],[212,105654],{"className":105655,"style":355},[354],[212,105657,320],{"className":105658},[359],[212,105660],{"className":105661,"style":355},[354],[212,105663,105665,105668,105711,105714,105717,105720,105723,105726],{"className":105664},[247],[212,105666],{"className":105667,"style":336},[251],[212,105669,105671,105674],{"className":105670},[256],[212,105672,396],{"className":105673,"style":474},[256,257],[212,105675,105677],{"className":105676},[478],[212,105678,105680,105703],{"className":105679},[482,483],[212,105681,105683,105700],{"className":105682},[487],[212,105684,105686],{"className":105685,"style":45129},[491],[212,105687,105688,105691],{"style":495},[212,105689],{"className":105690,"style":500},[499],[212,105692,105694],{"className":105693},[504,505,506,507],[212,105695,105697],{"className":105696},[256,507],[212,105698,7759],{"className":105699},[256,257,507],[212,105701,515],{"className":105702},[514],[212,105704,105706],{"className":105705},[487],[212,105707,105709],{"className":105708,"style":8166},[491],[212,105710],{},[212,105712,310],{"className":105713},[343],[212,105715,971],{"className":105716},[256,257],[212,105718,317],{"className":105719},[350],[212,105721],{"className":105722,"style":355},[354],[212,105724,6107],{"className":105725},[359],[212,105727],{"className":105728,"style":355},[354],[212,105730,105732,105735,105738,105741,105744,105747,105750],{"className":105731},[247],[212,105733],{"className":105734,"style":336},[251],[212,105736,310],{"className":105737},[343],[212,105739,323],{"className":105740},[256],[212,105742,748],{"className":105743},[770],[212,105745],{"className":105746,"style":603},[354],[212,105748,314],{"className":105749},[256],[212,105751,317],{"className":105752},[350],"，其目标等价于最小化 JS 散度下的对抗博弈。判别器写成 logit",[212,105755,105757],{"className":105756,"translate":216},[377],[212,105758,105760,105838],{"className":105759,"translate":216},[215],[212,105761,105763],{"className":105762},[220],[222,105764,105765],{"xmlns":224,"display":386},[226,105766,105767,105835],{},[229,105768,105769,105771,105773,105775,105777,105779,105781,105783,105789,105791,105793,105795,105797,105799,105801,105803,105805,105807,105813,105815,105817,105819,105821,105823,105825,105827,105833],{},[232,105770,4356],{},[307,105772,310],{"stretchy":309},[232,105774,971],{},[307,105776,317],{"stretchy":309},[307,105778,320],{},[232,105780,4298],{},[307,105782,4301],{},[392,105784,105785,105787],{},[232,105786,396],{},[232,105788,7759],{},[307,105790,310],{"stretchy":309},[232,105792,971],{},[307,105794,317],{"stretchy":309},[307,105796,5011],{},[232,105798,4298],{},[307,105800,4301],{},[307,105802,310],{"stretchy":309},[312,105804,314],{},[307,105806,5011],{},[392,105808,105809,105811],{},[232,105810,396],{},[232,105812,7759],{},[307,105814,310],{"stretchy":309},[232,105816,971],{},[307,105818,317],{"stretchy":309},[307,105820,317],{"stretchy":309},[307,105822,320],{},[232,105824,4298],{},[307,105826,4301],{},[435,105828,105829,105831],{},[232,105830,11],{},[232,105832,1141],{},[307,105834,748],{"separator":243},[236,105836,105837],{"encoding":238},"g(x)=\\log D_s(x)-\\log(1-D_s(x))\n=\\log\\frac{p}{q},",[212,105839,105841,105868,105940,105966,106030],{"className":105840,"ariaHidden":243},[242],[212,105842,105844,105847,105850,105853,105856,105859,105862,105865],{"className":105843},[247],[212,105845],{"className":105846,"style":336},[251],[212,105848,4356],{"className":105849,"style":1178},[256,257],[212,105851,310],{"className":105852},[343],[212,105854,971],{"className":105855},[256,257],[212,105857,317],{"className":105858},[350],[212,105860],{"className":105861,"style":355},[354],[212,105863,320],{"className":105864},[359],[212,105866],{"className":105867,"style":355},[354],[212,105869,105871,105874,105879,105882,105922,105925,105928,105931,105934,105937],{"className":105870},[247],[212,105872],{"className":105873,"style":336},[251],[212,105875,4352,105877],{"className":105876},[1682],[212,105878,4356],{"style":4355},[212,105880],{"className":105881,"style":603},[354],[212,105883,105885,105888],{"className":105884},[256],[212,105886,396],{"className":105887,"style":474},[256,257],[212,105889,105891],{"className":105890},[478],[212,105892,105894,105914],{"className":105893},[482,483],[212,105895,105897,105911],{"className":105896},[487],[212,105898,105900],{"className":105899,"style":45129},[491],[212,105901,105902,105905],{"style":495},[212,105903],{"className":105904,"style":500},[499],[212,105906,105908],{"className":105907},[504,505,506,507],[212,105909,7759],{"className":105910},[256,257,507],[212,105912,515],{"className":105913},[514],[212,105915,105917],{"className":105916},[487],[212,105918,105920],{"className":105919,"style":8166},[491],[212,105921],{},[212,105923,310],{"className":105924},[343],[212,105926,971],{"className":105927},[256,257],[212,105929,317],{"className":105930},[350],[212,105932],{"className":105933,"style":2785},[354],[212,105935,5011],{"className":105936},[2789],[212,105938],{"className":105939,"style":2785},[354],[212,105941,105943,105946,105951,105954,105957,105960,105963],{"className":105942},[247],[212,105944],{"className":105945,"style":336},[251],[212,105947,4352,105949],{"className":105948},[1682],[212,105950,4356],{"style":4355},[212,105952,310],{"className":105953},[343],[212,105955,314],{"className":105956},[256],[212,105958],{"className":105959,"style":2785},[354],[212,105961,5011],{"className":105962},[2789],[212,105964],{"className":105965,"style":2785},[354],[212,105967,105969,105972,106012,106015,106018,106021,106024,106027],{"className":105968},[247],[212,105970],{"className":105971,"style":336},[251],[212,105973,105975,105978],{"className":105974},[256],[212,105976,396],{"className":105977,"style":474},[256,257],[212,105979,105981],{"className":105980},[478],[212,105982,105984,106004],{"className":105983},[482,483],[212,105985,105987,106001],{"className":105986},[487],[212,105988,105990],{"className":105989,"style":45129},[491],[212,105991,105992,105995],{"style":495},[212,105993],{"className":105994,"style":500},[499],[212,105996,105998],{"className":105997},[504,505,506,507],[212,105999,7759],{"className":106000},[256,257,507],[212,106002,515],{"className":106003},[514],[212,106005,106007],{"className":106006},[487],[212,106008,106010],{"className":106009,"style":8166},[491],[212,106011],{},[212,106013,310],{"className":106014},[343],[212,106016,971],{"className":106017},[256,257],[212,106019,19247],{"className":106020},[350],[212,106022],{"className":106023,"style":355},[354],[212,106025,320],{"className":106026},[359],[212,106028],{"className":106029,"style":355},[354],[212,106031,106033,106036,106041,106044,106106],{"className":106032},[247],[212,106034],{"className":106035,"style":22210},[251],[212,106037,4352,106039],{"className":106038},[1682],[212,106040,4356],{"style":4355},[212,106042],{"className":106043,"style":603},[354],[212,106045,106047,106050,106103],{"className":106046},[256],[212,106048],{"className":106049},[343,638],[212,106051,106053],{"className":106052},[435],[212,106054,106056,106095],{"className":106055},[482,483],[212,106057,106059,106092],{"className":106058},[487],[212,106060,106062,106073,106081],{"className":106061,"style":3752},[491],[212,106063,106064,106067],{"style":654},[212,106065],{"className":106066,"style":658},[499],[212,106068,106070],{"className":106069},[256],[212,106071,1141],{"className":106072,"style":1178},[256,257],[212,106074,106075,106078],{"style":670},[212,106076],{"className":106077,"style":658},[499],[212,106079],{"className":106080,"style":678},[677],[212,106082,106083,106086],{"style":681},[212,106084],{"className":106085,"style":658},[499],[212,106087,106089],{"className":106088},[256],[212,106090,11],{"className":106091},[256,257],[212,106093,515],{"className":106094},[514],[212,106096,106098],{"className":106097},[487],[212,106099,106101],{"className":106100,"style":703},[491],[212,106102],{},[212,106104],{"className":106105},[350,638],[212,106107,748],{"className":106108},[770],[11,106110,106111],{},"它与 5.2 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E_P\\Big[\\log\\frac{2p}{p+q}\\Big]\n=\\mathbb E_P[\\log D_s]+\\log2,",[212,107874,107876,107912,108067,108176],{"className":107875,"ariaHidden":243},[242],[212,107877,107879,107882,107888,107891,107894,107897,107900,107903,107906,107909],{"className":107878},[247],[212,107880],{"className":107881,"style":336},[251],[212,107883,107885],{"className":107884},[256],[212,107886,32863],{"className":107887},[256,32862],[212,107889,310],{"className":107890},[343],[212,107892,403],{"className":107893,"style":531},[256,257],[212,107895,407],{"className":107896},[256],[212,107898,25767],{"className":107899,"style":25801},[256,257],[212,107901,317],{"className":107902},[350],[212,107904],{"className":107905,"style":355},[354],[212,107907,320],{"className":107908},[359],[212,107910],{"className":107911,"style":355},[354],[212,107913,107915,107918,107958,107964,107967,107972,107975,108052,108058,108061,108064],{"className":107914},[247],[212,107916],{"className":107917,"style":31503},[251],[212,107919,107921,107924],{"className":107920},[256],[212,107922,420],{"className":107923},[256,563],[212,107925,107927],{"className":107926},[478],[212,107928,107930,107950],{"className":107929},[482,483],[212,107931,107933,107947],{"className":107932},[487],[212,107934,107936],{"className":107935,"style":576},[491],[212,107937,107938,107941],{"style":579},[212,107939],{"className":107940,"style":500},[499],[212,107942,107944],{"className":107943},[504,505,506,507],[212,107945,403],{"className":107946,"style":531},[256,257,507],[212,107948,515],{"className":107949},[514],[212,107951,107953],{"className":107952},[487],[212,107954,107956],{"className":107955,"style":8166},[491],[212,107957],{},[212,107959,107961],{"className":107960},[256],[212,107962,427],{"className":107963},[616,3918],[212,107965],{"className":107966,"style":603},[354],[212,107968,4352,107970],{"className":107969},[1682],[212,107971,4356],{"style":4355},[212,107973],{"className":107974,"style":603},[354],[212,107976,107978,107981,108049],{"className":107977},[256],[212,107979],{"className":107980},[343,638],[212,107982,107984],{"className":107983},[435],[212,107985,107987,108041],{"className":107986},[482,483],[212,107988,107990,108038],{"className":107989},[487],[212,107991,107993,108016,108024],{"className":107992,"style":23089},[491],[212,107994,107995,107998],{"style":654},[212,107996],{"className":107997,"style":658},[499],[212,107999,108001,108004,108007,108010,108013],{"className":108000},[256],[212,108002,11],{"className":108003},[256,257],[212,108005],{"className":108006,"style":2785},[354],[212,108008,2668],{"className":108009},[2789],[212,108011],{"className":108012,"style":2785},[354],[212,108014,1141],{"className":108015,"style":1178},[256,257],[212,108017,108018,108021],{"style":670},[212,108019],{"className":108020,"style":658},[499],[212,108022],{"className":108023,"style":678},[677],[212,108025,108026,108029],{"style":681},[212,108027],{"className":108028,"style":658},[499],[212,108030,108032,108035],{"className":108031},[256],[212,108033,2661],{"className":108034},[256],[212,108036,11],{"className":108037},[256,257],[212,108039,515],{"className":108040},[514],[212,108042,108044],{"className":108043},[487],[212,108045,108047],{"className":108046,"style":703},[491],[212,108048],{},[212,108050],{"className":108051},[350,638],[212,108053,108055],{"className":108054},[256],[212,108056,454],{"className":108057},[616,3918],[212,108059],{"className":108060,"style":355},[354],[212,108062,320],{"className":108063},[359],[212,108065],{"className":108066,"style":355},[354],[212,108068,108070,108073,108113,108116,108121,108124,108164,108167,108170,108173],{"className":108069},[247],[212,108071],{"className":108072,"style":336},[251],[212,108074,108076,108079],{"className":108075},[256],[212,108077,420],{"className":108078},[256,563],[212,108080,108082],{"className":108081},[478],[212,108083,108085,108105],{"className":108084},[482,483],[212,108086,108088,108102],{"className":108087},[487],[212,108089,108091],{"className":108090,"style":576},[491],[212,108092,108093,108096],{"style":579},[212,108094],{"className":108095,"style":500},[499],[212,108097,108099],{"className":108098},[504,505,506,507],[212,108100,403],{"className":108101,"style":531},[256,257,507],[212,108103,515],{"className":108104},[514],[212,108106,108108],{"className":108107},[487],[212,108109,108111],{"className":108110,"style":8166},[491],[212,108112],{},[212,108114,427],{"className":108115},[343],[212,108117,4352,108119],{"className":108118},[1682],[212,108120,4356],{"style":4355},[212,108122],{"className":108123,"style":603},[354],[212,108125,108127,108130],{"className":108126},[256],[212,108128,396],{"className":108129,"style":474},[256,257],[212,108131,108133],{"className":108132},[478],[212,108134,108136,108156],{"className":108135},[482,483],[212,108137,108139,108153],{"className":108138},[487],[212,108140,108142],{"className":108141,"style":45129},[491],[212,108143,108144,108147],{"style":495},[212,108145],{"className":108146,"style":500},[499],[212,108148,108150],{"className":108149},[504,505,506,507],[212,108151,7759],{"className":108152},[256,257,507],[212,108154,515],{"className":108155},[514],[212,108157,108159],{"className":108158},[487],[212,108160,108162],{"className":108161,"style":8166},[491],[212,108163],{},[212,108165,454],{"className":108166},[350],[212,108168],{"className":108169,"style":2785},[354],[212,108171,2668],{"className":108172},[2789],[212,108174],{"className":108175,"style":2785},[354],[212,108177,108179,108182,108187,108190,108193],{"className":108178},[247],[212,108180],{"className":108181,"style":252},[251],[212,108183,4352,108185],{"className":108184},[1682],[212,108186,4356],{"style":4355},[212,108188],{"className":108189,"style":603},[354],[212,108191,2661],{"className":108192},[256],[212,108194,748],{"className":108195},[770],[11,108197,14461,108198,108226,108227,108281,108282,108396,108397,108455],{},[212,108199,108201,108214],{"className":108200,"translate":216},[215],[212,108202,108204],{"className":108203},[220],[222,108205,108206],{"xmlns":224},[226,108207,108208,108212],{},[229,108209,108210],{},[232,108211,410],{},[236,108213,410],{"encoding":238},[212,108215,108217],{"className":108216,"ariaHidden":243},[242],[212,108218,108220,108223],{"className":108219},[247],[212,108221],{"className":108222,"style":763},[251],[212,108224,410],{"className":108225},[256,257]," 同理，两式相加即得。于是「最小化 JS」与「在最优判别器下最大化 GAN 目标」是同一件事，而常数 ",[212,108228,108230,108252],{"className":108229,"translate":216},[215],[212,108231,108233],{"className":108232},[220],[222,108234,108235],{"xmlns":224},[226,108236,108237,108249],{},[229,108238,108239,108241,108243,108245,108247],{},[307,108240,5011],{},[312,108242,2661],{},[232,108244,4298],{},[307,108246,4301],{},[312,108248,2661],{},[236,108250,108251],{"encoding":238},"-2\\log2",[212,108253,108255],{"className":108254,"ariaHidden":243},[242],[212,108256,108258,108261,108264,108267,108270,108275,108278],{"className":108257},[247],[212,108259],{"className":108260,"style":252},[251],[212,108262,5011],{"className":108263},[256],[212,108265,2661],{"className":108266},[256],[212,108268],{"className":108269,"style":603},[354],[212,108271,4352,108273],{"className":108272},[1682],[212,108274,4356],{"style":4355},[212,108276],{"className":108277,"style":603},[354],[212,108279,2661],{"className":108280},[256]," 与生成器无关。这解释了「GAN 训练不收敛」的来源：JS 有界，一旦支撑集几近不重叠，",[212,108283,108285,108315],{"className":108284,"translate":216},[215],[212,108286,108288],{"className":108287},[220],[222,108289,108290],{"xmlns":224},[226,108291,108292,108312],{},[229,108293,108294,108304,108306,108308,108310],{},[392,108295,108296,108298],{},[232,108297,396],{},[229,108299,108300,108302],{},[232,108301,23943],{},[232,108303,25937],{},[307,108305,1228],{},[232,108307,4298],{},[307,108309,4301],{},[312,108311,2661],{},[236,108313,108314],{"encoding":238},"D_{JS}\\to\\log2",[212,108316,108318,108379],{"className":108317,"ariaHidden":243},[242],[212,108319,108321,108324,108370,108373,108376],{"className":108320},[247],[212,108322],{"className":108323,"style":16161},[251],[212,108325,108327,108330],{"className":108326},[256],[212,108328,396],{"className":108329,"style":474},[256,257],[212,108331,108333],{"className":108332},[478],[212,108334,108336,108362],{"className":108335},[482,483],[212,108337,108339,108359],{"className":108338},[487],[212,108340,108342],{"className":108341,"style":576},[491],[212,108343,108344,108347],{"style":495},[212,108345],{"className":108346,"style":500},[499],[212,108348,108350],{"className":108349},[504,505,506,507],[212,108351,108353,108356],{"className":108352},[256,507],[212,108354,23943],{"className":108355,"style":24353},[256,257,507],[212,108357,25937],{"className":108358,"style":26061},[256,257,507],[212,108360,515],{"className":108361},[514],[212,108363,108365],{"className":108364},[487],[212,108366,108368],{"className":108367,"style":8166},[491],[212,108369],{},[212,108371],{"className":108372,"style":355},[354],[212,108374,1228],{"className":108375},[359],[212,108377],{"className":108378,"style":355},[354],[212,108380,108382,108385,108390,108393],{"className":108381},[247],[212,108383],{"className":108384,"style":252},[251],[212,108386,4352,108388],{"className":108387},[1682],[212,108389,4356],{"style":4355},[212,108391],{"className":108392,"style":603},[354],[212,108394,2661],{"className":108395},[256],"，判别器梯度饱和，生成器梯度消失。反过来，换成 LSGAN（",[212,108398,108400,108417],{"className":108399,"translate":216},[215],[212,108401,108403],{"className":108402},[220],[222,108404,108405],{"xmlns":224},[226,108406,108407,108415],{},[229,108408,108409],{},[7012,108410,108411,108413],{},[232,108412,37649],{},[312,108414,2661],{},[236,108416,40594],{"encoding":238},[212,108418,108420],{"className":108419,"ariaHidden":243},[242],[212,108421,108423,108426],{"className":108422},[247],[212,108424],{"className":108425,"style":40604},[251],[212,108427,108429,108432],{"className":108428},[256],[212,108430,37649],{"className":108431},[256,257],[212,108433,108435],{"className":108434},[478],[212,108436,108438],{"className":108437},[482],[212,108439,108441],{"className":108440},[487],[212,108442,108444],{"className":108443,"style":20228},[491],[212,108445,108446,108449],{"style":7063},[212,108447],{"className":108448,"style":500},[499],[212,108450,108452],{"className":108451},[504,505,506,507],[212,108453,2661],{"className":108454},[256,507],"）、Wasserstein（非 f-散度）或 α-GAN 就能改变这一点。",[2509,108457,108459],{"id":108458},"_55-估计性质","5.5 估计性质",[11,108461,108462],{},"用 5.1 的 Monte Carlo 下界做估计时：",[10225,108464,108465,108610,108765],{},[6863,108466,108467,108468,34025,108537,108539,108540,108609],{},"它是 ",[212,108469,108471,108488],{"className":108470,"translate":216},[215],[212,108472,108474],{"className":108473},[220],[222,108475,108476],{"xmlns":224},[226,108477,108478,108486],{},[229,108479,108480],{},[392,108481,108482,108484],{},[232,108483,396],{},[232,108485,234],{},[236,108487,4220],{"encoding":238},[212,108489,108491],{"className":108490,"ariaHidden":243},[242],[212,108492,108494,108497],{"className":108493},[247],[212,108495],{"className":108496,"style":4230},[251],[212,108498,108500,108503],{"className":108499},[256],[212,108501,396],{"className":108502,"style":474},[256,257],[212,108504,108506],{"className":108505},[478],[212,108507,108509,108529],{"className":108508},[482,483],[212,108510,108512,108526],{"className":108511},[487],[212,108513,108515],{"className":108514,"style":492},[491],[212,108516,108517,108520],{"style":495},[212,108518],{"className":108519,"style":500},[499],[212,108521,108523],{"className":108522},[504,505,506,507],[212,108524,234],{"className":108525,"style":258},[256,257,507],[212,108527,515],{"className":108528},[514],[212,108530,108532],{"className":108531},[487],[212,108533,108535],{"className":108534,"style":522},[491],[212,108536],{},[1194,108538,100056],{},"（偏差向下），且偏差来自 ",[212,108541,108543,108560],{"className":108542,"translate":216},[215],[212,108544,108546],{"className":108545},[220],[222,108547,108548],{"xmlns":224},[226,108549,108550,108558],{},[229,108551,108552],{},[392,108553,108554,108556],{},[232,108555,4356],{},[232,108557,100076],{},[236,108559,100079],{"encoding":238},[212,108561,108563],{"className":108562,"ariaHidden":243},[242],[212,108564,108566,108569],{"className":108565},[247],[212,108567],{"className":108568,"style":2474},[251],[212,108570,108572,108575],{"className":108571},[256],[212,108573,4356],{"className":108574,"style":1178},[256,257],[212,108576,108578],{"className":108577},[478],[212,108579,108581,108601],{"className":108580},[482,483],[212,108582,108584,108598],{"className":108583},[487],[212,108585,108587],{"className":108586,"style":45129},[491],[212,108588,108589,108592],{"style":19043},[212,108590],{"className":108591,"style":500},[499],[212,108593,108595],{"className":108594},[504,505,506,507],[212,108596,100076],{"className":108597,"style":1178},[256,257,507],[212,108599,515],{"className":108600},[514],[212,108602,108604],{"className":108603},[487],[212,108605,108607],{"className":108606,"style":8166},[491],[212,108608],{}," 未达到最优 + 样本有限；",[6863,108611,68342,108612,108642,108643,108701,108702,108764],{},[212,108613,108615,108630],{"className":108614,"translate":216},[215],[212,108616,108618],{"className":108617},[220],[222,108619,108620],{"xmlns":224},[226,108621,108622,108628],{},[229,108623,108624,108626],{},[232,108625,35632],{},[307,108627,4301],{},[236,108629,57350],{"encoding":238},[212,108631,108633],{"className":108632,"ariaHidden":243},[242],[212,108634,108636,108639],{"className":108635},[247],[212,108637],{"className":108638,"style":2474},[251],[212,108640,35632],{"className":108641},[1682]," 取到极值时，估计量方差随 ",[212,108644,108646,108663],{"className":108645,"translate":216},[215],[212,108647,108649],{"className":108648},[220],[222,108650,108651],{"xmlns":224},[226,108652,108653,108661],{},[229,108654,108655],{},[7012,108656,108657,108659],{},[232,108658,234],{},[307,108660,7771],{},[236,108662,60918],{"encoding":238},[212,108664,108666],{"className":108665,"ariaHidden":243},[242],[212,108667,108669,108672],{"className":108668},[247],[212,108670],{"className":108671,"style":252},[251],[212,108673,108675,108678],{"className":108674},[256],[212,108676,234],{"className":108677,"style":258},[256,257],[212,108679,108681],{"className":108680},[478],[212,108682,108684],{"className":108683},[482],[212,108685,108687],{"className":108686},[487],[212,108688,108690],{"className":108689,"style":8697},[491],[212,108691,108692,108695],{"style":7063},[212,108693],{"className":108694,"style":500},[499],[212,108696,108698],{"className":108697},[504,505,506,507],[212,108699,7771],{"className":108700},[2789,507]," 增长而增大（如 KL 的 ",[212,108703,108705,108723],{"className":108704,"translate":216},[215],[212,108706,108708],{"className":108707},[220],[222,108709,108710],{"xmlns":224},[226,108711,108712,108720],{},[229,108713,108714],{},[7012,108715,108716,108718],{},[232,108717,7765],{},[232,108719,4356],{},[236,108721,108722],{"encoding":238},"e^{g}",[212,108724,108726],{"className":108725,"ariaHidden":243},[242],[212,108727,108729,108732],{"className":108728},[247],[212,108730],{"className":108731,"style":50552},[251],[212,108733,108735,108738],{"className":108734},[256],[212,108736,7765],{"className":108737},[256,257],[212,108739,108741],{"className":108740},[478],[212,108742,108744],{"className":108743},[482],[212,108745,108747],{"className":108746},[487],[212,108748,108750],{"className":108749,"style":50552},[491],[212,108751,108752,108755],{"style":7063},[212,108753],{"className":108754,"style":500},[499],[212,108756,108758],{"className":108757},[504,505,506,507],[212,108759,108761],{"className":108760},[256,507],[212,108762,4356],{"className":108763,"style":1178},[256,257,507]," 会重尾）；",[6863,108766,108767,108768,108796],{},"一个常用替代是「对称化」或「有界化」",[212,108769,108771,108784],{"className":108770,"translate":216},[215],[212,108772,108774],{"className":108773},[220],[222,108775,108776],{"xmlns":224},[226,108777,108778,108782],{},[229,108779,108780],{},[232,108781,234],{},[236,108783,234],{"encoding":238},[212,108785,108787],{"className":108786,"ariaHidden":243},[242],[212,108788,108790,108793],{"className":108789},[247],[212,108791],{"className":108792,"style":252},[251],[212,108794,234],{"className":108795,"style":258},[256,257],"（如 JS、TV），牺牲敏感性换取稳定梯度。这与第 6 节讨论的「有界\u002F无界」准确性—稳健性权衡是同一件事。",[725,108798,108800],{"id":108799},"_6-与其他散度的比较","6. 与其他散度的比较",[2509,108802,108804],{"id":108803},"_61-汇总","6.1 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88},[256,34567,507],[212,112690,112692,112733],{"className":112691},[482,483],[212,112693,112695,112730],{"className":112694},[487],[212,112696,112699,112717],{"className":112697,"style":112698},[491],"height:0.8156em;",[212,112700,112702,112705],{"className":112701,"style":12063},[6505],[212,112703],{"className":112704,"style":658},[499],[212,112706,112708,112711,112714],{"className":112707,"style":34587},[256,507],[212,112709,314],{"className":112710},[256,507],[212,112712,5011],{"className":112713},[2789,507],[212,112715,40437],{"className":112716,"style":1178},[256,257,507],[212,112718,112720,112723],{"style":112719},"top:-2.7756em;",[212,112721],{"className":112722,"style":658},[499],[212,112724,112726],{"className":112725,"style":34644},[34643,507],[6521,112727,112728],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,112729],{"d":34651},[212,112731,515],{"className":112732},[514],[212,112734,112736],{"className":112735},[487],[212,112737,112740],{"className":112738,"style":112739},[491],"height:0.2244em;",[212,112741],{},[212,112743,112744,112747],{"style":670},[212,112745],{"className":112746,"style":658},[499],[212,112748],{"className":112749,"style":678},[677],[212,112751,112752,112755],{"style":2748},[212,112753],{"className":112754,"style":658},[499],[212,112756,112758],{"className":112757},[504,505,506,507],[212,112759,112761],{"className":112760},[256,507],[212,112762,314],{"className":112763},[256,507],[212,112765,515],{"className":112766},[514],[212,112768,112770],{"className":112769},[487],[212,112771,112773],{"className":112772,"style":98469},[491],[212,112774],{},[212,112776],{"className":112777},[350,638],[212,112779,112781,112798],{"className":112780,"translate":216},[215],[212,112782,112784],{"className":112783},[220],[222,112785,112786],{"xmlns":224},[226,112787,112788,112796],{},[229,112789,112790,112792,112794],{},[232,112791,40437],{},[307,112793,7449],{},[312,112795,314],{},[236,112797,66983],{"encoding":238},[212,112799,112801,112819],{"className":112800,"ariaHidden":243},[242],[212,112802,112804,112807,112810,112813,112816],{"className":112803},[247],[212,112805],{"className":112806,"style":31892},[251],[212,112808,40437],{"className":112809,"style":1178},[256,257],[212,112811],{"className":112812,"style":355},[354],[212,112814,7449],{"className":112815},[359],[212,112817],{"className":112818,"style":355},[354],[212,112820,112822,112825],{"className":112821},[247],[212,112823],{"className":112824,"style":369},[251],[212,112826,314],{"className":112827},[256],"），代回得 ",[212,112830,112832,112924],{"className":112831,"translate":216},[215],[212,112833,112835],{"className":112834},[220],[222,112836,112837],{"xmlns":224},[226,112838,112839,112921],{},[229,112840,112841,112847,112849,112851,112853,112855,112857,112859,112861,112863,112865,112867,112873,112875,112877,112887,112889,112891,112893,112903,112905,112907,112909,112911],{},[7012,112842,112843,112845],{},[232,112844,234],{},[307,112846,7771],{},[307,112848,320],{},[232,112850,966],{},[307,112852,310],{"stretchy":309},[232,112854,40437],{},[307,112856,5011],{},[312,112858,314],{},[307,112860,317],{"stretchy":309},[307,112862,2668],{},[312,112864,2661],{},[307,112866,5011],{},[435,112868,112869,112871],{},[312,112870,314],{},[232,112872,966],{},[307,112874,320],{},[307,112876,5011],{},[34539,112878,112879],{},[229,112880,112881,112883,112885],{},[312,112882,314],{},[307,112884,5011],{},[232,112886,40437],{},[307,112888,2668],{},[312,112890,2661],{},[307,112892,5011],{},[34539,112894,112895],{},[229,112896,112897,112899,112901],{},[312,112898,314],{},[307,112900,5011],{},[232,112902,40437],{},[307,112904,320],{},[312,112906,2661],{},[307,112908,5011],{},[312,112910,2661],{},[34539,112912,112913],{},[229,112914,112915,112917,112919],{},[312,112916,314],{},[307,112918,5011],{},[232,112920,40437],{},[236,112922,112923],{"encoding":238},"f^*=t(y-1)+2-\\frac1t=-\\sqrt{1-y}+2-\\sqrt{1-y}=2-2\\sqrt{1-y}",[212,112925,112927,112971,112995,113016,113034,113117,113194,113212,113286,113304],{"className":112926,"ariaHidden":243},[242],[212,112928,112930,112933,112962,112965,112968],{"className":112929},[247],[212,112931],{"className":112932,"style":252},[251],[212,112934,112936,112939],{"className":112935},[256],[212,112937,234],{"className":112938,"style":258},[256,257],[212,112940,112942],{"className":112941},[478],[212,112943,112945],{"className":112944},[482],[212,112946,112948],{"className":112947},[487],[212,112949,112951],{"className":112950,"style":8697},[491],[212,112952,112953,112956],{"style":7063},[212,112954],{"className":112955,"style":500},[499],[212,112957,112959],{"className":112958},[504,505,506,507],[212,112960,7771],{"className":112961},[2789,507],[212,112963],{"className":112964,"style":355},[354],[212,112966,320],{"className":112967},[359],[212,112969],{"className":112970,"style":355},[354],[212,112972,112974,112977,112980,112983,112986,112989,112992],{"className":112973},[247],[212,112975],{"className":112976,"style":336},[251],[212,112978,966],{"className":112979},[256,257],[212,112981,310],{"className":112982},[343],[212,112984,40437],{"className":112985,"style":1178},[256,257],[212,112987],{"className":112988,"style":2785},[354],[212,112990,5011],{"className":112991},[2789],[212,112993],{"className":112994,"style":2785},[354],[212,112996,112998,113001,113004,113007,113010,113013],{"className":112997},[247],[212,112999],{"className":113000,"style":336},[251],[212,113002,314],{"className":113003},[256],[212,113005,317],{"className":113006},[350],[212,113008],{"className":113009,"style":2785},[354],[212,113011,2668],{"className":113012},[2789],[212,113014],{"className":113015,"style":2785},[354],[212,113017,113019,113022,113025,113028,113031],{"className":113018},[247],[212,113020],{"className":113021,"style":12778},[251],[212,113023,2661],{"className":113024},[256],[212,113026],{"className":113027,"style":2785},[354],[212,113029,5011],{"className":113030},[2789],[212,113032],{"className":113033,"style":2785},[354],[212,113035,113037,113040,113108,113111,113114],{"className":113036},[247],[212,113038],{"className":113039,"style":2703},[251],[212,113041,113043,113046,113105],{"className":113042},[256],[212,113044],{"className":113045},[343,638],[212,113047,113049],{"className":113048},[435],[212,113050,113052,113097],{"className":113051},[482,483],[212,113053,113055,113094],{"className":113054},[487],[212,113056,113058,113072,113080],{"className":113057,"style":2722},[491],[212,113059,113060,113063],{"style":2725},[212,113061],{"className":113062,"style":658},[499],[212,113064,113066],{"className":113065},[504,505,506,507],[212,113067,113069],{"className":113068},[256,507],[212,113070,966],{"className":113071},[256,257,507],[212,113073,113074,113077],{"style":670},[212,113075],{"className":113076,"style":658},[499],[212,113078],{"className":113079,"style":678},[677],[212,113081,113082,113085],{"style":2748},[212,113083],{"className":113084,"style":658},[499],[212,113086,113088],{"className":113087},[504,505,506,507],[212,113089,113091],{"className":113090},[256,507],[212,113092,314],{"className":113093},[256,507],[212,113095,515],{"className":113096},[514],[212,113098,113100],{"className":113099},[487],[212,113101,113103],{"className":113102,"style":2770},[491],[212,113104],{},[212,113106],{"className":113107},[350,638],[212,113109],{"className":113110,"style":355},[354],[212,113112,320],{"className":113113},[359],[212,113115],{"className":113116,"style":355},[354],[212,113118,113120,113123,113126,113185,113188,113191],{"className":113119},[247],[212,113121],{"className":113122,"style":110612},[251],[212,113124,5011],{"className":113125},[256],[212,113127,113129],{"className":113128},[256,34567],[212,113130,113132,113177],{"className":113131},[482,483],[212,113133,113135,113174],{"className":113134},[487],[212,113136,113138,113162],{"className":113137,"style":110628},[491],[212,113139,113141,113144],{"className":113140,"style":12063},[6505],[212,113142],{"className":113143,"style":658},[499],[212,113145,113147,113150,113153,113156,113159],{"className":113146,"style":34587},[256],[212,113148,314],{"className":113149},[256],[212,113151],{"className":113152,"style":2785},[354],[212,113154,5011],{"className":113155},[2789],[212,113157],{"className":113158,"style":2785},[354],[212,113160,40437],{"className":113161,"style":1178},[256,257],[212,113163,113164,113167],{"style":110655},[212,113165],{"className":113166,"style":658},[499],[212,113168,113170],{"className":113169,"style":34644},[34643],[6521,113171,113172],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,113173],{"d":34651},[212,113175,515],{"className":113176},[514],[212,113178,113180],{"className":113179},[487],[212,113181,113183],{"className":113182,"style":110675},[491],[212,113184],{},[212,113186],{"className":113187,"style":2785},[354],[212,113189,2668],{"className":113190},[2789],[212,113192],{"className":113193,"style":2785},[354],[212,113195,113197,113200,113203,113206,113209],{"className":113196},[247],[212,113198],{"className":113199,"style":12778},[251],[212,113201,2661],{"className":113202},[256],[212,113204],{"className":113205,"style":2785},[354],[212,113207,5011],{"className":113208},[2789],[212,113210],{"className":113211,"style":2785},[354],[212,113213,113215,113218,113277,113280,113283],{"className":113214},[247],[212,113216],{"className":113217,"style":110612},[251],[212,113219,113221],{"className":113220},[256,34567],[212,113222,113224,113269],{"className":113223},[482,483],[212,113225,113227,113266],{"className":113226},[487],[212,113228,113230,113254],{"className":113229,"style":110628},[491],[212,113231,113233,113236],{"className":113232,"style":12063},[6505],[212,113234],{"className":113235,"style":658},[499],[212,113237,113239,113242,113245,113248,113251],{"className":113238,"style":34587},[256],[212,113240,314],{"className":113241},[256],[212,113243],{"className":113244,"style":2785},[354],[212,113246,5011],{"className":113247},[2789],[212,113249],{"className":113250,"style":2785},[354],[212,113252,40437],{"className":113253,"style":1178},[256,257],[212,113255,113256,113259],{"style":110655},[212,113257],{"className":113258,"style":658},[499],[212,113260,113262],{"className":113261,"style":34644},[34643],[6521,113263,113264],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,113265],{"d":34651},[212,113267,515],{"className":113268},[514],[212,113270,113272],{"className":113271},[487],[212,113273,113275],{"className":113274,"style":110675},[491],[212,113276],{},[212,113278],{"className":113279,"style":355},[354],[212,113281,320],{"className":113282},[359],[212,113284],{"className":113285,"style":355},[354],[212,113287,113289,113292,113295,113298,113301],{"className":113288},[247],[212,113290],{"className":113291,"style":12778},[251],[212,113293,2661],{"className":113294},[256],[212,113296],{"className":113297,"style":2785},[354],[212,113299,5011],{"className":113300},[2789],[212,113302],{"className":113303,"style":2785},[354],[212,113305,113307,113310,113313],{"className":113306},[247],[212,113308],{"className":113309,"style":110612},[251],[212,113311,2661],{"className":113312},[256],[212,113314,113316],{"className":113315},[256,34567],[212,113317,113319,113364],{"className":113318},[482,483],[212,113320,113322,113361],{"className":113321},[487],[212,113323,113325,113349],{"className":113324,"style":110628},[491],[212,113326,113328,113331],{"className":113327,"style":12063},[6505],[212,113329],{"className":113330,"style":658},[499],[212,113332,113334,113337,113340,113343,113346],{"className":113333,"style":34587},[256],[212,113335,314],{"className":113336},[256],[212,113338],{"className":113339,"style":2785},[354],[212,113341,5011],{"className":113342},[2789],[212,113344],{"className":113345,"style":2785},[354],[212,113347,40437],{"className":113348,"style":1178},[256,257],[212,113350,113351,113354],{"style":110655},[212,113352],{"className":113353,"style":658},[499],[212,113355,113357],{"className":113356,"style":34644},[34643],[6521,113358,113359],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,113360],{"d":34651},[212,113362,515],{"className":113363},[514],[212,113365,113367],{"className":113366},[487],[212,113368,113370],{"className":113369,"style":110675},[491],[212,113371],{},"。α 一行取 ",[212,113374,113376,113415],{"className":113375,"translate":216},[215],[212,113377,113379],{"className":113378},[220],[222,113380,113381],{"xmlns":224},[226,113382,113383,113413],{},[229,113384,113385,113387,113389,113401,113403,113405,113407,113409,113411],{},[232,113386,15],{},[307,113388,320],{},[435,113390,113391,113399],{},[229,113392,113393,113395,113397],{},[312,113394,314],{},[307,113396,2668],{},[232,113398,44954],{},[312,113400,2661],{},[307,113402,6107],{},[307,113404,310],{"stretchy":309},[312,113406,323],{},[307,113408,748],{"separator":243},[312,113410,314],{},[307,113412,317],{"stretchy":309},[236,113414,45408],{"encoding":238},[212,113416,113418,113436,113525],{"className":113417,"ariaHidden":243},[242],[212,113419,113421,113424,113427,113430,113433],{"className":113420},[247],[212,113422],{"className":113423,"style":2543},[251],[212,113425,15],{"className":113426},[256,257],[212,113428],{"className":113429,"style":355},[354],[212,113431,320],{"className":113432},[359],[212,113434],{"className":113435,"style":355},[354],[212,113437,113439,113442,113516,113519,113522],{"className":113438},[247],[212,113440],{"className":113441,"style":2703},[251],[212,113443,113445,113448,113513],{"className":113444},[256],[212,113446],{"className":113447},[343,638],[212,113449,113451],{"className":113450},[435],[212,113452,113454,113505],{"className":113453},[482,483],[212,113455,113457,113502],{"className":113456},[487],[212,113458,113460,113474,113482],{"className":113459,"style":2722},[491],[212,113461,113462,113465],{"style":2725},[212,113463],{"className":113464,"style":658},[499],[212,113466,113468],{"className":113467},[504,505,506,507],[212,113469,113471],{"className":113470},[256,507],[212,113472,2661],{"className":113473},[256,507],[212,113475,113476,113479],{"style":670},[212,113477],{"className":113478,"style":658},[499],[212,113480],{"className":113481,"style":678},[677],[212,113483,113484,113487],{"style":2748},[212,113485],{"className":113486,"style":658},[499],[212,113488,113490],{"className":113489},[504,505,506,507],[212,113491,113493,113496,113499],{"className":113492},[256,507],[212,113494,314],{"className":113495},[256,507],[212,113497,2668],{"className":113498},[2789,507],[212,113500,44954],{"className":113501,"style":44984},[256,257,507],[212,113503,515],{"className":113504},[514],[212,113506,113508],{"className":113507},[487],[212,113509,113511],{"className":113510,"style":2770},[491],[212,113512],{},[212,113514],{"className":113515},[350,638],[212,113517],{"className":113518,"style":355},[354],[212,113520,6107],{"className":113521},[359],[212,113523],{"className":113524,"style":355},[354],[212,113526,113528,113531,113534,113537,113540,113543,113546],{"className":113527},[247],[212,113529],{"className":113530,"style":336},[251],[212,113532,310],{"className":113533},[343],[212,113535,323],{"className":113536},[256],[212,113538,748],{"className":113539},[770],[212,113541],{"className":113542,"style":603},[354],[212,113544,314],{"className":113545},[256],[212,113547,317],{"className":113548},[350],"，验证：",[212,113551,113553,113629],{"className":113552,"translate":216},[215],[212,113554,113556],{"className":113555},[220],[222,113557,113558],{"xmlns":224},[226,113559,113560,113626],{},[229,113561,113562,113570,113572,113574,113576,113578,113588,113590,113592,113594,113596,113624],{},[7751,113563,113564,113566,113568],{},[232,113565,234],{},[232,113567,44954],{},[307,113569,7771],{},[307,113571,310],{"stretchy":309},[232,113573,40437],{},[307,113575,317],{"stretchy":309},[307,113577,320],{},[392,113579,113580,113586],{},[229,113581,113582,113584],{},[232,113583,35632],{},[307,113585,4301],{},[232,113587,966],{},[307,113589,3096],{"stretchy":309},[232,113591,966],{},[232,113593,40437],{},[307,113595,5011],{},[435,113597,113598,113610],{},[229,113599,113600,113602,113604],{},[312,113601,314],{},[307,113603,5011],{},[7012,113605,113606,113608],{},[232,113607,966],{},[232,113609,15],{},[229,113611,113612,113614,113616,113618,113620,113622],{},[232,113613,15],{},[307,113615,310],{"stretchy":309},[312,113617,314],{},[307,113619,5011],{},[232,113621,15],{},[307,113623,317],{"stretchy":309},[307,113625,3106],{"stretchy":309},[236,113627,113628],{"encoding":238},"f_\\alpha^*(y)=\\sup_t\\{ty-\\frac{1-t^a}{a(1-a)}\\}",[212,113630,113632,113707,113771],{"className":113631,"ariaHidden":243},[242],[212,113633,113635,113638,113689,113692,113695,113698,113701,113704],{"className":113634},[247],[212,113636],{"className":113637,"style":336},[251],[212,113639,113641,113644],{"className":113640},[256],[212,113642,234],{"className":113643,"style":258},[256,257],[212,113645,113647],{"className":113646},[478],[212,113648,113650,113681],{"className":113649},[482,483],[212,113651,113653,113678],{"className":113652},[487],[212,113654,113656,113667],{"className":113655,"style":8697},[491],[212,113657,113658,113661],{"style":8449},[212,113659],{"className":113660,"style":500},[499],[212,113662,113664],{"className":113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],{"className":113948},[247],[212,113950],{"className":113951,"style":40521},[251],[212,113953,40437],{"className":113954,"style":1178},[256,257],[212,113956],{"className":113957,"style":2785},[354],[212,113959,2668],{"className":113960},[2789],[212,113962],{"className":113963,"style":2785},[354],[212,113965,113967,113971,114081,114084,114087],{"className":113966},[247],[212,113968],{"className":113969,"style":113970},[251],"height:1.4213em;vertical-align:-0.4033em;",[212,113972,113974,113977,114078],{"className":113973},[256],[212,113975],{"className":113976},[343,638],[212,113978,113980],{"className":113979},[435],[212,113981,113983,114070],{"className":113982},[482,483],[212,113984,113986,114067],{"className":113985},[487],[212,113987,113990,114010,114018],{"className":113988,"style":113989},[491],"height:1.0179em;",[212,113991,113992,113995],{"style":2725},[212,113993],{"className":113994,"style":658},[499],[212,113996,113998],{"className":113997},[504,505,506,507],[212,113999,114001,114004,114007],{"className":114000},[256,507],[212,114002,314],{"className":114003},[256,507],[212,114005,5011],{"className":114006},[2789,507],[212,114008,15],{"className":114009},[256,257,507],[212,114011,114012,114015],{"style":670},[212,114013],{"className":114014,"style":658},[499],[212,114016],{"className":114017,"style":678},[677],[212,114019,114020,114023],{"style":2748},[212,114021],{"className":114022,"style":658},[499],[212,114024,114026],{"className":114025},[504,505,506,507],[212,114027,114029],{"className":114028},[256,507],[212,114030,114032,114035],{"className":114031},[256,507],[212,114033,966],{"className":114034},[256,257,507],[212,114036,114038],{"className":114037},[478],[212,114039,114041],{"className":114040},[482],[212,114042,114044],{"className":114043},[487],[212,114045,114047],{"className":114046,"style":38712},[491],[212,114048,114049,114052],{"style":38715},[212,114050],{"className":114051,"style":30406},[499],[212,114053,114055],{"className":114054},[504,30410,9872,507],[212,114056,114058,114061,114064],{"className":114057},[256,507],[212,114059,15],{"className":114060},[256,257,507],[212,114062,5011],{"className":114063},[2789,507],[212,114065,314],{"className":114066},[256,507],[212,114068,515],{"className":114069},[514],[212,114071,114073],{"className":114072},[487],[212,114074,114076],{"className":114075,"style":16629},[491],[212,114077],{},[212,114079],{"className":114080},[350,638],[212,114082],{"className":114083,"style":355},[354],[212,114085,320],{"className":114086},[359],[212,114088],{"className":114089,"style":355},[354],[212,114091,114093,114096],{"className":114092},[247],[212,114094],{"className":114095,"style":369},[251],[212,114097,323],{"className":114098},[256],[212,114100,114102,114158],{"className":114101,"translate":216},[215],[212,114103,114105],{"className":114104},[220],[222,114106,114107],{"xmlns":224},[226,114108,114109,114155],{},[229,114110,114111,114113,114115,114117,114119,114121,114123,114125,114127,114129,114131,114133,114135],{},[232,114112,966],{},[307,114114,320],{},[307,114116,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,114118,310],{"stretchy":309},[312,114120,314],{},[307,114122,5011],{},[232,114124,15],{},[307,114126,317],{"stretchy":309},[307,114128,310],{"stretchy":309},[307,114130,5011],{},[232,114132,40437],{},[307,114134,317],{"stretchy":309},[7012,114136,114137,114139],{},[307,114138,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[229,114140,114141,114143],{},[307,114142,5011],{},[435,114144,114145,114147],{},[312,114146,314],{},[229,114148,114149,114151,114153],{},[312,114150,314],{},[307,114152,5011],{},[232,114154,15],{},[236,114156,114157],{"encoding":238},"t=\\big((1-a)(-y)\\big)^{-\\frac{1}{1-a}}",[212,114159,114161,114179,114206],{"className":114160,"ariaHidden":243},[242],[212,114162,114164,114167,114170,114173,114176],{"className":114163},[247],[212,114165],{"className":114166,"style":5541},[251],[212,114168,966],{"className":114169},[256,257],[212,114171],{"className":114172,"style":355},[354],[212,114174,320],{"className":114175},[359],[212,114177],{"className":114178,"style":355},[354],[212,114180,114182,114185,114191,114194,114197,114200,114203],{"className":114181},[247],[212,114183],{"className":114184,"style":20763},[251],[212,114186,114188],{"className":114187},[256],[212,114189,310],{"className":114190},[616,9872],[212,114192,310],{"className":114193},[343],[212,114195,314],{"className":114196},[256],[212,114198],{"className":114199,"style":2785},[354],[212,114201,5011],{"className":114202},[2789],[212,114204],{"className":114205,"style":2785},[354],[212,114207,114209,114213,114216,114219,114222,114225,114228,114231],{"className":114208},[247],[212,114210],{"className":114211,"style":114212},[251],"height:1.5439em;vertical-align:-0.35em;",[212,114214,15],{"className":114215},[256,257],[212,114217,317],{"className":114218},[350],[212,114220,310],{"className":114221},[343],[212,114223,5011],{"className":114224},[256],[212,114226,40437],{"className":114227,"style":1178},[256,257],[212,114229,317],{"className":114230},[350],[212,114232,114234,114240],{"className":114233},[256],[212,114235,114237],{"className":114236},[256],[212,114238,317],{"className":114239},[616,9872],[212,114241,114243],{"className":114242},[478],[212,114244,114246],{"className":114245},[482],[212,114247,114249],{"className":114248},[487],[212,114250,114253],{"className":114251,"style":114252},[491],"height:1.1939em;",[212,114254,114255,114258],{"style":111521},[212,114256],{"className":114257,"style":658},[499],[212,114259,114261],{"className":114260},[504,505,506,507],[212,114262,114264,114267],{"className":114263},[256,507],[212,114265,5011],{"className":114266},[256,507],[212,114268,114270,114273,114339],{"className":114269},[256,507],[212,114271],{"className":114272},[343,638,504,30410,111540],[212,114274,114276],{"className":114275},[435],[212,114277,114279,114331],{"className":114278},[482,483],[212,114280,114282,114328],{"className":114281},[487],[212,114283,114286,114306,114314],{"className":114284,"style":114285},[491],"height:0.8443em;",[212,114287,114288,114291],{"style":111556},[212,114289],{"className":114290,"style":658},[499],[212,114292,114294],{"className":114293},[504,30410,9872,507],[212,114295,114297,114300,114303],{"className":114296},[256,507],[212,114298,314],{"className":114299},[256,507],[212,114301,5011],{"className":114302},[2789,507],[212,114304,15],{"className":114305},[256,257,507],[212,114307,114308,114311],{"style":111577},[212,114309],{"className":114310,"style":658},[499],[212,114312],{"className":114313,"style":111584},[677,507],[212,114315,114316,114319],{"style":111587},[212,114317],{"className":114318,"style":658},[499],[212,114320,114322],{"className":114321},[504,30410,9872,507],[212,114323,114325],{"className":114324},[256,507],[212,114326,314],{"className":114327},[256,507],[212,114329,515],{"className":114330},[514],[212,114332,114334],{"className":114333},[487],[212,114335,114337],{"className":114336,"style":111609},[491],[212,114338],{},[212,114340],{"className":114341},[350,638,504,30410,111540],[212,114343,114345,114362],{"className":114344,"translate":216},[215],[212,114346,114348],{"className":114347},[220],[222,114349,114350],{"xmlns":224},[226,114351,114352,114360],{},[229,114353,114354,114356,114358],{},[232,114355,40437],{},[307,114357,7449],{},[312,114359,323],{},[236,114361,65351],{"encoding":238},[212,114363,114365,114383],{"className":114364,"ariaHidden":243},[242],[212,114366,114368,114371,114374,114377,114380],{"className":114367},[247],[212,114369],{"className":114370,"style":31892},[251],[212,114372,40437],{"className":114373,"style":1178},[256,257],[212,114375],{"className":114376,"style":355},[354],[212,114378,7449],{"className":114379},[359],[212,114381],{"className":114382,"style":355},[354],[212,114384,114386,114389],{"className":114385},[247],[212,114387],{"className":114388,"style":369},[251],[212,114390,323],{"className":114391},[256],"），代回即得上式；",[212,114394,114396,114418],{"className":114395,"translate":216},[215],[212,114397,114399],{"className":114398},[220],[222,114400,114401],{"xmlns":224},[226,114402,114403,114415],{},[229,114404,114405,114407,114409],{},[232,114406,15],{},[307,114408,320],{},[435,114410,114411,114413],{},[312,114412,314],{},[312,114414,2661],{},[236,114416,114417],{"encoding":238},"a=\\frac12",[212,114419,114421,114439],{"className":114420,"ariaHidden":243},[242],[212,114422,114424,114427,114430,114433,114436],{"className":114423},[247],[212,114425],{"className":114426,"style":2543},[251],[212,114428,15],{"className":114429},[256,257],[212,114431],{"className":114432,"style":355},[354],[212,114434,320],{"className":114435},[359],[212,114437],{"className":114438,"style":355},[354],[212,114440,114442,114445],{"className":114441},[247],[212,114443],{"className":114444,"style":2703},[251],[212,114446,114448,114451,114510],{"className":114447},[256],[212,114449],{"className":114450},[343,638],[212,114452,114454],{"className":114453},[435],[212,114455,114457,114502],{"className":114456},[482,483],[212,114458,114460,114499],{"className":114459},[487],[212,114461,114463,114477,114485],{"className":114462,"style":2722},[491],[212,114464,114465,114468],{"style":2725},[212,114466],{"className":114467,"style":658},[499],[212,114469,114471],{"className":114470},[504,505,506,507],[212,114472,114474],{"className":114473},[256,507],[212,114475,2661],{"className":114476},[256,507],[212,114478,114479,114482],{"style":670},[212,114480],{"className":114481,"style":658},[499],[212,114483],{"className":114484,"style":678},[677],[212,114486,114487,114490],{"style":2748},[212,114488],{"className":114489,"style":658},[499],[212,114491,114493],{"className":114492},[504,505,506,507],[212,114494,114496],{"className":114495},[256,507],[212,114497,314],{"className":114498},[256,507],[212,114500,515],{"className":114501},[514],[212,114503,114505],{"className":114504},[487],[212,114506,114508],{"className":114507,"style":2770},[491],[212,114509],{},[212,114511],{"className":114512},[350,638],[212,114514,114516,114533],{"className":114515,"translate":216},[215],[212,114517,114519],{"className":114518},[220],[222,114520,114521],{"xmlns":224},[226,114522,114523,114531],{},[229,114524,114525,114527,114529],{},[232,114526,44954],{},[307,114528,320],{},[312,114530,323],{},[236,114532,46687],{"encoding":238},[212,114534,114536,114554],{"className":114535,"ariaHidden":243},[242],[212,114537,114539,114542,114545,114548,114551],{"className":114538},[247],[212,114540],{"className":114541,"style":2543},[251],[212,114543,44954],{"className":114544,"style":44984},[256,257],[212,114546],{"className":114547,"style":355},[354],[212,114549,320],{"className":114550},[359],[212,114552],{"className":114553,"style":355},[354],[212,114555,114557,114560],{"className":114556},[247],[212,114558],{"className":114559,"style":369},[251],[212,114561,323],{"className":114562},[256],[212,114564,114566,114596],{"className":114565,"translate":216},[215],[212,114567,114569],{"className":114568},[220],[222,114570,114571],{"xmlns":224},[226,114572,114573,114593],{},[229,114574,114575,114577,114579,114581,114583,114585,114587,114591],{},[232,114576,234],{},[307,114578,320],{},[312,114580,39189],{},[307,114582,310],{"stretchy":309},[312,114584,314],{},[307,114586,5011],{},[34539,114588,114589],{},[232,114590,966],{},[307,114592,317],{"stretchy":309},[236,114594,114595],{"encoding":238},"f=4(1-\\sqrt t)",[212,114597,114599,114617,114641],{"className":114598,"ariaHidden":243},[242],[212,114600,114602,114605,114608,114611,114614],{"className":114601},[247],[212,114603],{"className":114604,"style":252},[251],[212,114606,234],{"className":114607,"style":258},[256,257],[212,114609],{"className":114610,"style":355},[354],[212,114612,320],{"className":114613},[359],[212,114615],{"className":114616,"style":355},[354],[212,114618,114620,114623,114626,114629,114632,114635,114638],{"className":114619},[247],[212,114621],{"className":114622,"style":336},[251],[212,114624,39189],{"className":114625},[256],[212,114627,310],{"className":114628},[343],[212,114630,314],{"className":114631},[256],[212,114633],{"className":114634,"style":2785},[354],[212,114636,5011],{"className":114637},[2789],[212,114639],{"className":114640,"style":2785},[354],[212,114642,114644,114647,114691],{"className":114643},[247],[212,114645],{"className":114646,"style":42867},[251],[212,114648,114650],{"className":114649},[256,34567],[212,114651,114653,114683],{"className":114652},[482,483],[212,114654,114656,114680],{"className":114655},[487],[212,114657,114659,114668],{"className":114658,"style":42883},[491],[212,114660,114662,114665],{"className":114661,"style":12063},[6505],[212,114663],{"className":114664,"style":658},[499],[212,114666,966],{"className":114667,"style":34587},[256,257],[212,114669,114670,114673],{"style":42895},[212,114671],{"className":114672,"style":658},[499],[212,114674,114676],{"className":114675,"style":34644},[34643],[6521,114677,114678],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,114679],{"d":34651},[212,114681,515],{"className":114682},[514],[212,114684,114686],{"className":114685},[487],[212,114687,114689],{"className":114688,"style":42915},[491],[212,114690],{},[212,114692,317],{"className":114693},[350],"）时公式给出 ",[212,114696,114698,114724],{"className":114697,"translate":216},[215],[212,114699,114701],{"className":114700},[220],[222,114702,114703],{"xmlns":224},[226,114704,114705,114721],{},[229,114706,114707,114717,114719],{},[435,114708,114709,114711],{},[312,114710,39189],{},[229,114712,114713,114715],{},[307,114714,5011],{},[232,114716,40437],{},[307,114718,5011],{},[312,114720,39189],{},[236,114722,114723],{"encoding":238},"\\frac{4}{-y}-4",[212,114725,114727,114814],{"className":114726,"ariaHidden":243},[242],[212,114728,114730,114734,114805,114808,114811],{"className":114729},[247],[212,114731],{"className":114732,"style":114733},[251],"height:1.3262em;vertical-align:-0.4811em;",[212,114735,114737,114740,114802],{"className":114736},[256],[212,114738],{"className":114739},[343,638],[212,114741,114743],{"className":114742},[435],[212,114744,114746,114794],{"className":114745},[482,483],[212,114747,114749,114791],{"className":114748},[487],[212,114750,114752,114769,114777],{"className":114751,"style":2722},[491],[212,114753,114754,114757],{"style":2725},[212,114755],{"className":114756,"style":658},[499],[212,114758,114760],{"className":114759},[504,505,506,507],[212,114761,114763,114766],{"className":114762},[256,507],[212,114764,5011],{"className":114765},[256,507],[212,114767,40437],{"className":114768,"style":1178},[256,257,507],[212,114770,114771,114774],{"style":670},[212,114772],{"className":114773,"style":658},[499],[212,114775],{"className":114776,"style":678},[677],[212,114778,114779,114782],{"style":2748},[212,114780],{"className":114781,"style":658},[499],[212,114783,114785],{"className":114784},[504,505,506,507],[212,114786,114788],{"className":114787},[256,507],[212,114789,39189],{"className":114790},[256,507],[212,114792,515],{"className":114793},[514],[212,114795,114797],{"className":114796},[487],[212,114798,114800],{"className":114799,"style":2937},[491],[212,114801],{},[212,114803],{"className":114804},[350,638],[212,114806],{"className":114807,"style":2785},[354],[212,114809,5011],{"className":114810},[2789],[212,114812],{"className":114813,"style":2785},[354],[212,114815,114817,114820],{"className":114816},[247],[212,114818],{"className":114819,"style":369},[251],[212,114821,39189],{"className":114822},[256],"，可与直接展开互相验证。）",[11,114825,114826],{},"可见，f-散度族统一了「不对称\u002F对称」「有界\u002F无界」的多种散度。",[2509,114828,114830],{"id":114829},"_62-积分概率度量ipm","6.2 积分概率度量（IPM）",[11,114832,114833,114834,114883],{},"f-散度只依赖似然比 ",[212,114835,114837,114859],{"className":114836,"translate":216},[215],[212,114838,114840],{"className":114839},[220],[222,114841,114842],{"xmlns":224},[226,114843,114844,114856],{},[229,114845,114846,114848,114850,114852,114854],{},[232,114847,441],{},[232,114849,403],{},[232,114851,1138],{"mathvariant":406},[232,114853,441],{},[232,114855,410],{},[236,114857,114858],{"encoding":238},"dP\u002FdQ",[212,114860,114862],{"className":114861,"ariaHidden":243},[242],[212,114863,114865,114868,114871,114874,114877,114880],{"className":114864},[247],[212,114866],{"className":114867,"style":336},[251],[212,114869,441],{"className":114870},[256,257],[212,114872,403],{"className":114873,"style":531},[256,257],[212,114875,1138],{"className":114876},[256],[212,114878,441],{"className":114879},[256,257],[212,114881,410],{"className":114882},[256,257],"，因此把两个分布同时「搬到别处」值不变。这带来一个根本局限：",[212,114885,114887],{"className":114886,"translate":216},[377],[212,114888,114890,114945],{"className":114889,"translate":216},[215],[212,114891,114893],{"className":114892},[220],[222,114894,114895],{"xmlns":224,"display":386},[226,114896,114897,114942],{},[229,114898,114899,114901,114903,114905,114907,114909,114911,114914,114916,114918,114924,114926,114928,114930,114932,114938,114940],{},[1495,114900,4536],{},[232,114902,403],{},[307,114904,33747],{},[232,114906,410],{},[1495,114908,4481],{},[307,114910,310],{"stretchy":309},[1495,114912,114913],{},"支撑集不重叠，如 ",[232,114915,403],{},[307,114917,320],{},[392,114919,114920,114922],{},[232,114921,15912],{},[312,114923,323],{},[307,114925,748],{"separator":243},[1495,114927,4481],{},[232,114929,410],{},[307,114931,320],{},[392,114933,114934,114936],{},[232,114935,15912],{},[312,114937,314],{},[307,114939,317],{"stretchy":309},[307,114941,748],{"separator":243},[236,114943,114944],{"encoding":238},"\\text{若 } P\\perp Q\\\n(\\text{支撑集不重叠，如 } P=\\delta_0,\\ Q=\\delta_1),",[212,114946,114948,114975,115012,115079],{"className":114947,"ariaHidden":243},[242],[212,114949,114951,114954,114963,114966,114969,114972],{"className":114950},[247],[212,114952],{"className":114953,"style":12797},[251],[212,114955,114957,114960],{"className":114956},[256,4796],[212,114958,4847],{"className":114959},[256,4800],[212,114961,4481],{"className":114962},[256],[212,114964,403],{"className":114965,"style":531},[256,257],[212,114967],{"className":114968,"style":355},[354],[212,114970,33747],{"className":114971},[359],[212,114973],{"className":114974,"style":355},[354],[212,114976,114978,114981,114984,114987,114990,115000,115003,115006,115009],{"className":114977},[247],[212,114979],{"className":114980,"style":336},[251],[212,114982,410],{"className":114983},[256,257],[212,114985,4481],{"className":114986},[354],[212,114988,310],{"className":114989},[343],[212,114991,114993,114997],{"className":114992},[256,4796],[212,114994,114996],{"className":114995},[256,4800],"支撑集不重叠，如",[212,114998,4481],{"className":114999},[256],[212,115001,403],{"className":115002,"style":531},[256,257],[212,115004],{"className":115005,"style":355},[354],[212,115007,320],{"className":115008},[359],[212,115010],{"className":115011,"style":355},[354],[212,115013,115015,115018,115058,115061,115064,115067,115070,115073,115076],{"className":115014},[247],[212,115016],{"className":115017,"style":252},[251],[212,115019,115021,115024],{"className":115020},[256],[212,115022,15912],{"className":115023,"style":15961},[256,257],[212,115025,115027],{"className":115026},[478],[212,115028,115030,115050],{"className":115029},[482,483],[212,115031,115033,115047],{"className":115032},[487],[212,115034,115036],{"className":115035,"style":11333},[491],[212,115037,115038,115041],{"style":94959},[212,115039],{"className":115040,"style":500},[499],[212,115042,115044],{"className":115043},[504,505,506,507],[212,115045,323],{"className":115046},[256,507],[212,115048,515],{"className":115049},[514],[212,115051,115053],{"className":115052},[487],[212,115054,115056],{"className":115055,"style":8166},[491],[212,115057],{},[212,115059,748],{"className":115060},[770],[212,115062,4481],{"className":115063},[354],[212,115065],{"className":115066,"style":603},[354],[212,115068,410],{"className":115069},[256,257],[212,115071],{"className":115072,"style":355},[354],[212,115074,320],{"className":115075},[359],[212,115077],{"className":115078,"style":355},[354],[212,115080,115082,115085,115125,115128],{"className":115081},[247],[212,115083],{"className":115084,"style":336},[251],[212,115086,115088,115091],{"className":115087},[256],[212,115089,15912],{"className":115090,"style":15961},[256,257],[212,115092,115094],{"className":115093},[478],[212,115095,115097,115117],{"className":115096},[482,483],[212,115098,115100,115114],{"className":115099},[487],[212,115101,115103],{"className":115102,"style":11333},[491],[212,115104,115105,115108],{"style":94959},[212,115106],{"className":115107,"style":500},[499],[212,115109,115111],{"className":115110},[504,505,506,507],[212,115112,314],{"className":115113},[256,507],[212,115115,515],{"className":115116},[514],[212,115118,115120],{"className":115119},[487],[212,115121,115123],{"className":115122,"style":8166},[491],[212,115124],{},[212,115126,317],{"className":115127},[350],[212,115129,748],{"className":115130},[770],[212,115132,115134],{"className":115133,"translate":216},[377],[212,115135,115137,115187],{"className":115136,"translate":216},[215],[212,115138,115140],{"className":115139},[220],[222,115141,115142],{"xmlns":224,"display":386},[226,115143,115144,115184],{},[229,115145,115146,115156,115158,115160,115162,115164,115166,115168,115178,115180,115182],{},[392,115147,115148,115150],{},[232,115149,396],{},[229,115151,115152,115154],{},[232,115153,23943],{},[232,115155,25937],{},[307,115157,320],{},[232,115159,4298],{},[307,115161,4301],{},[312,115163,2661],{},[307,115165,748],{"separator":243},[354,115167],{"width":4513},[392,115169,115170,115172],{},[232,115171,396],{},[229,115173,115174,115176],{},[232,115175,5590],{},[232,115177,35050],{},[307,115179,320],{},[312,115181,314],{},[307,115183,748],{"separator":243},[236,115185,115186],{"encoding":238},"D_{JS}=\\log2,\\quad D_{TV}=1,",[212,115188,115190,115251,115332],{"className":115189,"ariaHidden":243},[242],[212,115191,115193,115196,115242,115245,115248],{"className":115192},[247],[212,115194],{"className":115195,"style":16161},[251],[212,115197,115199,115202],{"className":115198},[256],[212,115200,396],{"className":115201,"style":474},[256,257],[212,115203,115205],{"className":115204},[478],[212,115206,115208,115234],{"className":115207},[482,483],[212,115209,115211,115231],{"className":115210},[487],[212,115212,115214],{"className":115213,"style":576},[491],[212,115215,115216,115219],{"style":495},[212,115217],{"className":115218,"style":500},[499],[212,115220,115222],{"className":115221},[504,505,506,507],[212,115223,115225,115228],{"className":115224},[256,507],[212,115226,23943],{"className":115227,"style":24353},[256,257,507],[212,115229,25937],{"className":115230,"style":26061},[256,257,507],[212,115232,515],{"className":115233},[514],[212,115235,115237],{"className":115236},[487],[212,115238,115240],{"className":115239,"style":8166},[491],[212,115241],{},[212,115243],{"className":115244,"style":355},[354],[212,115246,320],{"className":115247},[359],[212,115249],{"className":115250,"style":355},[354],[212,115252,115254,115257,115262,115265,115268,115271,115274,115277,115323,115326,115329],{"className":115253},[247],[212,115255],{"className":115256,"style":252},[251],[212,115258,4352,115260],{"className":115259},[1682],[212,115261,4356],{"style":4355},[212,115263],{"className":115264,"style":603},[354],[212,115266,2661],{"className":115267},[256],[212,115269,748],{"className":115270},[770],[212,115272],{"className":115273,"style":88182},[354],[212,115275],{"className":115276,"style":603},[354],[212,115278,115280,115283],{"className":115279},[256],[212,115281,396],{"className":115282,"style":474},[256,257],[212,115284,115286],{"className":115285},[478],[212,115287,115289,115315],{"className":115288},[482,483],[212,115290,115292,115312],{"className":115291},[487],[212,115293,115295],{"className":115294,"style":576},[491],[212,115296,115297,115300],{"style":495},[212,115298],{"className":115299,"style":500},[499],[212,115301,115303],{"className":115302},[504,505,506,507],[212,115304,115306,115309],{"className":115305},[256,507],[212,115307,5590],{"className":115308,"style":531},[256,257,507],[212,115310,35050],{"className":115311,"style":2785},[256,257,507],[212,115313,515],{"className":115314},[514],[212,115316,115318],{"className":115317},[487],[212,115319,115321],{"className":115320,"style":8166},[491],[212,115322],{},[212,115324],{"className":115325,"style":355},[354],[212,115327,320],{"className":115328},[359],[212,115330],{"className":115331,"style":355},[354],[212,115333,115335,115338,115341],{"className":115334},[247],[212,115336],{"className":115337,"style":9556},[251],[212,115339,314],{"className":115340},[256],[212,115342,748],{"className":115343},[770],[11,115345,115346,115347,115350,115351,115415,115416,115466,115467,9598],{},"也就是说，f-散度在支撑分离时",[1194,115348,115349],{},"饱和到常数上界，对生成器参数的微小改动失去梯度","：因为被积分的量 ",[212,115352,115354,115382],{"className":115353,"translate":216},[215],[212,115355,115357],{"className":115356},[220],[222,115358,115359],{"xmlns":224},[226,115360,115361,115379],{},[229,115362,115363,115365,115367,115369,115371,115373,115375,115377],{},[232,115364,1141],{},[1495,115366,1497],{},[232,115368,234],{},[307,115370,310],{"stretchy":309},[232,115372,11],{},[232,115374,1138],{"mathvariant":406},[232,115376,1141],{},[307,115378,317],{"stretchy":309},[236,115380,115381],{"encoding":238},"q\\,f(p\u002Fq)",[212,115383,115385],{"className":115384,"ariaHidden":243},[242],[212,115386,115388,115391,115394,115397,115400,115403,115406,115409,115412],{"className":115387},[247],[212,115389],{"className":115390,"style":336},[251],[212,115392,1141],{"className":115393,"style":1178},[256,257],[212,115395],{"className":115396,"style":603},[354],[212,115398,234],{"className":115399,"style":258},[256,257],[212,115401,310],{"className":115402},[343],[212,115404,11],{"className":115405},[256,257],[212,115407,1138],{"className":115408},[256],[212,115410,1141],{"className":115411,"style":1178},[256,257],[212,115413,317],{"className":115414},[350]," 只在 ",[212,115417,115419,115436],{"className":115418,"translate":216},[215],[212,115420,115422],{"className":115421},[220],[222,115423,115424],{"xmlns":224},[226,115425,115426,115434],{},[229,115427,115428,115430,115432],{},[232,115429,1141],{},[307,115431,3101],{},[312,115433,323],{},[236,115435,31882],{"encoding":238},[212,115437,115439,115457],{"className":115438,"ariaHidden":243},[242],[212,115440,115442,115445,115448,115451,115454],{"className":115441},[247],[212,115443],{"className":115444,"style":31892},[251],[212,115446,1141],{"className":115447,"style":1178},[256,257],[212,115449],{"className":115450,"style":355},[354],[212,115452,3101],{"className":115453},[359],[212,115455],{"className":115456,"style":355},[354],[212,115458,115460,115463],{"className":115459},[247],[212,115461],{"className":115462,"style":369},[251],[212,115464,323],{"className":115465},[256]," 处有定义，当两个支撑几乎不重叠时，极小化散度的博弈只剩\"常数项 − 常数项\"，梯度信息全部丢失（这正是原 GAN 训练崩溃的理论根源）。Wasserstein 距离与 MMD 属于另一族——",[1194,115468,115469],{},"积分概率度量",[212,115471,115473],{"className":115472,"translate":216},[377],[212,115474,115476,115551],{"className":115475,"translate":216},[215],[212,115477,115479],{"className":115478},[220],[222,115480,115481],{"xmlns":224,"display":386},[226,115482,115483,115548],{},[229,115484,115485,115492,115494,115496,115498,115500,115502,115504,115520,115522,115524,115526,115528,115530,115532,115534,115536,115538,115540,115542,115544,115546],{},[392,115486,115487,115490],{},[1495,115488,115489],{},"IPM",[232,115491,37083],{"mathvariant":794},[307,115493,310],{"stretchy":309},[232,115495,403],{},[307,115497,748],{"separator":243},[232,115499,410],{},[307,115501,317],{"stretchy":309},[307,115503,320],{},[6214,115505,115506,115512],{},[229,115507,115508,115510],{},[232,115509,35632],{},[307,115511,4301],{},[229,115513,115514,115516,115518],{},[232,115515,38865],{},[307,115517,6107],{},[232,115519,37083],{"mathvariant":794},[307,115521,5006],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[307,115523,1485],{},[232,115525,38865],{},[1495,115527,1497],{},[232,115529,441],{},[232,115531,403],{},[307,115533,5011],{},[307,115535,1485],{},[232,115537,38865],{},[1495,115539,1497],{},[232,115541,441],{},[232,115543,410],{},[307,115545,5006],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[232,115547,4573],{"mathvariant":406},[236,115549,115550],{"encoding":238},"\\text{IPM}_{\\mathcal F}(P,Q)\n=\\sup_{h\\in\\mathcal F}\\Big|\\int h\\,dP\n-\\int h\\,dQ\\Big| .",[212,115552,115554,115634,115767],{"className":115553,"ariaHidden":243},[242],[212,115555,115557,115560,115607,115610,115613,115616,115619,115622,115625,115628,115631],{"className":115556},[247],[212,115558],{"className":115559,"style":336},[251],[212,115561,115563,115569],{"className":115562},[256],[212,115564,115566],{"className":115565},[256,4796],[212,115567,115489],{"className":115568},[256],[212,115570,115572],{"className":115571},[478],[212,115573,115575,115599],{"className":115574},[482,483],[212,115576,115578,115596],{"className":115577},[487],[212,115579,115581],{"className":115580,"style":576},[491],[212,115582,115583,115586],{"style":52645},[212,115584],{"className":115585,"style":500},[499],[212,115587,115589],{"className":115588},[504,505,506,507],[212,115590,115592],{"className":115591},[256,507],[212,115593,37083],{"className":115594,"style":115595},[256,821,507],"margin-right:0.0993em;",[212,115597,515],{"className":115598},[514],[212,115600,115602],{"className":115601},[487],[212,115603,115605],{"className":115604,"style":8166},[491],[212,115606],{},[212,115608,310],{"className":115609},[343],[212,115611,403],{"className":115612,"style":531},[256,257],[212,115614,748],{"className":115615},[770],[212,115617],{"className":115618,"style":603},[354],[212,115620,410],{"className":115621},[256,257],[212,115623,317],{"className":115624},[350],[212,115626],{"className":115627,"style":355},[354],[212,115629,320],{"className":115630},[359],[212,115632],{"className":115633,"style":355},[354],[212,115635,115637,115641,115694,115697,115737,115740,115743,115746,115749,115752,115755,115758,115761,115764],{"className":115636},[247],[212,115638],{"className":115639,"style":115640},[251],"height:2.3339em;vertical-align:-0.9739em;",[212,115642,115644],{"className":115643},[1682,13916],[212,115645,115647,115686],{"className":115646},[482,483],[212,115648,115650,115683],{"className":115649},[487],[212,115651,115653,115673],{"className":115652,"style":2543},[491],[212,115654,115655,115658],{"style":51905},[212,115656],{"className":115657,"style":658},[499],[212,115659,115661],{"className":115660},[504,505,506,507],[212,115662,115664,115667,115670],{"className":115663},[256,507],[212,115665,38865],{"className":115666},[256,257,507],[212,115668,6107],{"className":115669},[359,507],[212,115671,37083],{"className":115672,"style":115595},[256,821,507],[212,115674,115675,115678],{"style":12063},[212,115676],{"className":115677,"style":658},[499],[212,115679,115680],{},[212,115681,35632],{"className":115682},[1682],[212,115684,515],{"className":115685},[514],[212,115687,115689],{"className":115688},[487],[212,115690,115692],{"className":115691,"style":51949},[491],[212,115693],{},[212,115695],{"className":115696,"style":603},[354],[212,115698,115700],{"className":115699},[256],[212,115701,115703],{"className":115702},[616,15029],[212,115704,115706,115729],{"className":115705},[482,483],[212,115707,115709,115726],{"className":115708},[487],[212,115710,115712],{"className":115711,"style":85729},[491],[212,115713,115714,115717],{"style":73734},[212,115715],{"className":115716,"style":82801},[499],[212,115718,115720],{"style":115719},"width:0.333em;height:1.8em;",[6521,115721,115723],{"xmlns":6523,"width":35251,"height":17639,"viewBox":115722},"0 0 333 1800",[6529,115724],{"d":115725},"M145 15 v585 v600 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-600 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v600 v585 h43z",[212,115727,515],{"className":115728},[514],[212,115730,115732],{"className":115731},[487],[212,115733,115735],{"className":115734,"style":85753},[491],[212,115736],{},[212,115738],{"className":115739,"style":603},[354],[212,115741,1485],{"className":115742,"style":1685},[1682,1683,1684],[212,115744],{"className":115745,"style":603},[354],[212,115747,38865],{"className":115748},[256,257],[212,115750],{"className":115751,"style":603},[354],[212,115753,441],{"className":115754},[256,257],[212,115756,403],{"className":115757,"style":531},[256,257],[212,115759],{"className":115760,"style":2785},[354],[212,115762,5011],{"className":115763},[2789],[212,115765],{"className":115766,"style":2785},[354],[212,115768,115770,115773,115776,115779,115782,115785,115788,115791,115828],{"className":115769},[247],[212,115771],{"className":115772,"style":5975},[251],[212,115774,1485],{"className":115775,"style":1685},[1682,1683,1684],[212,115777],{"className":115778,"style":603},[354],[212,115780,38865],{"className":115781},[256,257],[212,115783],{"className":115784,"style":603},[354],[212,115786,441],{"className":115787},[256,257],[212,115789,410],{"className":115790},[256,257],[212,115792,115794],{"className":115793},[256],[212,115795,115797],{"className":115796},[616,15029],[212,115798,115800,115820],{"className":115799},[482,483],[212,115801,115803,115817],{"className":115802},[487],[212,115804,115806],{"className":115805,"style":85729},[491],[212,115807,115808,115811],{"style":73734},[212,115809],{"className":115810,"style":82801},[499],[212,115812,115813],{"style":115719},[6521,115814,115815],{"xmlns":6523,"width":35251,"height":17639,"viewBox":115722},[6529,115816],{"d":115725},[212,115818,515],{"className":115819},[514],[212,115821,115823],{"className":115822},[487],[212,115824,115826],{"className":115825,"style":85753},[491],[212,115827],{},[212,115829,4573],{"className":115830},[256],[11,115832,115833,115834,115863,115864,115915,115916,115945,115946,115996,115997,116025,116026,116076,116077,116105],{},"它们比较的是「在函数类 ",[212,115835,115837,115851],{"className":115836,"translate":216},[215],[212,115838,115840],{"className":115839},[220],[222,115841,115842],{"xmlns":224},[226,115843,115844,115848],{},[229,115845,115846],{},[232,115847,37083],{"mathvariant":794},[236,115849,115850],{"encoding":238},"\\mathcal F",[212,115852,115854],{"className":115853,"ariaHidden":243},[242],[212,115855,115857,115860],{"className":115856},[247],[212,115858],{"className":115859,"style":861},[251],[212,115861,37083],{"className":115862,"style":115595},[256,821]," 上积分的差」，而不是似然比，因此利用了样本空间的度量\u002F几何结构。KS 距离（",[212,115865,115867,115885],{"className":115866,"translate":216},[215],[212,115868,115870],{"className":115869},[220],[222,115871,115872],{"xmlns":224},[226,115873,115874,115882],{},[229,115875,115876,115878,115880],{},[232,115877,37083],{"mathvariant":794},[307,115879,320],{},[307,115881,3096],{"stretchy":309},[236,115883,115884],{"encoding":238},"\\mathcal F=\\{",[212,115886,115888,115906],{"className":115887,"ariaHidden":243},[242],[212,115889,115891,115894,115897,115900,115903],{"className":115890},[247],[212,115892],{"className":115893,"style":861},[251],[212,115895,37083],{"className":115896,"style":115595},[256,821],[212,115898],{"className":115899,"style":355},[354],[212,115901,320],{"className":115902},[359],[212,115904],{"className":115905,"style":355},[354],[212,115907,115909,115912],{"className":115908},[247],[212,115910],{"className":115911,"style":336},[251],[212,115913,3096],{"className":115914},[343],"一维区间指示函数",[212,115917,115919,115933],{"className":115918,"translate":216},[215],[212,115920,115922],{"className":115921},[220],[222,115923,115924],{"xmlns":224},[226,115925,115926,115930],{},[229,115927,115928],{},[307,115929,3106],{"stretchy":309},[236,115931,115932],{"encoding":238},"\\}",[212,115934,115936],{"className":115935,"ariaHidden":243},[242],[212,115937,115939,115942],{"className":115938},[247],[212,115940],{"className":115941,"style":336},[251],[212,115943,3106],{"className":115944},[350],"）、Wasserstein（",[212,115947,115949,115966],{"className":115948,"translate":216},[215],[212,115950,115952],{"className":115951},[220],[222,115953,115954],{"xmlns":224},[226,115955,115956,115964],{},[229,115957,115958,115960,115962],{},[232,115959,37083],{"mathvariant":794},[307,115961,320],{},[307,115963,3096],{"stretchy":309},[236,115965,115884],{"encoding":238},[212,115967,115969,115987],{"className":115968,"ariaHidden":243},[242],[212,115970,115972,115975,115978,115981,115984],{"className":115971},[247],[212,115973],{"className":115974,"style":861},[251],[212,115976,37083],{"className":115977,"style":115595},[256,821],[212,115979],{"className":115980,"style":355},[354],[212,115982,320],{"className":115983},[359],[212,115985],{"className":115986,"style":355},[354],[212,115988,115990,115993],{"className":115989},[247],[212,115991],{"className":115992,"style":336},[251],[212,115994,3096],{"className":115995},[343],"1-Lipschitz 函数",[212,115998,116000,116013],{"className":115999,"translate":216},[215],[212,116001,116003],{"className":116002},[220],[222,116004,116005],{"xmlns":224},[226,116006,116007,116011],{},[229,116008,116009],{},[307,116010,3106],{"stretchy":309},[236,116012,115932],{"encoding":238},[212,116014,116016],{"className":116015,"ariaHidden":243},[242],[212,116017,116019,116022],{"className":116018},[247],[212,116020],{"className":116021,"style":336},[251],[212,116023,3106],{"className":116024},[350],"）、MMD（",[212,116027,116029,116046],{"className":116028,"translate":216},[215],[212,116030,116032],{"className":116031},[220],[222,116033,116034],{"xmlns":224},[226,116035,116036,116044],{},[229,116037,116038,116040,116042],{},[232,116039,37083],{"mathvariant":794},[307,116041,320],{},[307,116043,3096],{"stretchy":309},[236,116045,115884],{"encoding":238},[212,116047,116049,116067],{"className":116048,"ariaHidden":243},[242],[212,116050,116052,116055,116058,116061,116064],{"className":116051},[247],[212,116053],{"className":116054,"style":861},[251],[212,116056,37083],{"className":116057,"style":115595},[256,821],[212,116059],{"className":116060,"style":355},[354],[212,116062,320],{"className":116063},[359],[212,116065],{"className":116066,"style":355},[354],[212,116068,116070,116073],{"className":116069},[247],[212,116071],{"className":116072,"style":336},[251],[212,116074,3096],{"className":116075},[343],"RKHS 单位球",[212,116078,116080,116093],{"className":116079,"translate":216},[215],[212,116081,116083],{"className":116082},[220],[222,116084,116085],{"xmlns":224},[226,116086,116087,116091],{},[229,116088,116089],{},[307,116090,3106],{"stretchy":309},[236,116092,115932],{"encoding":238},[212,116094,116096],{"className":116095,"ariaHidden":243},[242],[212,116097,116099,116102],{"className":116098},[247],[212,116100],{"className":116101,"style":336},[251],[212,116103,3106],{"className":116104},[350],"）都是 IPM。上面对 f-散度的变分表示其实是「带惩罚的 IPM」：",[212,116107,116109],{"className":116108,"translate":216},[377],[212,116110,116112,116194],{"className":116111,"translate":216},[215],[212,116113,116115],{"className":116114},[220],[222,116116,116117],{"xmlns":224,"display":386},[226,116118,116119,116191],{},[229,116120,116121,116127,116129,116131,116133,116135,116137,116139,116149,116151,116157,116159,116161,116163,116165,116171,116173,116179,116181,116183,116185,116187,116189],{},[392,116122,116123,116125],{},[232,116124,396],{},[232,116126,234],{},[307,116128,310],{"stretchy":309},[232,116130,403],{},[232,116132,407],{"mathvariant":406},[232,116134,410],{},[307,116136,317],{"stretchy":309},[307,116138,320],{},[6214,116140,116141,116147],{},[229,116142,116143,116145],{},[232,116144,35632],{},[307,116146,4301],{},[232,116148,4356],{},[307,116150,3096],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[392,116152,116153,116155],{},[232,116154,420],{"mathvariant":419},[232,116156,403],{},[307,116158,427],{"stretchy":309},[232,116160,4356],{},[307,116162,454],{"stretchy":309},[307,116164,5011],{},[392,116166,116167,116169],{},[232,116168,420],{"mathvariant":419},[232,116170,410],{},[307,116172,427],{"stretchy":309},[7012,116174,116175,116177],{},[232,116176,234],{},[307,116178,7771],{},[307,116180,310],{"stretchy":309},[232,116182,4356],{},[307,116184,317],{"stretchy":309},[307,116186,454],{"stretchy":309},[307,116188,3106],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[307,116190,748],{"separator":243},[236,116192,116193],{"encoding":238},"D_f(P\\|Q)\n=\\sup_{g}\\Big\\{\\mathbb E_P[g]\n-\\mathbb E_Q[f^*(g)]\\Big\\},",[212,116195,116197,116267,116387],{"className":116196,"ariaHidden":243},[242],[212,116198,116200,116203,116243,116246,116249,116252,116255,116258,116261,116264],{"className":116199},[247],[212,116201],{"className":116202,"style":467},[251],[212,116204,116206,116209],{"className":116205},[256],[212,116207,396],{"className":116208,"style":474},[256,257],[212,116210,116212],{"className":116211},[478],[212,116213,116215,116235],{"className":116214},[482,483],[212,116216,116218,116232],{"className":116217},[487],[212,116219,116221],{"className":116220,"style":492},[491],[212,116222,116223,116226],{"style":495},[212,116224],{"className":116225,"style":500},[499],[212,116227,116229],{"className":116228},[504,505,506,507],[212,116230,234],{"className":116231,"style":258},[256,257,507],[212,116233,515],{"className":116234},[514],[212,116236,116238],{"className":116237},[487],[212,116239,116241],{"className":116240,"style":522},[491],[212,116242],{},[212,116244,310],{"className":116245},[343],[212,116247,403],{"className":116248,"style":531},[256,257],[212,116250,407],{"className":116251},[256],[212,116253,410],{"className":116254},[256,257],[212,116256,317],{"className":116257},[350],[212,116259],{"className":116260,"style":355},[354],[212,116262,320],{"className":116263},[359],[212,116265],{"className":116266,"style":355},[354],[212,116268,116270,116273,116320,116323,116329,116369,116372,116375,116378,116381,116384],{"className":116269},[247],[212,116271],{"className":116272,"style":99700},[251],[212,116274,116276],{"className":116275},[1682,13916],[212,116277,116279,116312],{"className":116278},[482,483],[212,116280,116282,116309],{"className":116281},[487],[212,116283,116285,116299],{"className":116284,"style":2543},[491],[212,116286,116287,116290],{"style":61400},[212,116288],{"className":116289,"style":658},[499],[212,116291,116293],{"className":116292},[504,505,506,507],[212,116294,116296],{"className":116295},[256,507],[212,116297,4356],{"className":116298,"style":1178},[256,257,507],[212,116300,116301,116304],{"style":12063},[212,116302],{"className":116303,"style":658},[499],[212,116305,116306],{},[212,116307,35632],{"className":116308},[1682],[212,116310,515],{"className":116311},[514],[212,116313,116315],{"className":116314},[487],[212,116316,116318],{"className":116317,"style":61432},[491],[212,116319],{},[212,116321],{"className":116322,"style":603},[354],[212,116324,116326],{"className":116325},[256],[212,116327,3096],{"className":116328},[616,3918],[212,116330,116332,116335],{"className":116331},[256],[212,116333,420],{"className":116334},[256,563],[212,116336,116338],{"className":116337},[478],[212,116339,116341,116361],{"className":116340},[482,483],[212,116342,116344,116358],{"className":116343},[487],[212,116345,116347],{"className":116346,"style":576},[491],[212,116348,116349,116352],{"style":579},[212,116350],{"className":116351,"style":500},[499],[212,116353,116355],{"className":116354},[504,505,506,507],[212,116356,403],{"className":116357,"style":531},[256,257,507],[212,116359,515],{"className":116360},[514],[212,116362,116364],{"className":116363},[487],[212,116365,116367],{"className":116366,"style":8166},[491],[212,116368],{},[212,116370,427],{"className":116371},[343],[212,116373,4356],{"className":116374,"style":1178},[256,257],[212,116376,454],{"className":116377},[350],[212,116379],{"className":116380,"style":2785},[354],[212,116382,5011],{"className":116383},[2789],[212,116385],{"className":116386,"style":2785},[354],[212,116388,116390,116393,116433,116436,116465,116468,116471,116474,116480],{"className":116389},[247],[212,116391],{"className":116392,"style":68327},[251],[212,116394,116396,116399],{"className":116395},[256],[212,116397,420],{"className":116398},[256,563],[212,116400,116402],{"className":116401},[478],[212,116403,116405,116425],{"className":116404},[482,483],[212,116406,116408,116422],{"className":116407},[487],[212,116409,116411],{"className":116410,"style":576},[491],[212,116412,116413,116416],{"style":579},[212,116414],{"className":116415,"style":500},[499],[212,116417,116419],{"className":116418},[504,505,506,507],[212,116420,410],{"className":116421},[256,257,507],[212,116423,515],{"className":116424},[514],[212,116426,116428],{"className":116427},[487],[212,116429,116431],{"className":116430,"style":522},[491],[212,116432],{},[212,116434,427],{"className":116435},[343],[212,116437,116439,116442],{"className":116438},[256],[212,116440,234],{"className":116441,"style":258},[256,257],[212,116443,116445],{"className":116444},[478],[212,116446,116448],{"className":116447},[482],[212,116449,116451],{"className":116450},[487],[212,116452,116454],{"className":116453,"style":8446},[491],[212,116455,116456,116459],{"style":8475},[212,116457],{"className":116458,"style":500},[499],[212,116460,116462],{"className":116461},[504,505,506,507],[212,116463,7771],{"className":116464},[2789,507],[212,116466,310],{"className":116467},[343],[212,116469,4356],{"className":116470,"style":1178},[256,257],[212,116472,20590],{"className":116473},[350],[212,116475,116477],{"className":116476},[256],[212,116478,3106],{"className":116479},[616,3918],[212,116481,748],{"className":116482},[770],[11,116484,116485,116486,116560,116561,116603],{},"它的被估计量是 ",[212,116487,116489,116513],{"className":116488,"translate":216},[215],[212,116490,116492],{"className":116491},[220],[222,116493,116494],{"xmlns":224},[226,116495,116496,116510],{},[229,116497,116498,116504,116506,116508],{},[7012,116499,116500,116502],{},[232,116501,234],{},[307,116503,7771],{},[307,116505,310],{"stretchy":309},[232,116507,4356],{},[307,116509,317],{"stretchy":309},[236,116511,116512],{"encoding":238},"f^*(g)",[212,116514,116516],{"className":116515,"ariaHidden":243},[242],[212,116517,116519,116522,116551,116554,116557],{"className":116518},[247],[212,116520],{"className":116521,"style":336},[251],[212,116523,116525,116528],{"className":116524},[256],[212,116526,234],{"className":116527,"style":258},[256,257],[212,116529,116531],{"className":116530},[478],[212,116532,116534],{"className":116533},[482],[212,116535,116537],{"className":116536},[487],[212,116538,116540],{"className":116539,"style":8697},[491],[212,116541,116542,116545],{"style":7063},[212,116543],{"className":116544,"style":500},[499],[212,116546,116548],{"className":116547},[504,505,506,507],[212,116549,7771],{"className":116550},[2789,507],[212,116552,310],{"className":116553},[343],[212,116555,4356],{"className":116556,"style":1178},[256,257],[212,116558,317],{"className":116559},[350],"，而不是 ",[212,116562,116564,116582],{"className":116563,"translate":216},[215],[212,116565,116567],{"className":116566},[220],[222,116568,116569],{"xmlns":224},[226,116570,116571,116579],{},[229,116572,116573,116575,116577],{},[232,116574,5006],{"mathvariant":406},[307,116576,3497],{"lspace":1445,"rspace":1445},[232,116578,5006],{"mathvariant":406},[236,116580,116581],{"encoding":238},"|{\\cdot}|",[212,116583,116585],{"className":116584,"ariaHidden":243},[242],[212,116586,116588,116591,116594,116600],{"className":116587},[247],[212,116589],{"className":116590,"style":336},[251],[212,116592,5006],{"className":116593},[256],[212,116595,116597],{"className":116596},[256],[212,116598,3497],{"className":116599},[256],[212,116601,5006],{"className":116602},[256],"，所以是「非对称 IPM」。",[11,116605,116606,116608],{},[1194,116607,6691],{}," Wasserstein\u002FMMD 不是 f-散度，也不能写成 f-散度；它们的关键区别在于是否利用几何、是否在支撑分离时仍给梯度、以及是否满足数据处理不等式（Wasserstein 一般不满足数据处理不等式，因为传输方案可以随条件分布\"重新安排\"质量；MMD 由核特征映射的条件期望是收缩算子，沿核的具体结构可证其满足数据处理不等式）。",[2509,116610,116612],{"id":116611},"_63-支撑不重叠的极限","6.3 支撑不重叠的极限",[52691,116614,116615,116695],{},[52694,116616,116617],{},[52697,116618,116619,116622,116624,116626,116628,116630,116690,116692],{},[52700,116620,116621],{},"情形",[52700,116623,32863],{},[52700,116625,109076],{},[52700,116627,53323],{},[52700,116629,86976],{},[52700,116631,116632],{},[212,116633,116635,116652],{"className":116634,"translate":216},[215],[212,116636,116638],{"className":116637},[220],[222,116639,116640],{"xmlns":224},[226,116641,116642,116650],{},[229,116643,116644],{},[7012,116645,116646,116648],{},[232,116647,37649],{},[312,116649,2661],{},[236,116651,40594],{"encoding":238},[212,116653,116655],{"className":116654,"ariaHidden":243},[242],[212,116656,116658,116661],{"className":116657},[247],[212,116659],{"className":116660,"style":40604},[251],[212,116662,116664,116667],{"className":116663},[256],[212,116665,37649],{"className":116666},[256,257],[212,116668,116670],{"className":116669},[478],[212,116671,116673],{"className":116672},[482],[212,116674,116676],{"className":116675},[487],[212,116677,116679],{"className":116678,"style":20228},[491],[212,116680,116681,116684],{"style":7063},[212,116682],{"className":116683,"style":500},[499],[212,116685,116687],{"className":116686},[504,505,506,507],[212,116688,2661],{"className":116689},[256,507],[52700,116691,105390],{},[52700,116693,116694],{},"Wasserstein",[52789,116696,116697,117107],{},[52697,116698,116699,116870,116905,116940,116982,117012,117047,117077],{},[52794,116700,116701,116869],{},[212,116702,116704,116738],{"className":116703,"translate":216},[215],[212,116705,116707],{"className":116706},[220],[222,116708,116709],{"xmlns":224},[226,116710,116711,116735],{},[229,116712,116713,116715,116717,116723,116725,116727,116729],{},[232,116714,403],{},[307,116716,320],{},[392,116718,116719,116721],{},[232,116720,15912],{},[312,116722,323],{},[307,116724,748],{"separator":243},[232,116726,410],{},[307,116728,320],{},[392,116730,116731,116733],{},[232,116732,15912],{},[312,116734,314],{},[236,116736,116737],{"encoding":238},"P=\\delta_0,Q=\\delta_1",[212,116739,116741,116759,116823],{"className":116740,"ariaHidden":243},[242],[212,116742,116744,116747,116750,116753,116756],{"className":116743},[247],[212,116745],{"className":116746,"style":861},[251],[212,116748,403],{"className":116749,"style":531},[256,257],[212,116751],{"className":116752,"style":355},[354],[212,116754,320],{"className":116755},[359],[212,116757],{"className":116758,"style":355},[354],[212,116760,116762,116765,116805,116808,116811,116814,116817,116820],{"className":116761},[247],[212,116763],{"className":116764,"style":252},[251],[212,116766,116768,116771],{"className":116767},[256],[212,116769,15912],{"className":116770,"style":15961},[256,257],[212,116772,116774],{"className":116773},[478],[212,116775,116777,116797],{"className":116776},[482,483],[212,116778,116780,116794],{"className":116779},[487],[212,116781,116783],{"className":116782,"style":11333},[491],[212,116784,116785,116788],{"style":94959},[212,116786],{"className":116787,"style":500},[499],[212,116789,116791],{"className":116790},[504,505,506,507],[212,116792,323],{"className":116793},[256,507],[212,116795,515],{"className":116796},[514],[212,116798,116800],{"className":116799},[487],[212,116801,116803],{"className":116802,"style":8166},[491],[212,116804],{},[212,116806,748],{"className":116807},[770],[212,116809],{"className":116810,"style":603},[354],[212,116812,410],{"className":116813},[256,257],[212,116815],{"className":116816,"style":355},[354],[212,116818,320],{"className":116819},[359],[212,116821],{"className":116822,"style":355},[354],[212,116824,116826,116829],{"className":116825},[247],[212,116827],{"className":116828,"style":11674},[251],[212,116830,116832,116835],{"className":116831},[256],[212,116833,15912],{"className":116834,"style":15961},[256,257],[212,116836,116838],{"className":116837},[478],[212,116839,116841,116861],{"className":116840},[482,483],[212,116842,116844,116858],{"className":116843},[487],[212,116845,116847],{"className":116846,"style":11333},[491],[212,116848,116849,116852],{"style":94959},[212,116850],{"className":116851,"style":500},[499],[212,116853,116855],{"className":116854},[504,505,506,507],[212,116856,314],{"className":116857},[256,507],[212,116859,515],{"className":116860},[514],[212,116862,116864],{"className":116863},[487],[212,116865,116867],{"className":116866,"style":8166},[491],[212,116868],{},"（约）",[52794,116871,116872],{},[212,116873,116875,116890],{"className":116874,"translate":216},[215],[212,116876,116878],{"className":116877},[220],[222,116879,116880],{"xmlns":224},[226,116881,116882,116888],{},[229,116883,116884,116886],{},[307,116885,2668],{},[232,116887,1223],{"mathvariant":406},[236,116889,4439],{"encoding":238},[212,116891,116893],{"className":116892,"ariaHidden":243},[242],[212,116894,116896,116899,116902],{"className":116895},[247],[212,116897],{"className":116898,"style":4449},[251],[212,116900,2668],{"className":116901},[256],[212,1169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e^{10^4}",[212,117478,117480,117492],{"className":117479,"ariaHidden":243},[242],[212,117481,117483,117486,117489],{"className":117482},[247],[212,117484],{"className":117485,"style":117378},[251],[212,117487,33159],{"className":117488},[359],[212,117490],{"className":117491,"style":355},[354],[212,117493,117495,117499],{"className":117494},[247],[212,117496],{"className":117497,"style":117498},[251],"height:0.9869em;",[212,117500,117502,117505],{"className":117501},[256],[212,117503,7765],{"className":117504},[256,257],[212,117506,117508],{"className":117507},[478],[212,117509,117511],{"className":117510},[482],[212,117512,117514],{"className":117513},[487],[212,117515,117517],{"className":117516,"style":117498},[491],[212,117518,117519,117522],{"style":7063},[212,117520],{"className":117521,"style":500},[499],[212,117523,117525],{"className":117524},[504,505,506,507],[212,117526,117528,117531],{"className":117527},[256,507],[212,117529,314],{"className":117530},[256,507],[212,117532,117534,117537],{"className":117533},[256,507],[212,117535,323],{"className":117536},[256,507],[212,117538,117540],{"className":117539},[478],[212,117541,117543],{"className":117542},[482],[212,117544,117546],{"className":117545},[487],[212,117547,117549],{"className":117548,"style":38712},[491],[212,117550,117551,117554],{"style":38715},[212,117552],{"className":117553,"style":30406},[499],[212,117555,117557],{"className":117556},[504,30410,9872,507],[212,117558,39189],{"className":117559},[256,507],[52794,117561,117562],{},[212,117563,117565,117581],{"className":117564,"translate":216},[215],[212,117566,117568],{"className":117567},[220],[222,117569,117570],{"xmlns":224},[226,117571,117572,117578],{},[229,117573,117574,117576],{},[307,117575,33159],{},[312,117577,2661],{},[236,117579,117580],{"encoding":238},"\\approx2",[212,117582,117584,117596],{"className":117583,"ariaHidden":243},[242],[212,117585,117587,117590,117593],{"className":117586},[247],[212,117588],{"className":117589,"style":117378},[251],[212,117591,33159],{"className":117592},[359],[212,117594],{"className":117595,"style":355},[354],[212,117597,117599,117602],{"className":117598},[247],[212,117600],{"className":117601,"style":369},[251],[212,117603,2661],{"className":117604},[256],[52794,117606,117607],{},[212,117608,117610,117626],{"className":117609,"translate":216},[215],[212,117611,117613],{"className":117612},[220],[222,117614,117615],{"xmlns":224},[226,117616,117617,117623],{},[229,117618,117619,117621],{},[307,117620,320],{},[312,117622,117151],{},[236,117624,117625],{"encoding":238},"=100",[212,117627,117629,117641],{"className":117628,"ariaHidden":243},[242],[212,117630,117632,117635,117638],{"className":117631},[247],[212,117633],{"className":117634,"style":11203},[251],[212,117636,320],{"className":117637},[359],[212,117639],{"className":117640,"style":355},[354],[212,117642,117644,117647],{"className":117643},[247],[212,117645],{"className":117646,"style":369},[251],[212,117648,117151],{"className":117649},[256],[11,117651,117652],{},"f-散度在第二行全部「饱和到下界\u002F上界」，而 Wasserstein 随距离线性增长——这正是词嵌入、最优传输、Wasserstein GAN 的动机。",[725,117654,117656],{"id":117655},"_7-机器学习应用","7. 机器学习应用",[11,117658,117659],{},"f-散度族之所以重要，是因为：",[6860,117661,117662,117668,117678,117713],{},[6863,117663,117664,117667],{},[1194,117665,117666],{},"统一框架","：许多生成模型的目标函数可以写成 f-散度。",[6863,117669,117670,117673,117674,117677],{},[1194,117671,117672],{},"变分估计","：通过凸共轭，可以用神经网络估计 f-散度，这就是 ",[1194,117675,117676],{},"f-GAN"," 的核心思想。",[6863,117679,117680,117683,117684,117712],{},[1194,117681,117682],{},"灵活选择","：不同 ",[212,117685,117687,117700],{"className":117686,"translate":216},[215],[212,117688,117690],{"className":117689},[220],[222,117691,117692],{"xmlns":224},[226,117693,117694,117698],{},[229,117695,117696],{},[232,117697,234],{},[236,117699,234],{"encoding":238},[212,117701,117703],{"className":117702,"ariaHidden":243},[242],[212,117704,117706,117709],{"className":117705},[247],[212,117707],{"className":117708,"style":252},[251],[212,117710,234],{"className":117711,"style":258},[256,257]," 对应不同训练性质。例如 JS 有界但可能梯度消失，KL 无界但敏感。",[6863,117714,117715,117718],{},[1194,117716,117717],{},"理论分析","：数据处理不等式、凸性、对偶表示等为收敛性和泛化分析提供工具。",[11,117720,117721],{},"下面把这几条落到具体场景。",[2509,117723,117725],{"id":117724},"_71-f-gan","7.1 f-GAN",[11,117727,117728,117729,117857,117858,117886,117887,117915],{},"见第 5 节。核心是：",[212,117730,117732,117764],{"className":117731,"translate":216},[215],[212,117733,117735],{"className":117734},[220],[222,117736,117737],{"xmlns":224},[226,117738,117739,117761],{},[229,117740,117741,117751],{},[392,117742,117743,117749],{},[229,117744,117745,117747],{},[232,117746,51807],{},[307,117748,4301],{},[232,117750,100974],{},[392,117752,117753,117759],{},[229,117754,117755,117757],{},[232,117756,52586],{},[307,117758,4301],{},[232,117760,100076],{},[236,117762,117763],{"encoding":238},"\\min_\\theta\\max_\\omega",[212,117765,117767],{"className":117766,"ariaHidden":243},[242],[212,117768,117770,117774,117814,117817],{"className":117769},[247],[212,117771],{"className":117772,"style":117773},[251],"height:0.8179em;vertical-align:-0.15em;",[212,117775,117777,117780],{"className":117776},[1682],[212,117778,51807],{"className":117779},[1682],[212,117781,117783],{"className":117782},[478],[212,117784,117786,117806],{"className":117785},[482,483],[212,117787,117789,117803],{"className":117788},[487],[212,117790,117792],{"className":117791,"style":492},[491],[212,117793,117794,117797],{"style":52645},[212,117795],{"className":117796,"style":500},[499],[212,117798,117800],{"className":117799},[504,505,506,507],[212,117801,100974],{"className":117802,"style":474},[256,257,507],[212,117804,515],{"className":117805},[514],[212,117807,117809],{"className":117808},[487],[212,117810,117812],{"className":117811,"style":8166},[491],[212,117813],{},[212,117815],{"className":117816,"style":603},[354],[212,117818,117820,117823],{"className":117819},[1682],[212,117821,52586],{"className":117822},[1682],[212,117824,117826],{"className":117825},[478],[212,117827,117829,117849],{"className":117828},[482,483],[212,117830,117832,117846],{"className":117831},[487],[212,117833,117835],{"className":117834,"style":45129},[491],[212,117836,117837,117840],{"style":52645},[212,117838],{"className":117839,"style":500},[499],[212,117841,117843],{"className":117842},[504,505,506,507],[212,117844,100076],{"className":117845,"style":1178},[256,257,507],[212,117847,515],{"className":117848},[514],[212,117850,117852],{"className":117851},[487],[212,117853,117855],{"className":117854,"style":8166},[491],[212,117856],{}," 的对抗目标 = 对 ",[212,117859,117861,117874],{"className":117860,"translate":216},[215],[212,117862,117864],{"className":117863},[220],[222,117865,117866],{"xmlns":224},[226,117867,117868,117872],{},[229,117869,117870],{},[232,117871,234],{},[236,117873,234],{"encoding":238},[212,117875,117877],{"className":117876,"ariaHidden":243},[242],[212,117878,117880,117883],{"className":117879},[247],[212,117881],{"className":117882,"style":252},[251],[212,117884,234],{"className":117885,"style":258},[256,257]," 做对偶后的 f-散度估计。选择 ",[212,117888,117890,117903],{"className":117889,"translate":216},[215],[212,117891,117893],{"className":117892},[220],[222,117894,117895],{"xmlns":224},[226,117896,117897,117901],{},[229,117898,117899],{},[232,117900,234],{},[236,117902,234],{"encoding":238},[212,117904,117906],{"className":117905,"ariaHidden":243},[242],[212,117907,117909,117912],{"className":117908},[247],[212,117910],{"className":117911,"style":252},[251],[212,117913,234],{"className":117914,"style":258},[256,257]," 就是选择「用哪种散度训练生成器」，这直接决定模式崩塌、梯度消失与训练稳定性的权衡。",[2509,117917,117919],{"id":117918},"_72-变分推断与-elbo","7.2 变分推断与 ELBO",[11,117921,117922],{},"变分推断里最大化证据下界",[212,117924,117926],{"className":117925,"translate":216},[377],[212,117927,117929,118088],{"className":117928,"translate":216},[215],[212,117930,117932],{"className":117931},[220],[222,117933,117934],{"xmlns":224,"display":386},[226,117935,117936,118085],{},[1441,117937,117938,118015],{"rowspacing":1443,"columnalign":1444,"columnspacing":1445},[1447,117939,117940,117954],{},[1450,117941,117942],{},[1453,117943,117944],{"scriptlevel":323,"displaystyle":243},[229,117945,117946,117948,117950,117952],{},[232,117947,22093],{"mathvariant":794},[307,117949,310],{"stretchy":309},[232,117951,1141],{},[307,117953,317],{"stretchy":309},[1450,117955,117956],{},[1453,117957,117958],{"scriptlevel":323,"displaystyle":243},[229,117959,117960,117962,117964,117970,117972,117974,117976,117978,117980,117982,117984,117987,117989,117991,117993,117999,118001,118003,118005,118007,118009,118011,118013],{},[229,117961],{},[307,117963,320],{},[392,117965,117966,117968],{},[232,117967,420],{"mathvariant":419},[232,117969,1141],{},[307,117971,427],{"stretchy":309},[232,117973,4298],{},[307,117975,4301],{},[232,117977,11],{},[307,117979,310],{"stretchy":309},[232,117981,971],{},[307,117983,748],{"separator":243},[232,117985,117986],{},"z",[307,117988,317],{"stretchy":309},[307,117990,454],{"stretchy":309},[307,117992,5011],{},[392,117994,117995,117997],{},[232,117996,420],{"mathvariant":419},[232,117998,1141],{},[307,118000,427],{"stretchy":309},[232,118002,4298],{},[307,118004,4301],{},[232,118006,1141],{},[307,118008,310],{"stretchy":309},[232,118010,117986],{},[307,118012,317],{"stretchy":309},[307,118014,454],{"stretchy":309},[1447,118016,118017,118023],{},[1450,118018,118019],{},[1453,118020,118021],{"scriptlevel":323,"displaystyle":243},[229,118022],{},[1450,118024,118025],{},[1453,118026,118027],{"scriptlevel":323,"displaystyle":243},[229,118028,118029,118031,118033,118035,118037,118039,118041,118043,118045,118047,118053,118055,118057,118059,118061,118063,118065,118067,118069,118071,118073,118075,118077,118079,118081,118083],{},[229,118030],{},[307,118032,320],{},[232,118034,4298],{},[307,118036,4301],{},[232,118038,11],{},[307,118040,310],{"stretchy":309},[232,118042,971],{},[307,118044,317],{"stretchy":309},[307,118046,5011],{},[229,118048,118049,118051],{},[232,118050,10894],{"mathvariant":406},[232,118052,22093],{"mathvariant":406},[307,118054,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,118056,1141],{},[307,118058,310],{"stretchy":309},[232,118060,117986],{},[307,118062,317],{"stretchy":309},[1495,118064,1497],{},[232,118066,407],{"mathvariant":406},[1495,118068,1497],{},[232,118070,11],{},[307,118072,310],{"stretchy":309},[232,118074,117986],{},[232,118076,5006],{"mathvariant":406},[232,118078,971],{},[307,118080,317],{"stretchy":309},[307,118082,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,118084,748],{"separator":243},[236,118086,118087],{"encoding":238},"\\begin{aligned}\n\\mathcal L(q)\n&=\\mathbb E_q[\\log p(x,z)]\n-\\mathbb E_q[\\log q(z)]\\\\\n&=\\log p(x)\n-\\mathrm{KL}\\big(q(z)\\,\\|\\,p(z|x)\\big),\n\\end{aligned}",[212,118089,118091],{"className":118090,"ariaHidden":243},[242],[212,118092,118094,118097],{"className":118093},[247],[212,118095],{"className":118096,"style":14786},[251],[212,118098,118100],{"className":118099},[256],[212,118101,118103,118155],{"className":118102},[1441],[212,118104,118106],{"className":118105},[1558],[212,118107,118109,118147],{"className":118108},[482,483],[212,118110,118112,118144],{"className":118111},[487],[212,118113,118115,118136],{"className":118114,"style":14805},[491],[212,118116,118118,118121],{"style":118117},"top:-3.765em;",[212,118119],{"className":118120,"style":658},[499],[212,118122,118124,118127,118130,118133],{"className":118123},[256],[212,118125,22093],{"className":118126},[256,821],[212,118128,310],{"className":118129},[343],[212,118131,1141],{"className":118132,"style":1178},[256,257],[212,118134,317],{"className":118135},[350],[212,118137,118138,118141],{"style":15193},[212,118139],{"className":118140,"style":658},[499],[212,118142],{"className":118143},[256],[212,118145,515],{"className":118146},[514],[212,118148,118150],{"className":118149},[487],[212,118151,118153],{"className":118152,"style":14834},[491],[212,118154],{},[212,118156,118158],{"className":118157},[1649],[212,118159,118161,118444],{"className":118160},[482,483],[212,118162,118164,118441],{"className":118163},[487],[212,118165,118167,118332],{"className":118166,"style":14805},[491],[212,118168,118169,118172],{"style":118117},[212,118170],{"className":118171,"style":658},[499],[212,118173,118175,118178,118181,118184,118187,118227,118230,118235,118238,118241,118244,118247,118250,118253,118257,118260,118263,118266,118269,118309,118312,118317,118320,118323,118326,118329],{"className":118174},[256],[212,118176],{"className":118177},[256],[212,118179],{"className":118180,"style":355},[354],[212,118182,320],{"className":118183},[359],[212,118185],{"className":118186,"style":355},[354],[212,118188,118190,118193],{"className":118189},[256],[212,118191,420],{"className":118192},[256,563],[212,118194,118196],{"className":118195},[478],[212,118197,118199,118219],{"className":118198},[482,483],[212,118200,118202,118216],{"className":118201},[487],[212,118203,118205],{"className":118204,"style":45129},[491],[212,118206,118207,118210],{"style":579},[212,118208],{"className":118209,"style":500},[499],[212,118211,118213],{"className":118212},[504,505,506,507],[212,118214,1141],{"className":118215,"style":1178},[256,257,507],[212,118217,515],{"className":118218},[514],[212,118220,118222],{"className":118221},[487],[212,118223,118225],{"className":118224,"style":522},[491],[212,118226],{},[212,118228,427],{"className":118229},[343],[212,118231,4352,118233],{"className":118232},[1682],[212,118234,4356],{"style":4355},[212,118236],{"className":118237,"style":603},[354],[212,118239,11],{"className":118240},[256,257],[212,118242,310],{"className":118243},[343],[212,118245,971],{"className":118246},[256,257],[212,118248,748],{"className":118249},[770],[212,118251],{"className":118252,"style":603},[354],[212,118254,117986],{"className":118255,"style":118256},[256,257],"margin-right:0.044em;",[212,118258,20590],{"className":118259},[350],[212,118261],{"className":118262,"style":2785},[354],[212,118264,5011],{"className":118265},[2789],[212,118267],{"className":118268,"style":2785},[354],[212,118270,118272,118275],{"className":118271},[256],[212,118273,420],{"className":118274},[256,563],[212,118276,118278],{"className":118277},[478],[212,118279,118281,118301],{"className":118280},[482,483],[212,118282,118284,118298],{"className":118283},[487],[212,118285,118287],{"className":118286,"style":45129},[491],[212,118288,118289,118292],{"style":579},[212,118290],{"className":118291,"style":500},[499],[212,118293,118295],{"className":118294},[504,505,506,507],[212,118296,1141],{"className":118297,"style":1178},[256,257,507],[212,118299,515],{"className":118300},[514],[212,118302,118304],{"className":118303},[487],[212,118305,118307],{"className":118306,"style":522},[491],[212,118308],{},[212,118310,427],{"className":118311},[343],[212,118313,4352,118315],{"className":118314},[1682],[212,118316,4356],{"style":4355},[212,118318],{"className":118319,"style":603},[354],[212,118321,1141],{"className":118322,"style":1178},[256,257],[212,118324,310],{"className":118325},[343],[212,118327,117986],{"className":118328,"style":118256},[256,257],[212,118330,20590],{"className":118331},[350],[212,118333,118334,118337],{"style":15193},[212,118335],{"className":118336,"style":658},[499],[212,118338,118340,118343,118346,118349,118352,118357,118360,118363,118366,118369,118372,118375,118378,118381,118387,118393,118396,118399,118402,118405,118408,118411,118414,118417,118420,118423,118426,118429,118432,118438],{"className":118339},[256],[212,118341],{"className":118342},[256],[212,118344],{"className":118345,"style":355},[354],[212,118347,320],{"className":118348},[359],[212,118350],{"className":118351,"style":355},[354],[212,118353,4352,118355],{"className":118354},[1682],[212,118356,4356],{"style":4355},[212,118358],{"className":118359,"style":603},[354],[212,118361,11],{"className":118362},[256,257],[212,118364,310],{"className":118365},[343],[212,118367,971],{"className":118368},[256,257],[212,118370,317],{"className":118371},[350],[212,118373],{"className":118374,"style":2785},[354],[212,118376,5011],{"className":118377},[2789],[212,118379],{"className":118380,"style":2785},[354],[212,118382,118384],{"className":118383},[256],[212,118385,32863],{"className":118386},[256,32862],[212,118388,118390],{"className":118389},[256],[212,118391,310],{"className":118392},[616,9872],[212,118394,1141],{"className":118395,"style":1178},[256,257],[212,118397,310],{"className":118398},[343],[212,118400,117986],{"className":118401,"style":118256},[256,257],[212,118403,317],{"className":118404},[350],[212,118406],{"className":118407,"style":603},[354],[212,118409,407],{"className":118410},[256],[212,118412],{"className":118413,"style":603},[354],[212,118415,11],{"className":118416},[256,257],[212,118418,310],{"className":118419},[343],[212,118421,117986],{"className":118422,"style":118256},[256,257],[212,118424,5006],{"className":118425},[256],[212,118427,971],{"className":118428},[256,257],[212,118430,317],{"className":118431},[350],[212,118433,118435],{"className":118434},[256],[212,118436,317],{"className":118437},[616,9872],[212,118439,748],{"className":118440},[770],[212,118442,515],{"className":118443},[514],[212,118445,118447],{"className":118446},[487],[212,118448,118450],{"className":118449,"style":14834},[491],[212,118451],{},[11,118453,2448,118454,118515,118516,118587,118588,118689,118690,118718,118719,118777,118778,118806],{},[212,118455,118457,118485],{"className":118456,"translate":216},[215],[212,118458,118460],{"className":118459},[220],[222,118461,118462],{"xmlns":224},[226,118463,118464,118482],{},[229,118465,118466,118472,118474,118476,118478,118480],{},[229,118467,118468,118470],{},[232,118469,10894],{"mathvariant":406},[232,118471,22093],{"mathvariant":406},[307,118473,310],{"stretchy":309},[232,118475,1141],{},[232,118477,407],{"mathvariant":406},[232,118479,11],{},[307,118481,317],{"stretchy":309},[236,118483,118484],{"encoding":238},"\\mathrm{KL}(q\\|p)",[212,118486,118488],{"className":118487,"ariaHidden":243},[242],[212,118489,118491,118494,118500,118503,118506,118509,118512],{"className":118490},[247],[212,118492],{"className":118493,"style":336},[251],[212,118495,118497],{"className":118496},[256],[212,118498,32863],{"className":118499},[256,32862],[212,118501,310],{"className":118502},[343],[212,118504,1141],{"className":118505,"style":1178},[256,257],[212,118507,407],{"className":118508},[256],[212,118510,11],{"className":118511},[256,257],[212,118513,317],{"className":118514},[350]," 是 f-散度（",[212,118517,118519,118543],{"className":118518,"translate":216},[215],[212,118520,118522],{"className":118521},[220],[222,118523,118524],{"xmlns":224},[226,118525,118526,118540],{},[229,118527,118528,118530,118532,118534,118536,118538],{},[232,118529,234],{},[307,118531,320],{},[232,118533,966],{},[232,118535,4298],{},[307,118537,4301],{},[232,118539,966],{},[236,118541,118542],{"encoding":238},"f=t\\log t",[212,118544,118546,118564],{"className":118545,"ariaHidden":243},[242],[212,118547,118549,118552,118555,118558,118561],{"className":118548},[247],[212,118550],{"className":118551,"style":252},[251],[212,118553,234],{"className":118554,"style":258},[256,257],[212,118556],{"className":118557,"style":355},[354],[212,118559,320],{"className":118560},[359],[212,118562],{"className":118563,"style":355},[354],[212,118565,118567,118570,118573,118576,118581,118584],{"className":118566},[247],[212,118568],{"className":118569,"style":252},[251],[212,118571,966],{"className":118572},[256,257],[212,118574],{"className":118575,"style":603},[354],[212,118577,4352,118579],{"className":118578},[1682],[212,118580,4356],{"style":4355},[212,118582],{"className":118583,"style":603},[354],[212,118585,966],{"className":118586},[256,257],"）。反过来，任何以 ",[212,118589,118591,118623],{"className":118590,"translate":216},[215],[212,118592,118594],{"className":118593},[220],[222,118595,118596],{"xmlns":224},[226,118597,118598,118620],{},[229,118599,118600,118606,118608,118610,118612,118614,118616,118618],{},[392,118601,118602,118604],{},[232,118603,420],{"mathvariant":419},[232,118605,1141],{},[307,118607,427],{"stretchy":309},[232,118609,4298],{},[307,118611,4301],{},[307,118613,310],{"stretchy":309},[307,118615,3497],{},[307,118617,317],{"stretchy":309},[307,118619,454],{"stretchy":309},[236,118621,118622],{"encoding":238},"\\mathbb E_q[\\log(\\cdot)]",[212,118624,118626],{"className":118625,"ariaHidden":243},[242],[212,118627,118629,118632,118672,118675,118680,118683,118686],{"className":118628},[247],[212,118630],{"className":118631,"style":467},[251],[212,118633,118635,118638],{"className":118634},[256],[212,118636,420],{"className":118637},[256,563],[212,118639,118641],{"className":118640},[478],[212,118642,118644,118664],{"className":118643},[482,483],[212,118645,118647,118661],{"className":118646},[487],[212,118648,118650],{"className":118649,"style":45129},[491],[212,118651,118652,118655],{"style":579},[212,118653],{"className":118654,"style":500},[499],[212,118656,118658],{"className":118657},[504,505,506,507],[212,118659,1141],{"className":118660,"style":1178},[256,257,507],[212,118662,515],{"className":118663},[514],[212,118665,118667],{"className":118666},[487],[212,118668,118670],{"className":118669,"style":522},[491],[212,118671],{},[212,118673,427],{"className":118674},[343],[212,118676,4352,118678],{"className":118677},[1682],[212,118679,4356],{"style":4355},[212,118681,310],{"className":118682},[343],[212,118684,3497],{"className":118685},[256],[212,118687,20590],{"className":118688},[350]," 为组成部分的目标都可以用 f-散度的语言重写；",[212,118691,118693,118706],{"className":118692,"translate":216},[215],[212,118694,118696],{"className":118695},[220],[222,118697,118698],{"xmlns":224},[226,118699,118700,118704],{},[229,118701,118702],{},[232,118703,44954],{},[236,118705,49289],{"encoding":238},[212,118707,118709],{"className":118708,"ariaHidden":243},[242],[212,118710,118712,118715],{"className":118711},[247],[212,118713],{"className":118714,"style":2543},[251],[212,118716,44954],{"className":118717,"style":44984},[256,257],"-VI、",[212,118720,118722,118739],{"className":118721,"translate":216},[215],[212,118723,118725],{"className":118724},[220],[222,118726,118727],{"xmlns":224},[226,118728,118729,118737],{},[229,118730,118731],{},[7012,118732,118733,118735],{},[232,118734,37649],{},[312,118736,2661],{},[236,118738,40594],{"encoding":238},[212,118740,118742],{"className":118741,"ariaHidden":243},[242],[212,118743,118745,118748],{"className":118744},[247],[212,118746],{"className":118747,"style":40604},[251],[212,118749,118751,118754],{"className":118750},[256],[212,118752,37649],{"className":118753},[256,257],[212,118755,118757],{"className":118756},[478],[212,118758,118760],{"className":118759},[482],[212,118761,118763],{"className":118762},[487],[212,118764,118766],{"className":118765,"style":20228},[491],[212,118767,118768,118771],{"style":7063},[212,118769],{"className":118770,"style":500},[499],[212,118772,118774],{"className":118773},[504,505,506,507],[212,118775,2661],{"className":118776},[256,507],"-VI 等就换用别的 ",[212,118779,118781,118794],{"className":118780,"translate":216},[215],[212,118782,118784],{"className":118783},[220],[222,118785,118786],{"xmlns":224},[226,118787,118788,118792],{},[229,118789,118790],{},[232,118791,234],{},[236,118793,234],{"encoding":238},[212,118795,118797],{"className":118796,"ariaHidden":243},[242],[212,118798,118800,118803],{"className":118799},[247],[212,118801],{"className":118802,"style":252},[251],[212,118804,234],{"className":118805,"style":258},[256,257],"，在 3.1 节所说的「零回避」（mass-covering）与「零强制」（mode-seeking）两种极端行为之间取舍。",[2509,118808,118810],{"id":118809},"_73-互信息估计","7.3 互信息估计",[11,118812,118813],{},"互信息可写成",[212,118815,118817],{"className":118816,"translate":216},[377],[212,118818,118820,118935],{"className":118819,"translate":216},[215],[212,118821,118823],{"className":118822},[220],[222,118824,118825],{"xmlns":224,"display":386},[226,118826,118827,118932],{},[229,118828,118829,118831,118833,118835,118837,118839,118841,118843,118849,118851,118861,118863,118865,118867,118873,118876,118882,118884,118886,118900,118902,118912,118914,118920,118922,118928,118930],{},[232,118830,34068],{},[307,118832,310],{"stretchy":309},[232,118834,795],{},[307,118836,34075],{"separator":243},[232,118838,5599],{},[307,118840,317],{"stretchy":309},[307,118842,320],{},[229,118844,118845,118847],{},[232,118846,10894],{"mathvariant":406},[232,118848,22093],{"mathvariant":406},[307,118850,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[392,118852,118853,118855],{},[232,118854,403],{},[229,118856,118857,118859],{},[232,118858,795],{},[232,118860,5599],{},[1495,118862,1497],{},[232,118864,407],{"mathvariant":406},[1495,118866,1497],{},[392,118868,118869,118871],{},[232,118870,403],{},[232,118872,795],{},[307,118874,118875],{},"⊗",[392,118877,118878,118880],{},[232,118879,403],{},[232,118881,5599],{},[307,118883,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,118885,320],{},[392,118887,118888,118890],{},[232,118889,396],{},[229,118891,118892,118894,118896,118898],{},[232,118893,966],{},[232,118895,4298],{},[307,118897,4301],{},[232,118899,966],{},[307,118901,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[392,118903,118904,118906],{},[232,118905,403],{},[229,118907,118908,118910],{},[232,118909,795],{},[232,118911,5599],{},[232,118913,407],{"mathvariant":406},[392,118915,118916,118918],{},[232,118917,403],{},[232,118919,795],{},[307,118921,118875],{},[392,118923,118924,118926],{},[232,118925,403],{},[232,118927,5599],{},[307,118929,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,118931,748],{"separator":243},[236,118933,118934],{"encoding":238},"I(X;Y)\n=\\mathrm{KL}\\big(P_{XY}\\,\\|\\,P_X\\otimes P_Y\\big)\n=D_{t\\log t}\\big(P_{XY}\\|P_X\\otimes P_Y\\big),",[212,118936,118938,118974,119096,119157,119331],{"className":118937,"ariaHidden":243},[242],[212,118939,118941,118944,118947,118950,118953,118956,118959,118962,118965,118968,118971],{"className":118940},[247],[212,118942],{"className":118943,"style":336},[251],[212,118945,34068],{"className":118946,"style":9085},[256,257],[212,118948,310],{"className":118949},[343],[212,118951,795],{"className":118952,"style":9085},[256,257],[212,118954,34075],{"className":118955},[770],[212,118957],{"className":118958,"style":603},[354],[212,118960,5599],{"className":118961,"style":2785},[256,257],[212,118963,317],{"className":118964},[350],[212,118966],{"className":118967,"style":355},[354],[212,118969,320],{"className":118970},[359],[212,118972],{"className":118973,"style":355},[354],[212,118975,118977,118980,118986,118992,119038,119041,119044,119047,119087,119090,119093],{"className":118976},[247],[212,118978],{"className":118979,"style":20763},[251],[212,118981,118983],{"className":118982},[256],[212,118984,32863],{"className":118985},[256,32862],[212,118987,118989],{"className":118988},[256],[212,118990,310],{"className":118991},[616,9872],[212,118993,118995,118998],{"className":118994},[256],[212,118996,403],{"className":118997,"style":531},[256,257],[212,118999,119001],{"className":119000},[478],[212,119002,119004,119030],{"className":119003},[482,483],[212,119005,119007,119027],{"className":119006},[487],[212,119008,119010],{"className":119009,"style":576},[491],[212,119011,119012,119015],{"style":11336},[212,119013],{"className":119014,"style":500},[499],[212,119016,119018],{"className":119017},[504,505,506,507],[212,119019,119021,119024],{"className":119020},[256,507],[212,119022,795],{"className":119023,"style":9085},[256,257,507],[212,119025,5599],{"className":119026,"style":2785},[256,257,507],[212,119028,515],{"className":119029},[514],[212,119031,119033],{"className":119032},[487],[212,119034,119036],{"className":119035,"style":8166},[491],[212,119037],{},[212,119039],{"className":119040,"style":603},[354],[212,119042,407],{"className":119043},[256],[212,119045],{"className":119046,"style":603},[354],[212,119048,119050,119053],{"className":119049},[256],[212,119051,403],{"className":119052,"style":531},[256,257],[212,119054,119056],{"className":119055},[478],[212,119057,119059,119079],{"className":119058},[482,483],[212,119060,119062,119076],{"className":119061},[487],[212,119063,119065],{"className":119064,"style":576},[491],[212,119066,119067,119070],{"style":11336},[212,119068],{"className":119069,"style":500},[499],[212,119071,119073],{"className":119072},[504,505,506,507],[212,119074,795],{"className":119075,"style":9085},[256,257,507],[212,119077,515],{"className":119078},[514],[212,119080,119082],{"className":119081},[487],[212,119083,119085],{"className":119084,"style":8166},[491],[212,119086],{},[212,119088],{"className":119089,"style":2785},[354],[212,119091,118875],{"className":119092},[2789],[212,119094],{"className":119095,"style":2785},[354],[212,119097,119099,119102,119142,119148,119151,119154],{"className":119098},[247],[212,119100],{"className":119101,"style":20763},[251],[212,119103,119105,119108],{"className":119104},[256],[212,119106,403],{"className":119107,"style":531},[256,257],[212,119109,119111],{"className":119110},[478],[212,119112,119114,119134],{"className":119113},[482,483],[212,119115,119117,119131],{"className":119116},[487],[212,119118,119120],{"className":119119,"style":576},[491],[212,119121,119122,119125],{"style":11336},[212,119123],{"className":119124,"style":500},[499],[212,119126,119128],{"className":119127},[504,505,506,507],[212,119129,5599],{"className":119130,"style":2785},[256,257,507],[212,119132,515],{"className":119133},[514],[212,119135,119137],{"className":119136},[487],[212,119138,119140],{"className":119139,"style":8166},[491],[212,119141],{},[212,119143,119145],{"className":119144},[256],[212,119146,317],{"className":119147},[616,9872],[212,119149],{"className":119150,"style":355},[354],[212,119152,320],{"className":119153},[359],[212,119155],{"className":119156,"style":355},[354],[212,119158,119160,119163,119227,119233,119279,119282,119322,119325,119328],{"className":119159},[247],[212,119161],{"className":119162,"style":20763},[251],[212,119164,119166,119169],{"className":119165},[256],[212,119167,396],{"className":119168,"style":474},[256,257],[212,119170,119172],{"className":119171},[478],[212,119173,119175,119219],{"className":119174},[482,483],[212,119176,119178,119216],{"className":119177},[487],[212,119179,119181],{"className":119180,"style":492},[491],[212,119182,119183,119186],{"style":495},[212,119184],{"className":119185,"style":500},[499],[212,119187,119189],{"className":119188},[504,505,506,507],[212,119190,119192,119195,119198,119210,119213],{"className":119191},[256,507],[212,119193,966],{"className":119194},[256,257,507],[212,119196],{"className":119197,"style":42566},[354,507],[212,119199,119201,119204,119207],{"className":119200},[1682,507],[212,119202,47857],{"className":119203},[507],[212,119205,47861],{"className":119206},[507],[212,119208,4356],{"className":119209,"style":4355},[507],[212,119211],{"className":119212,"style":42566},[354,507],[212,119214,966],{"className":119215},[256,257,507],[212,119217,515],{"className":119218},[514],[212,119220,119222],{"className":119221},[487],[212,119223,119225],{"className":119224,"style":522},[491],[212,119226],{},[212,119228,119230],{"className":119229},[256],[212,119231,310],{"className":119232},[616,9872],[212,119234,119236,119239],{"className":119235},[256],[212,119237,403],{"className":119238,"style":531},[256,257],[212,119240,119242],{"className":119241},[478],[212,119243,119245,119271],{"className":119244},[482,483],[212,119246,119248,119268],{"className":119247},[487],[212,119249,119251],{"className":119250,"style":576},[491],[212,119252,119253,119256],{"style":11336},[212,119254],{"className":119255,"style":500},[499],[212,119257,119259],{"className":119258},[504,505,506,507],[212,119260,119262,119265],{"className":119261},[256,507],[212,119263,795],{"className":119264,"style":9085},[256,257,507],[212,119266,5599],{"className":119267,"style":2785},[256,257,507],[212,119269,515],{"className":119270},[514],[212,119272,119274],{"className":119273},[487],[212,119275,119277],{"className":119276,"style":8166},[491],[212,119278],{},[212,119280,407],{"className":119281},[256],[212,119283,119285,119288],{"className":119284},[256],[212,119286,403],{"className":119287,"style":531},[256,257],[212,119289,119291],{"className":119290},[478],[212,119292,119294,119314],{"className":119293},[482,483],[212,119295,119297,119311],{"className":119296},[487],[212,119298,119300],{"className":119299,"style":576},[491],[212,119301,119302,119305],{"style":11336},[212,119303],{"className":119304,"style":500},[499],[212,119306,119308],{"className":119307},[504,505,506,507],[212,119309,795],{"className":119310,"style":9085},[256,257,507],[212,119312,515],{"className":119313},[514],[212,119315,119317],{"className":119316},[487],[212,119318,119320],{"className":119319,"style":8166},[491],[212,119321],{},[212,119323],{"className":119324,"style":2785},[354],[212,119326,118875],{"className":119327},[2789],[212,119329],{"className":119330,"style":2785},[354],[212,119332,119334,119337,119377,119383],{"className":119333},[247],[212,119335],{"className":119336,"style":20763},[251],[212,119338,119340,119343],{"className":119339},[256],[212,119341,403],{"className":119342,"style":531},[256,257],[212,119344,119346],{"className":119345},[478],[212,119347,119349,119369],{"className":119348},[482,483],[212,119350,119352,119366],{"className":119351},[487],[212,119353,119355],{"className":119354,"style":576},[491],[212,119356,119357,119360],{"style":11336},[212,119358],{"className":119359,"style":500},[499],[212,119361,119363],{"className":119362},[504,505,506,507],[212,119364,5599],{"className":119365,"style":2785},[256,257,507],[212,119367,515],{"className":119368},[514],[212,119370,119372],{"className":119371},[487],[212,119373,119375],{"className":119374,"style":8166},[491],[212,119376],{},[212,119378,119380],{"className":119379},[256],[212,119381,317],{"className":119382},[616,9872],[212,119384,748],{"className":119385},[770],[11,119387,119388,119389,119417,119418,119446,119447,119505],{},"因此它是 f-散度的特例。MINE 用 Donsker–Varadhan 对偶估计它，f-MINE 则对一般 ",[212,119390,119392,119405],{"className":119391,"translate":216},[215],[212,119393,119395],{"className":119394},[220],[222,119396,119397],{"xmlns":224},[226,119398,119399,119403],{},[229,119400,119401],{},[232,119402,234],{},[236,119404,234],{"encoding":238},[212,119406,119408],{"className":119407,"ariaHidden":243},[242],[212,119409,119411,119414],{"className":119410},[247],[212,119412],{"className":119413,"style":252},[251],[212,119415,234],{"className":119416,"style":258},[256,257]," 用 4.4 节的对偶；不同 ",[212,119419,119421,119434],{"className":119420,"translate":216},[215],[212,119422,119424],{"className":119423},[220],[222,119425,119426],{"xmlns":224},[226,119427,119428,119432],{},[229,119429,119430],{},[232,119431,234],{},[236,119433,234],{"encoding":238},[212,119435,119437],{"className":119436,"ariaHidden":243},[242],[212,119438,119440,119443],{"className":119439},[247],[212,119441],{"className":119442,"style":252},[251],[212,119444,234],{"className":119445,"style":258},[256,257],"（KL、JS、",[212,119448,119450,119467],{"className":119449,"translate":216},[215],[212,119451,119453],{"className":119452},[220],[222,119454,119455],{"xmlns":224},[226,119456,119457,119465],{},[229,119458,119459],{},[7012,119460,119461,119463],{},[232,119462,37649],{},[312,119464,2661],{},[236,119466,40594],{"encoding":238},[212,119468,119470],{"className":119469,"ariaHidden":243},[242],[212,119471,119473,119476],{"className":119472},[247],[212,119474],{"className":119475,"style":40604},[251],[212,119477,119479,119482],{"className":119478},[256],[212,119480,37649],{"className":119481},[256,257],[212,119483,119485],{"className":119484},[478],[212,119486,119488],{"className":119487},[482],[212,119489,119491],{"className":119490},[487],[212,119492,119494],{"className":119493,"style":20228},[491],[212,119495,119496,119499],{"style":7063},[212,119497],{"className":119498,"style":500},[499],[212,119500,119502],{"className":119501},[504,505,506,507],[212,119503,2661],{"className":119504},[256,507],"）给出不同的「MI 下界」和不同的方差—偏差折衷。对比式学习的 InfoNCE 也是 KL 下界的一种变体。",[2509,119507,119509],{"id":119508},"_74-表示学习","7.4 表示学习",[11,119511,119512,119513,119557],{},"任何表示 ",[212,119514,119516,119536],{"className":119515,"translate":216},[215],[212,119517,119519],{"className":119518},[220],[222,119520,119521],{"xmlns":224},[226,119522,119523,119533],{},[229,119524,119525,119527,119529,119531],{},[232,119526,5590],{},[307,119528,310],{"stretchy":309},[232,119530,795],{},[307,119532,317],{"stretchy":309},[236,119534,119535],{"encoding":238},"T(X)",[212,119537,119539],{"className":119538,"ariaHidden":243},[242],[212,119540,119542,119545,119548,119551,119554],{"className":119541},[247],[212,119543],{"className":119544,"style":336},[251],[212,119546,5590],{"className":119547,"style":531},[256,257],[212,119549,310],{"className":119550},[343],[212,119552,795],{"className":119553,"style":9085},[256,257],[212,119555,317],{"className":119556},[350]," 都满足（4.5 节）",[212,119559,119561],{"className":119560,"translate":216},[377],[212,119562,119564,119644],{"className":119563,"translate":216},[215],[212,119565,119567],{"className":119566},[220],[222,119568,119569],{"xmlns":224,"display":386},[226,119570,119571,119641],{},[229,119572,119573,119579,119581,119595,119597,119611,119613,119615,119621,119623,119629,119631,119637,119639],{},[392,119574,119575,119577],{},[232,119576,396],{},[232,119578,234],{},[307,119580,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[392,119582,119583,119585],{},[232,119584,403],{},[229,119586,119587,119589,119591,119593],{},[232,119588,5590],{},[307,119590,310],{"stretchy":309},[232,119592,795],{},[307,119594,317],{"stretchy":309},[232,119596,407],{"mathvariant":406},[392,119598,119599,119601],{},[232,119600,410],{},[229,119602,119603,119605,119607,119609],{},[232,119604,5590],{},[307,119606,310],{"stretchy":309},[232,119608,795],{},[307,119610,317],{"stretchy":309},[307,119612,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,119614,10150],{},[392,119616,119617,119619],{},[232,119618,396],{},[232,119620,234],{},[307,119622,310],{"stretchy":309},[392,119624,119625,119627],{},[232,119626,403],{},[232,119628,795],{},[232,119630,407],{"mathvariant":406},[392,119632,119633,119635],{},[232,119634,410],{},[232,119636,795],{},[307,119638,317],{"stretchy":309},[307,119640,748],{"separator":243},[236,119642,119643],{"encoding":238},"D_f\\big(P_{T(X)}\\|Q_{T(X)}\\big)\n\\le D_f(P_X\\|Q_X),",[212,119645,119647,119823],{"className":119646,"ariaHidden":243},[242],[212,119648,119650,119654,119694,119700,119753,119756,119808,119814,119817,119820],{"className":119649},[247],[212,119651],{"className":119652,"style":119653},[251],"height:1.2052em;vertical-align:-0.3552em;",[212,119655,119657,119660],{"className":119656},[256],[212,119658,396],{"className":119659,"style":474},[256,257],[212,119661,119663],{"className":119662},[478],[212,119664,119666,119686],{"className":119665},[482,483],[212,119667,119669,119683],{"className":119668},[487],[212,119670,119672],{"className":119671,"style":492},[491],[212,119673,119674,119677],{"style":495},[212,119675],{"className":119676,"style":500},[499],[212,119678,119680],{"className":119679},[504,505,506,507],[212,119681,234],{"className":119682,"style":258},[256,257,507],[212,119684,515],{"className":119685},[514],[212,119687,119689],{"className":119688},[487],[212,119690,119692],{"className":119691,"style":522},[491],[212,119693],{},[212,119695,119697],{"className":119696},[256],[212,119698,310],{"className":119699},[616,9872],[212,119701,119703,119706],{"className":119702},[256],[212,119704,403],{"className":119705,"style":531},[256,257],[212,119707,119709],{"className":119708},[478],[212,119710,119712,119745],{"className":119711},[482,483],[212,119713,119715,119742],{"className":119714},[487],[212,119716,119718],{"className":119717,"style":6296},[491],[212,119719,119721,119724],{"style":119720},"top:-2.5198em;margin-left:-0.1389em;margin-right:0.05em;",[212,119722],{"className":119723,"style":500},[499],[212,119725,119727],{"className":119726},[504,505,506,507],[212,119728,119730,119733,119736,119739],{"className":119729},[256,507],[212,119731,5590],{"className":119732,"style":531},[256,257,507],[212,119734,310],{"className":119735},[343,507],[212,119737,795],{"className":119738,"style":9085},[256,257,507],[212,119740,317],{"className":119741},[350,507],[212,119743,515],{"className":119744},[514],[212,119746,119748],{"className":119747},[487],[212,119749,119751],{"className":119750,"style":6342},[491],[212,119752],{},[212,119754,407],{"className":119755},[256],[212,119757,119759,119762],{"className":119758},[256],[212,119760,410],{"className":119761},[256,257],[212,119763,119765],{"className":119764},[478],[212,119766,119768,119800],{"className":119767},[482,483],[212,119769,119771,119797],{"className":119770},[487],[212,119772,119774],{"className":119773,"style":6296},[491],[212,119775,119776,119779],{"style":75785},[212,119777],{"className":119778,"style":500},[499],[212,119780,119782],{"className":119781},[504,505,506,507],[212,119783,119785,119788,119791,119794],{"className":119784},[256,507],[212,119786,5590],{"className":119787,"style":531},[256,257,507],[212,119789,310],{"className":119790},[343,507],[212,119792,795],{"className":119793,"style":9085},[256,257,507],[212,119795,317],{"className":119796},[350,507],[212,119798,515],{"className":119799},[514],[212,119801,119803],{"className":119802},[487],[212,119804,119806],{"className":119805,"style":6342},[491],[212,119807],{},[212,119809,119811],{"className":119810},[256],[212,119812,317],{"className":119813},[616,9872],[212,119815],{"className":119816,"style":355},[354],[212,119818,10150],{"className":119819},[359],[212,119821],{"className":119822,"style":355},[354],[212,119824,119826,119829,119869,119872,119912,119915,119955,119958],{"className":119825},[247],[212,119827],{"className":119828,"style":467},[251],[212,119830,119832,119835],{"className":119831},[256],[212,119833,396],{"className":119834,"style":474},[256,257],[212,119836,119838],{"className":119837},[478],[212,119839,119841,119861],{"className":119840},[482,483],[212,119842,119844,119858],{"className":119843},[487],[212,119845,119847],{"className":119846,"style":492},[491],[212,119848,119849,119852],{"style":495},[212,119850],{"className":119851,"style":500},[499],[212,119853,119855],{"className":119854},[504,505,506,507],[212,119856,234],{"className":119857,"style":258},[256,257,507],[212,119859,515],{"className":119860},[514],[212,119862,119864],{"className":119863},[487],[212,119865,119867],{"className":119866,"style":522},[491],[212,119868],{},[212,119870,310],{"className":119871},[343],[212,119873,119875,119878],{"className":119874},[256],[212,119876,403],{"className":119877,"style":531},[256,257],[212,119879,119881],{"className":119880},[478],[212,119882,119884,119904],{"className":119883},[482,483],[212,119885,119887,119901],{"className":119886},[487],[212,119888,119890],{"className":119889,"style":576},[491],[212,119891,119892,119895],{"style":11336},[212,119893],{"className":119894,"style":500},[499],[212,119896,119898],{"className":119897},[504,505,506,507],[212,119899,795],{"className":119900,"style":9085},[256,257,507],[212,119902,515],{"className":119903},[514],[212,119905,119907],{"className":119906},[487],[212,119908,119910],{"className":119909,"style":8166},[491],[212,119911],{},[212,119913,407],{"className":119914},[256],[212,119916,119918,119921],{"className":119917},[256],[212,119919,410],{"className":119920},[256,257],[212,119922,119924],{"className":119923},[478],[212,119925,119927,119947],{"className":119926},[482,483],[212,119928,119930,119944],{"className":119929},[487],[212,119931,119933],{"className":119932,"style":576},[491],[212,119934,119935,119938],{"style":579},[212,119936],{"className":119937,"style":500},[499],[212,119939,119941],{"className":119940},[504,505,506,507],[212,119942,795],{"className":119943,"style":9085},[256,257,507],[212,119945,515],{"className":119946},[514],[212,119948,119950],{"className":119949},[487],[212,119951,119953],{"className":119952,"style":8166},[491],[212,119954],{},[212,119956,317],{"className":119957},[350],[212,119959,748],{"className":119960},[770],[11,119962,119963],{},"即「编码不会创造信息」。这为对比学习、域对齐、特征选择提供了可证伪的约束：任何声称「表示后差异更大」的方法都必然在某个环节违反了 DPI，需要解释为什么。",[2509,119965,119967],{"id":119966},"_75-域适应","7.5 域适应",[11,119969,119970,119971,120001,120002,120032],{},"在源域 ",[212,119972,119974,119988],{"className":119973,"translate":216},[215],[212,119975,119977],{"className":119976},[220],[222,119978,119979],{"xmlns":224},[226,119980,119981,119985],{},[229,119982,119983],{},[232,119984,25937],{"mathvariant":794},[236,119986,119987],{"encoding":238},"\\mathcal S",[212,119989,119991],{"className":119990,"ariaHidden":243},[242],[212,119992,119994,119997],{"className":119993},[247],[212,119995],{"className":119996,"style":861},[251],[212,119998,25937],{"className":119999,"style":120000},[256,821],"margin-right:0.075em;"," 与目标域 ",[212,120003,120005,120019],{"className":120004,"translate":216},[215],[212,120006,120008],{"className":120007},[220],[222,120009,120010],{"xmlns":224},[226,120011,120012,120016],{},[229,120013,120014],{},[232,120015,5590],{"mathvariant":794},[236,120017,120018],{"encoding":238},"\\mathcal T",[212,120020,120022],{"className":120021,"ariaHidden":243},[242],[212,120023,120025,120028],{"className":120024},[247],[212,120026],{"className":120027,"style":861},[251],[212,120029,5590],{"className":120030,"style":120031},[256,821],"margin-right:0.2542em;"," 上，衡量分布漂移的现代方法（DANN、ADDA）本质上用 f-散度或 IPM 对齐边缘分布；其中用 JS 的（GAN 式）对齐与用 MMD\u002FWasserstein 的对齐，区别正是 6.2 节的几何与支撑问题。",[2509,120034,120036],{"id":120035},"_76-假设检验","7.6 假设检验",[11,120038,120039],{},"f-散度是假设检验的错误指数：",[10225,120041,120042,120109],{},[6863,120043,120044,120047,120048,20166],{},[1194,120045,120046],{},"Stein 引理","：在固定第一类错误下，第二类错误的最优指数为 ",[212,120049,120051,120079],{"className":120050,"translate":216},[215],[212,120052,120054],{"className":120053},[220],[222,120055,120056],{"xmlns":224},[226,120057,120058,120076],{},[229,120059,120060,120066,120068,120070,120072,120074],{},[229,120061,120062,120064],{},[232,120063,10894],{"mathvariant":406},[232,120065,22093],{"mathvariant":406},[307,120067,310],{"stretchy":309},[232,120069,403],{},[232,120071,407],{"mathvariant":406},[232,120073,410],{},[307,120075,317],{"stretchy":309},[236,120077,120078],{"encoding":238},"\\mathrm{KL}(P\\|Q)",[212,120080,120082],{"className":120081,"ariaHidden":243},[242],[212,120083,120085,120088,120094,120097,120100,120103,120106],{"className":120084},[247],[212,120086],{"className":120087,"style":336},[251],[212,120089,120091],{"className":120090},[256],[212,120092,32863],{"className":120093},[256,32862],[212,120095,310],{"className":120096},[343],[212,120098,403],{"className":120099,"style":531},[256,257],[212,120101,407],{"className":120102},[256],[212,120104,410],{"className":120105},[256,257],[212,120107,317],{"className":120108},[350],[6863,120110,120111,9598,120114,120393],{},[1194,120112,120113],{},"Chernoff 信息",[212,120115,120117,120191],{"className":120116,"translate":216},[215],[212,120118,120120],{"className":120119},[220],[222,120121,120122],{"xmlns":224},[226,120123,120124,120188],{},[229,120125,120126,120128,120130,120132,120134,120136,120138,120140,120160,120162,120164,120166,120168,120170,120178,120180,120182,120184,120186],{},[232,120127,39494],{},[307,120129,310],{"stretchy":309},[232,120131,403],{},[307,120133,748],{"separator":243},[232,120135,410],{},[307,120137,317],{"stretchy":309},[307,120139,320],{},[392,120141,120142,120148],{},[229,120143,120144,120146],{},[232,120145,35632],{},[307,120147,4301],{},[229,120149,120150,120152,120154,120156,120158],{},[312,120151,323],{},[307,120153,7449],{},[232,120155,11539],{},[307,120157,7449],{},[312,120159,314],{},[307,120161,310],{"stretchy":309},[312,120163,314],{},[307,120165,5011],{},[232,120167,11539],{},[307,120169,317],{"stretchy":309},[7751,120171,120172,120174,120176],{},[232,120173,396],{},[232,120175,11539],{},[232,120177,1231],{},[307,120179,310],{"stretchy":309},[232,120181,403],{},[232,120183,407],{"mathvariant":406},[232,120185,410],{},[307,120187,317],{"stretchy":309},[236,120189,120190],{"encoding":238},"C(P,Q)=\\sup_{0\u003C\\lambda\u003C1}(1-\\lambda)D^{R}_{\\lambda}(P\\|Q)",[212,120192,120194,120230,120307],{"className":120193,"ariaHidden":243},[242],[212,120195,120197,120200,120203,120206,120209,120212,120215,120218,120221,120224,120227],{"className":120196},[247],[212,120198],{"className":120199,"style":336},[251],[212,120201,39494],{"className":120202,"style":10982},[256,257],[212,120204,310],{"className":120205},[343],[212,120207,403],{"className":120208,"style":531},[256,257],[212,120210,748],{"className":120211},[770],[212,120213],{"className":120214,"style":603},[354],[212,120216,410],{"className":120217},[256,257],[212,120219,317],{"className":120220},[350],[212,120222],{"className":120223,"style":355},[354],[212,120225,320],{"className":120226},[359],[212,120228],{"className":120229,"style":355},[354],[212,120231,120233,120236,120292,120295,120298,120301,120304],{"className":120232},[247],[212,120234],{"className":120235,"style":35756},[251],[212,120237,120239,120242],{"className":120238},[1682],[212,120240,35632],{"className":120241},[1682],[212,120243,120245],{"className":120244},[478],[212,120246,120248,120284],{"className":120247},[482,483],[212,120249,120251,120281],{"className":120250},[487],[212,120252,120255],{"className":120253,"style":120254},[491],"height:0.242em;",[212,120256,120257,120260],{"style":35778},[212,120258],{"className":120259,"style":500},[499],[212,120261,120263],{"className":120262},[504,505,506,507],[212,120264,120266,120269,120272,120275,120278],{"className":120265},[256,507],[212,120267,323],{"className":120268},[256,507],[212,120270,7449],{"className":120271},[359,507],[212,120273,11539],{"className":120274},[256,257,507],[212,120276,7449],{"className":120277},[359,507],[212,120279,314],{"className":120280},[256,507],[212,120282,515],{"className":120283},[514],[212,120285,120287],{"className":120286},[487],[212,120288,120290],{"className":120289,"style":35806},[491],[212,120291],{},[212,120293,310],{"className":120294},[343],[212,120296,314],{"className":120297},[256],[212,120299],{"className":120300,"style":2785},[354],[212,120302,5011],{"className":120303},[2789],[212,120305],{"className":120306,"style":2785},[354],[212,120308,120310,120314,120317,120320,120378,120381,120384,120387,120390],{"className":120309},[247],[212,120311],{"className":120312,"style":120313},[251],"height:1.1244em;vertical-align:-0.2831em;",[212,120315,11539],{"className":120316},[256,257],[212,120318,317],{"className":120319},[350],[212,120321,120323,120326],{"className":120322},[256],[212,120324,396],{"className":120325,"style":474},[256,257],[212,120327,120329],{"className":120328},[478],[212,120330,120332,120370],{"className":120331},[482,483],[212,120333,120335,120367],{"className":120334},[487],[212,120336,120338,120353],{"className":120337,"style":52284},[491],[212,120339,120341,120344],{"style":120340},"top:-2.4169em;margin-left:-0.0278em;margin-right:0.05em;",[212,120342],{"className":120343,"style":500},[499],[212,120345,120347],{"className":120346},[504,505,506,507],[212,120348,120350],{"className":120349},[256,507],[212,120351,11539],{"className":120352},[256,257,507],[212,120354,120355,120358],{"style":7063},[212,120356],{"className":120357,"style":500},[499],[212,120359,120361],{"className":120360},[504,505,506,507],[212,120362,120364],{"className":120363},[256,507],[212,120365,1231],{"className":120366,"style":49798},[256,257,507],[212,120368,515],{"className":120369},[514],[212,120371,120373],{"className":120372},[487],[212,120374,120376],{"className":120375,"style":8745},[491],[212,120377],{},[212,120379,310],{"className":120380},[343],[212,120382,403],{"className":120383,"style":531},[256,257],[212,120385,407],{"className":120386},[256],[212,120388,410],{"className":120389},[256,257],[212,120391,317],{"className":120392},[350],"，即 Rényi\u002Fα-族中的最优点；对称检验的指数由它决定。",[11,120395,120396],{},"因此 f-散度不只是「训练目标」，也是统计判决的极限性能。",[725,120398,120400],{"id":120399},"_8-差分隐私f-dp","8. 差分隐私（f-DP）",[11,120402,120403,120404,120407,120408,6692,120411,120439,120440,120481],{},"一个较新的应用是把 f-散度的语言搬到隐私保护。差分隐私（DP）要求相邻数据集的输出分布「难以区分」。Dong–Roth–Su 提出 ",[1194,120405,120406],{},"f-差分隐私（f-DP）","：用一个",[1194,120409,120410],{},"权衡函数（tradeoff function）",[212,120412,120414,120427],{"className":120413,"translate":216},[215],[212,120415,120417],{"className":120416},[220],[222,120418,120419],{"xmlns":224},[226,120420,120421,120425],{},[229,120422,120423],{},[232,120424,234],{},[236,120426,234],{"encoding":238},[212,120428,120430],{"className":120429,"ariaHidden":243},[242],[212,120431,120433,120436],{"className":120432},[247],[212,120434],{"className":120435,"style":252},[251],[212,120437,234],{"className":120438,"style":258},[256,257]," 刻画两个输出分布 ",[212,120441,120443,120460],{"className":120442,"translate":216},[215],[212,120444,120446],{"className":120445},[220],[222,120447,120448],{"xmlns":224},[226,120449,120450,120458],{},[229,120451,120452,120454,120456],{},[232,120453,403],{},[307,120455,748],{"separator":243},[232,120457,410],{},[236,120459,753],{"encoding":238},[212,120461,120463],{"className":120462,"ariaHidden":243},[242],[212,120464,120466,120469,120472,120475,120478],{"className":120465},[247],[212,120467],{"className":120468,"style":763},[251],[212,120470,403],{"className":120471,"style":531},[256,257],[212,120473,748],{"className":120474},[770],[212,120476],{"className":120477,"style":603},[354],[212,120479,410],{"className":120480},[256,257]," 上「漏报率—误报率」的权衡曲线：",[212,120483,120485],{"className":120484,"translate":216},[377],[212,120486,120488,120585],{"className":120487,"translate":216},[215],[212,120489,120491],{"className":120490},[220],[222,120492,120493],{"xmlns":224,"display":386},[226,120494,120495,120582],{},[229,120496,120497,120499,120501,120503,120505,120507,120509,120511,120513,120515,120517,120528,120530,120532,120534,120536,120538,120540,120542,120544,120546,120548,120550,120552,120554,120556,120558,120560,120562,120564,120566,120568,120570,120572,120574,120576,120578,120580],{},[232,120498,5590],{},[307,120500,310],{"stretchy":309},[232,120502,403],{},[307,120504,748],{"separator":243},[232,120506,410],{},[307,120508,317],{"stretchy":309},[307,120510,310],{"stretchy":309},[232,120512,44954],{},[307,120514,317],{"stretchy":309},[307,120516,320],{},[6214,120518,120519,120526],{},[229,120520,120521,120524],{},[232,120522,120523],{},"inf",[307,120525,4301],{},[232,120527,800],{},[307,120529,3096],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,120531,403],{},[307,120533,310],{"stretchy":309},[232,120535,800],{},[307,120537,317],{"stretchy":309},[1495,120539,4481],{},[307,120541,1214],{},[1495,120543,4481],{},[232,120545,410],{},[307,120547,310],{"stretchy":309},[232,120549,800],{},[307,120551,317],{"stretchy":309},[307,120553,7126],{},[312,120555,314],{},[307,120557,5011],{},[232,120559,44954],{},[307,120561,3106],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[307,120563,748],{"separator":243},[354,120565],{"width":3460},[232,120567,44954],{},[307,120569,6107],{},[307,120571,427],{"stretchy":309},[312,120573,323],{},[307,120575,748],{"separator":243},[312,120577,314],{},[307,120579,454],{"stretchy":309},[232,120581,4573],{"mathvariant":406},[236,120583,120584],{"encoding":238},"T(P,Q)(\\alpha)\n=\\inf_{A}\\big\\{P(A)\\ :\\ Q(A)\\ge1-\\alpha\\big\\},\n\\qquad \\alpha\\in[0,1] .",[212,120586,120588,120633,120728,120755,120773,120809],{"className":120587,"ariaHidden":243},[242],[212,120589,120591,120594,120597,120600,120603,120606,120609,120612,120615,120618,120621,120624,120627,120630],{"className":120590},[247],[212,120592],{"className":120593,"style":336},[251],[212,120595,5590],{"className":120596,"style":531},[256,257],[212,120598,310],{"className":120599},[343],[212,120601,403],{"className":120602,"style":531},[256,257],[212,120604,748],{"className":120605},[770],[212,120607],{"className":120608,"style":603},[354],[212,120610,410],{"className":120611},[256,257],[212,120613,317],{"className":120614},[350],[212,120616,310],{"className":120617},[343],[212,120619,44954],{"className":120620,"style":44984},[256,257],[212,120622,317],{"className":120623},[350],[212,120625],{"className":120626,"style":355},[354],[212,120628,320],{"className":120629},[359],[212,120631],{"className":120632,"style":355},[354],[212,120634,120636,120640,120692,120695,120701,120704,120707,120710,120713,120716,120719,120722,120725],{"className":120635},[247],[212,120637],{"className":120638,"style":120639},[251],"height:1.5943em;vertical-align:-0.7443em;",[212,120641,120643],{"className":120642},[1682,13916],[212,120644,120646,120683],{"className":120645},[482,483],[212,120647,120649,120680],{"className":120648},[487],[212,120650,120652,120667],{"className":120651,"style":12797},[491],[212,120653,120655,120658],{"style":120654},"top:-2.3557em;margin-left:0em;",[212,120656],{"className":120657,"style":658},[499],[212,120659,120661],{"className":120660},[504,505,506,507],[212,120662,120664],{"className":120663},[256,507],[212,120665,800],{"className":120666},[256,257,507],[212,120668,120669,120672],{"style":12063},[212,120670],{"className":120671,"style":658},[499],[212,120673,120674],{},[212,120675,120677,120678],{"className":120676},[1682],"in",[212,120679,234],{"style":95050},[212,120681,515],{"className":120682},[514],[212,120684,120686],{"className":120685},[487],[212,120687,120690],{"className":120688,"style":120689},[491],"height:0.7443em;",[212,120691],{},[212,120693],{"className":120694,"style":603},[354],[212,120696,120698],{"className":120697},[256],[212,120699,3096],{"className":120700},[616,9872],[212,120702,403],{"className":120703,"style":531},[256,257],[212,120705,310],{"className":120706},[343],[212,120708,800],{"className":120709},[256,257],[212,120711,317],{"className":120712},[350],[212,120714,4481],{"className":120715},[354],[212,120717],{"className":120718,"style":355},[354],[212,120720,1214],{"className":120721},[359],[212,120723,4481],{"className":120724},[354],[212,120726],{"className":120727,"style":355},[354],[212,120729,120731,120734,120737,120740,120743,120746,120749,120752],{"className":120730},[247],[212,120732],{"className":120733,"style":336},[251],[212,120735,410],{"className":120736},[256,257],[212,120738,310],{"className":120739},[343],[212,120741,800],{"className":120742},[256,257],[212,120744,317],{"className":120745},[350],[212,120747],{"className":120748,"style":355},[354],[212,120750,7126],{"className":120751},[359],[212,120753],{"className":120754,"style":355},[354],[212,120756,120758,120761,120764,120767,120770],{"className":120757},[247],[212,120759],{"className":120760,"style":12778},[251],[212,120762,314],{"className":120763},[256],[212,120765],{"className":120766,"style":2785},[354],[212,120768,5011],{"className":120769},[2789],[212,120771],{"className":120772,"style":2785},[354],[212,120774,120776,120779,120782,120788,120791,120794,120797,120800,120803,120806],{"className":120775},[247],[212,120777],{"className":120778,"style":20763},[251],[212,120780,44954],{"className":120781,"style":44984},[256,257],[212,120783,120785],{"className":120784},[256],[212,120786,3106],{"className":120787},[616,9872],[212,120789,748],{"className":120790},[770],[212,120792],{"className":120793,"style":3832},[354],[212,120795],{"className":120796,"style":603},[354],[212,120798,44954],{"className":120799,"style":44984},[256,257],[212,120801],{"className":120802,"style":355},[354],[212,120804,6107],{"className":120805},[359],[212,120807],{"className":120808,"style":355},[354],[212,120810,120812,120815,120818,120821,120824,120827,120830,120833],{"className":120811},[247],[212,120813],{"className":120814,"style":336},[251],[212,120816,427],{"className":120817},[343],[212,120819,323],{"className":120820},[256],[212,120822,748],{"className":120823},[770],[212,120825],{"className":120826,"style":603},[354],[212,120828,314],{"className":120829},[256],[212,120831,454],{"className":120832},[350],[212,120834,4573],{"className":120835},[256],[11,120837,120838,120839,78280,120867,120895,120896,120971,120972,121111],{},"机制 ",[212,120840,120842,120855],{"className":120841,"translate":216},[215],[212,120843,120845],{"className":120844},[220],[222,120846,120847],{"xmlns":224},[226,120848,120849,120853],{},[229,120850,120851],{},[232,120852,25767],{},[236,120854,25767],{"encoding":238},[212,120856,120858],{"className":120857,"ariaHidden":243},[242],[212,120859,120861,120864],{"className":120860},[247],[212,120862],{"className":120863,"style":861},[251],[212,120865,25767],{"className":120866,"style":25801},[256,257],[212,120868,120870,120883],{"className":120869,"translate":216},[215],[212,120871,120873],{"className":120872},[220],[222,120874,120875],{"xmlns":224},[226,120876,120877,120881],{},[229,120878,120879],{},[232,120880,234],{},[236,120882,234],{"encoding":238},[212,120884,120886],{"className":120885,"ariaHidden":243},[242],[212,120887,120889,120892],{"className":120888},[247],[212,120890],{"className":120891,"style":252},[251],[212,120893,234],{"className":120894,"style":258},[256,257],"-DP，若对所有相邻 ",[212,120897,120899,120921],{"className":120898,"translate":216},[215],[212,120900,120902],{"className":120901},[220],[222,120903,120904],{"xmlns":224},[226,120905,120906,120918],{},[229,120907,120908,120910,120912],{},[232,120909,396],{},[307,120911,748],{"separator":243},[7012,120913,120914,120916],{},[232,120915,396],{},[307,120917,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[236,120919,120920],{"encoding":238},"D,D'",[212,120922,120924],{"className":120923,"ariaHidden":243},[242],[212,120925,120927,120930,120933,120936,120939],{"className":120926},[247],[212,120928],{"className":120929,"style":64371},[251],[212,120931,396],{"className":120932,"style":474},[256,257],[212,120934,748],{"className":120935},[770],[212,120937],{"className":120938,"style":603},[354],[212,120940,120942,120945],{"className":120941},[256],[212,120943,396],{"className":120944,"style":474},[256,257],[212,120946,120948],{"className":120947},[478],[212,120949,120951],{"className":120950},[482],[212,120952,120954],{"className":120953},[487],[212,120955,120957],{"className":120956,"style":7060},[491],[212,120958,120959,120962],{"style":7063},[212,120960],{"className":120961,"style":500},[499],[212,120963,120965],{"className":120964},[504,505,506,507],[212,120966,120968],{"className":120967},[256,507],[212,120969,7018],{"className":120970},[256,507],"，恒有 ",[212,120973,120975,121019],{"className":120974,"translate":216},[215],[212,120976,120978],{"className":120977},[220],[222,120979,120980],{"xmlns":224},[226,120981,120982,121016],{},[229,120983,120984,120986,120988,120990,120992,120994,120996,120998,121000,121002,121008,121010,121012,121014],{},[232,120985,5590],{},[307,120987,310],{"stretchy":309},[232,120989,25767],{},[307,120991,310],{"stretchy":309},[232,120993,396],{},[307,120995,317],{"stretchy":309},[307,120997,748],{"separator":243},[232,120999,25767],{},[307,121001,310],{"stretchy":309},[7012,121003,121004,121006],{},[232,121005,396],{},[307,121007,7018],{"mathvariant":406,"lspace":1445,"rspace":1445},[307,121009,317],{"stretchy":309},[307,121011,317],{"stretchy":309},[307,121013,7126],{},[232,121015,234],{},[236,121017,121018],{"encoding":238},"T(M(D),M(D'))\\ge f",[212,121020,121022,121102],{"className":121021,"ariaHidden":243},[242],[212,121023,121025,121028,121031,121034,121037,121040,121043,121046,121049,121052,121055,121058,121090,121093,121096,121099],{"className":121024},[247],[212,121026],{"className":121027,"style":7041},[251],[212,121029,5590],{"className":121030,"style":531},[256,257],[212,121032,310],{"className":121033},[343],[212,121035,25767],{"className":121036,"style":25801},[256,257],[212,121038,310],{"className":121039},[343],[212,121041,396],{"className":121042,"style":474},[256,257],[212,121044,317],{"className":121045},[350],[212,121047,748],{"className":121048},[770],[212,121050],{"className":121051,"style":603},[354],[212,121053,25767],{"className":121054,"style":25801},[256,257],[212,121056,310],{"className":121057},[343],[212,121059,121061,121064],{"className":121060},[256],[212,121062,396],{"className":121063,"style":474},[256,257],[212,121065,121067],{"className":121066},[478],[212,121068,121070],{"className":121069},[482],[212,121071,121073],{"className":121072},[487],[212,121074,121076],{"className":121075,"style":7060},[491],[212,121077,121078,121081],{"style":7063},[212,121079],{"className":121080,"style":500},[499],[212,121082,121084],{"className":121083},[504,505,506,507],[212,121085,121087],{"className":121086},[256,507],[212,121088,7018],{"className":121089},[256,507],[212,121091,19247],{"className":121092},[350],[212,121094],{"className":121095,"style":355},[354],[212,121097,7126],{"className":121098},[359],[212,121100],{"className":121101,"style":355},[354],[212,121103,121105,121108],{"className":121104},[247],[212,121106],{"className":121107,"style":252},[251],[212,121109,234],{"className":121110,"style":258},[256,257],"。可以证明：",[10225,121113,121114],{},[6863,121115,121116,32289,121119,121191,121192,121240,121241,121269],{},[1194,121117,121118],{},"权衡曲线与 f-散度互相决定。",[212,121120,121122,121152],{"className":121121,"translate":216},[215],[212,121123,121125],{"className":121124},[220],[222,121126,121127],{"xmlns":224},[226,121128,121129,121149],{},[229,121130,121131,121133,121135,121137,121139,121141,121143,121145,121147],{},[232,121132,5590],{},[307,121134,310],{"stretchy":309},[232,121136,403],{},[307,121138,748],{"separator":243},[232,121140,410],{},[307,121142,317],{"stretchy":309},[307,121144,310],{"stretchy":309},[232,121146,44954],{},[307,121148,317],{"stretchy":309},[236,121150,121151],{"encoding":238},"T(P,Q)(\\alpha)",[212,121153,121155],{"className":121154,"ariaHidden":243},[242],[212,121156,121158,121161,121164,121167,121170,121173,121176,121179,121182,121185,121188],{"className":121157},[247],[212,121159],{"className":121160,"style":336},[251],[212,121162,5590],{"className":121163,"style":531},[256,257],[212,121165,310],{"className":121166},[343],[212,121168,403],{"className":121169,"style":531},[256,257],[212,121171,748],{"className":121172},[770],[212,121174],{"className":121175,"style":603},[354],[212,121177,410],{"className":121178},[256,257],[212,121180,317],{"className":121181},[350],[212,121183,310],{"className":121184},[343],[212,121186,44954],{"className":121187,"style":44984},[256,257],[212,121189,317],{"className":121190},[350]," 只依赖似然比 ",[212,121193,121195,121216],{"className":121194,"translate":216},[215],[212,121196,121198],{"className":121197},[220],[222,121199,121200],{"xmlns":224},[226,121201,121202,121214],{},[229,121203,121204,121206,121208,121210,121212],{},[232,121205,441],{},[232,121207,403],{},[232,121209,1138],{"mathvariant":406},[232,121211,441],{},[232,121213,410],{},[236,121215,114858],{"encoding":238},[212,121217,121219],{"className":121218,"ariaHidden":243},[242],[212,121220,121222,121225,121228,121231,121234,121237],{"className":121221},[247],[212,121223],{"className":121224,"style":336},[251],[212,121226,441],{"className":121227},[256,257],[212,121229,403],{"className":121230,"style":531},[256,257],[212,121232,1138],{"className":121233},[256],[212,121235,441],{"className":121236},[256,257],[212,121238,410],{"className":121239},[256,257]," 的分布，因此 ",[212,121242,121244,121257],{"className":121243,"translate":216},[215],[212,121245,121247],{"className":121246},[220],[222,121248,121249],{"xmlns":224},[226,121250,121251,121255],{},[229,121252,121253],{},[232,121254,5590],{},[236,121256,5590],{"encoding":238},[212,121258,121260],{"className":121259,"ariaHidden":243},[242],[212,121261,121263,121266],{"className":121262},[247],[212,121264],{"className":121265,"style":861},[251],[212,121267,5590],{"className":121268,"style":531},[256,257]," 与\"全体 f-散度\"携带同样的信息。对 hockey-stick 生成元族",[212,121271,121273],{"className":121272,"translate":216},[377],[212,121274,121276,121343],{"className":121275,"translate":216},[215],[212,121277,121279],{"className":121278},[220],[222,121280,121281],{"xmlns":224,"display":386},[226,121282,121283,121340],{},[229,121284,121285,121292,121294,121296,121298,121300,121302,121304,121306,121308,121310,121312,121314,121316,121318,121320,121322,121324,121326,121328,121330,121332,121334,121336,121338],{},[392,121286,121287,121289],{},[232,121288,4356],{},[232,121290,121291],{},"γ",[307,121293,310],{"stretchy":309},[232,121295,966],{},[307,121297,317],{"stretchy":309},[307,121299,320],{},[232,121301,52586],{},[307,121303,4301],{},[307,121305,3096],{"stretchy":309},[312,121307,323],{},[307,121309,748],{"separator":243},[1495,121311,1497],{},[232,121313,966],{},[307,121315,5011],{},[232,121317,121291],{},[307,121319,3106],{"stretchy":309},[307,121321,748],{"separator":243},[354,121323],{"width":3460},[232,121325,121291],{},[307,121327,6107],{},[307,121329,427],{"stretchy":309},[312,121331,323],{},[307,121333,748],{"separator":243},[312,121335,314],{},[307,121337,454],{"stretchy":309},[307,121339,748],{"separator":243},[236,121341,121342],{"encoding":238},"g_\\gamma(t)=\\max\\{0,\\,t-\\gamma\\},\n\\qquad \\gamma\\in[0,1],",[212,121344,121346,121411,121447,121480],{"className":121345,"ariaHidden":243},[242],[212,121347,121349,121352,121393,121396,121399,121402,121405,121408],{"className":121348},[247],[212,121350],{"className":121351,"style":467},[251],[212,121353,121355,121358],{"className":121354},[256],[212,121356,4356],{"className":121357,"style":1178},[256,257],[212,121359,121361],{"className":121360},[478],[212,121362,121364,121385],{"className":121363},[482,483],[212,121365,121367,121382],{"className":121366},[487],[212,121368,121370],{"className":121369,"style":45129},[491],[212,121371,121372,121375],{"style":19043},[212,121373],{"className":121374,"style":500},[499],[212,121376,121378],{"className":121377},[504,505,506,507],[212,121379,121291],{"className":121380,"style":121381},[256,257,507],"margin-right:0.0556em;",[212,121383,515],{"className":121384},[514],[212,121386,121388],{"className":121387},[487],[212,121389,121391],{"className":121390,"style":522},[491],[212,121392],{},[212,121394,310],{"className":121395},[343],[212,121397,966],{"className":121398},[256,257],[212,121400,317],{"className":121401},[350],[212,121403],{"className":121404,"style":355},[354],[212,121406,320],{"className":121407},[359],[212,121409],{"className":121410,"style":355},[354],[212,121412,121414,121417,121420,121423,121426,121429,121432,121435,121438,121441,121444],{"className":121413},[247],[212,121415],{"className":121416,"style":336},[251],[212,121418,52586],{"className":121419},[1682],[212,121421,3096],{"className":121422},[343],[212,121424,323],{"className":121425},[256],[212,121427,748],{"className":121428},[770],[212,121430],{"className":121431,"style":603},[354],[212,121433],{"className":121434,"style":603},[354],[212,121436,966],{"className":121437},[256,257],[212,121439],{"className":121440,"style":2785},[354],[212,121442,5011],{"className":121443},[2789],[212,121445],{"className":121446,"style":2785},[354],[212,121448,121450,121453,121456,121459,121462,121465,121468,121471,121474,121477],{"className":121449},[247],[212,121451],{"className":121452,"style":336},[251],[212,121454,121291],{"className":121455,"style":121381},[256,257],[212,121457,3106],{"className":121458},[350],[212,121460,748],{"className":121461},[770],[212,121463],{"className":121464,"style":3832},[354],[212,121466],{"className":121467,"style":603},[354],[212,121469,121291],{"className":121470,"style":121381},[256,257],[212,121472],{"className":121473,"style":355},[354],[212,121475,6107],{"className":121476},[359],[212,121478],{"className":121479,"style":355},[354],[212,121481,121483,121486,121489,121492,121495,121498,121501,121504],{"className":121482},[247],[212,121484],{"className":121485,"style":336},[251],[212,121487,427],{"className":121488},[343],[212,121490,323],{"className":121491},[256],[212,121493,748],{"className":121494},[770],[212,121496],{"className":121497,"style":603},[354],[212,121499,314],{"className":121500},[256],[212,121502,454],{"className":121503},[350],[212,121505,748],{"className":121506},[770],[11,121508,121509,121510,121691,121692,8865,121721,121772],{},"（Dong–Roth–Su 的 ",[212,121511,121513,121561],{"className":121512,"translate":216},[215],[212,121514,121516],{"className":121515},[220],[222,121517,121518],{"xmlns":224},[226,121519,121520,121558],{},[229,121521,121522,121528,121530,121532,121534,121536,121538,121540,121542,121544,121546,121548,121550,121552,121554,121556],{},[392,121523,121524,121526],{},[232,121525,38865],{},[232,121527,121291],{},[307,121529,310],{"stretchy":309},[232,121531,966],{},[307,121533,317],{"stretchy":309},[307,121535,320],{},[232,121537,52586],{},[307,121539,4301],{},[307,121541,3096],{"stretchy":309},[312,121543,323],{},[307,121545,748],{"separator":243},[232,121547,966],{},[307,121549,5011],{},[312,121551,314],{},[307,121553,2668],{},[232,121555,121291],{},[307,121557,3106],{"stretchy":309},[236,121559,121560],{"encoding":238},"h_\\gamma(t)=\\max\\{0,t-1+\\gamma\\}",[212,121562,121564,121628,121661,121679],{"className":121563,"ariaHidden":243},[242],[212,121565,121567,121570,121610,121613,121616,121619,121622,121625],{"className":121566},[247],[212,121568],{"className":121569,"style":467},[251],[212,121571,121573,121576],{"className":121572},[256],[212,121574,38865],{"className":121575},[256,257],[212,121577,121579],{"className":121578},[478],[212,121580,121582,121602],{"className":121581},[482,483],[212,121583,121585,121599],{"className":121584},[487],[212,121586,121588],{"className":121587,"style":45129},[491],[212,121589,121590,121593],{"style":579},[212,121591],{"className":121592,"style":500},[499],[212,121594,121596],{"className":121595},[504,505,506,507],[212,121597,121291],{"className":121598,"style":121381},[256,257,507],[212,121600,515],{"className":121601},[514],[212,121603,121605],{"className":121604},[487],[212,121606,121608],{"className":121607,"style":522},[491],[212,121609],{},[212,121611,310],{"className":121612},[343],[212,121614,966],{"className":121615},[256,257],[212,121617,317],{"className":121618},[350],[212,121620],{"className":121621,"style":355},[354],[212,121623,320],{"className":121624},[359],[212,121626],{"className":121627,"style":355},[354],[212,121629,121631,121634,121637,121640,121643,121646,121649,121652,121655,121658],{"className":121630},[247],[212,121632],{"className":121633,"style":336},[251],[212,121635,52586],{"className":121636},[1682],[212,121638,3096],{"className":121639},[343],[212,121641,323],{"className":121642},[256],[212,121644,748],{"className":121645},[770],[212,121647],{"className":121648,"style":603},[354],[212,121650,966],{"className":121651},[256,257],[212,121653],{"className":121654,"style":2785},[354],[212,121656,5011],{"className":121657},[2789],[212,121659],{"className":121660,"style":2785},[354],[212,121662,121664,121667,121670,121673,121676],{"className":121663},[247],[212,121665],{"className":121666,"style":12778},[251],[212,121668,314],{"className":121669},[256],[212,121671],{"className":121672,"style":2785},[354],[212,121674,2668],{"className":121675},[2789],[212,121677],{"className":121678,"style":2785},[354],[212,121680,121682,121685,121688],{"className":121681},[247],[212,121683],{"className":121684,"style":336},[251],[212,121686,121291],{"className":121687,"style":121381},[256,257],[212,121689,3106],{"className":121690},[350]," 就是把 ",[212,121693,121695,121709],{"className":121694,"translate":216},[215],[212,121696,121698],{"className":121697},[220],[222,121699,121700],{"xmlns":224},[226,121701,121702,121706],{},[229,121703,121704],{},[232,121705,121291],{},[236,121707,121708],{"encoding":238},"\\gamma",[212,121710,121712],{"className":121711,"ariaHidden":243},[242],[212,121713,121715,121718],{"className":121714},[247],[212,121716],{"className":121717,"style":2474},[251],[212,121719,121291],{"className":121720,"style":121381},[256,257],[212,121722,121724,121742],{"className":121723,"translate":216},[215],[212,121725,121727],{"className":121726},[220],[222,121728,121729],{"xmlns":224},[226,121730,121731,121739],{},[229,121732,121733,121735,121737],{},[312,121734,314],{},[307,121736,5011],{},[232,121738,121291],{},[236,121740,121741],{"encoding":238},"1-\\gamma",[212,121743,121745,121763],{"className":121744,"ariaHidden":243},[242],[212,121746,121748,121751,121754,121757,121760],{"className":121747},[247],[212,121749],{"className":121750,"style":12778},[251],[212,121752,314],{"className":121753},[256],[212,121755],{"className":121756,"style":2785},[354],[212,121758,5011],{"className":121759},[2789],[212,121761],{"className":121762,"style":2785},[354],[212,121764,121766,121769],{"className":121765},[247],[212,121767],{"className":121768,"style":2474},[251],[212,121770,121291],{"className":121771,"style":121381},[256,257]," 的同一族），变分表示给出干净的检验集形式：",[212,121774,121776],{"className":121775,"translate":216},[377],[212,121777,121779,121857],{"className":121778,"translate":216},[215],[212,121780,121782],{"className":121781},[220],[222,121783,121784],{"xmlns":224,"display":386},[226,121785,121786,121854],{},[229,121787,121788,121798,121800,121802,121804,121806,121808,121810,121826,121828,121830,121832,121834,121836,121838,121840,121842,121844,121846,121848,121850,121852],{},[392,121789,121790,121792],{},[232,121791,396],{},[392,121793,121794,121796],{},[232,121795,4356],{},[232,121797,121291],{},[307,121799,310],{"stretchy":309},[232,121801,403],{},[232,121803,407],{"mathvariant":406},[232,121805,410],{},[307,121807,317],{"stretchy":309},[307,121809,320],{},[6214,121811,121812,121818],{},[229,121813,121814,121816],{},[232,121815,35632],{},[307,121817,4301],{},[229,121819,121820,121822,121824],{},[232,121821,800],{},[307,121823,6107],{},[232,121825,800],{"mathvariant":794},[307,121827,3096],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,121829,403],{},[307,121831,310],{"stretchy":309},[232,121833,800],{},[307,121835,317],{"stretchy":309},[307,121837,5011],{},[232,121839,121291],{},[1495,121841,1497],{},[232,121843,410],{},[307,121845,310],{"stretchy":309},[232,121847,800],{},[307,121849,317],{"stretchy":309},[307,121851,3106],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[232,121853,4573],{"mathvariant":406},[236,121855,121856],{"encoding":238},"D_{g_\\gamma}(P\\|Q)\n=\\sup_{A\\in\\mathcal A}\\big\\{P(A)\n-\\gamma\\,Q(A)\\big\\}.",[212,121858,121860,121974,122063],{"className":121859,"ariaHidden":243},[242],[212,121861,121863,121867,121950,121953,121956,121959,121962,121965,121968,121971],{"className":121862},[247],[212,121864],{"className":121865,"style":121866},[251],"height:1.0973em;vertical-align:-0.3473em;",[212,121868,121870,121873],{"className":121869},[256],[212,121871,396],{"className":121872,"style":474},[256,257],[212,121874,121876],{"className":121875},[478],[212,121877,121879,121941],{"className":121878},[482,483],[212,121880,121882,121938],{"className":121881},[487],[212,121883,121885],{"className":121884,"style":45129},[491],[212,121886,121887,121890],{"style":495},[212,121888],{"className":121889,"style":500},[499],[212,121891,121893],{"className":121892},[504,505,506,507],[212,121894,121896],{"className":121895},[256,507],[212,121897,121899,121902],{"className":121898},[256,507],[212,121900,4356],{"className":121901,"style":1178},[256,257,507],[212,121903,121905],{"className":121904},[478],[212,121906,121908,121929],{"className":121907},[482,483],[212,121909,121911,121926],{"className":121910},[487],[212,121912,121914],{"className":121913,"style":74472},[491],[212,121915,121917,121920],{"style":121916},"top:-2.357em;margin-left:-0.0359em;margin-right:0.0714em;",[212,121918],{"className":121919,"style":30406},[499],[212,121921,121923],{"className":121922},[504,30410,9872,507],[212,121924,121291],{"className":121925,"style":121381},[256,257,507],[212,121927,515],{"className":121928},[514],[212,121930,121932],{"className":121931},[487],[212,121933,121936],{"className":121934,"style":121935},[491],"height:0.2819em;",[212,121937],{},[212,121939,515],{"className":121940},[514],[212,121942,121944],{"className":121943},[487],[212,121945,121948],{"className":121946,"style":121947},[491],"height:0.3473em;",[212,121949],{},[212,121951,310],{"className":121952},[343],[212,121954,403],{"className":121955,"style":531},[256,257],[212,121957,407],{"className":121958},[256],[212,121960,410],{"className":121961},[256,257],[212,121963,317],{"className":121964},[350],[212,121966],{"className":121967,"style":355},[354],[212,121969,320],{"className":121970},[359],[212,121972],{"className":121973,"style":355},[354],[212,121975,121977,121980,122033,122036,122042,122045,122048,122051,122054,122057,122060],{"className":121976},[247],[212,121978],{"className":121979,"style":36553},[251],[212,121981,121983],{"className":121982},[1682,13916],[212,121984,121986,122025],{"className":121985},[482,483],[212,121987,121989,122022],{"className":121988},[487],[212,121990,121992,122012],{"className":121991,"style":2543},[491],[212,121993,121994,121997],{"style":36568},[212,121995],{"className":121996,"style":658},[499],[212,121998,122000],{"className":121999},[504,505,506,507],[212,122001,122003,122006,122009],{"className":122002},[256,507],[212,122004,800],{"className":122005},[256,257,507],[212,122007,6107],{"className":122008},[359,507],[212,122010,800],{"className":122011},[256,821,507],[212,122013,122014,122017],{"style":12063},[212,122015],{"className":122016,"style":658},[499],[212,122018,122019],{},[212,122020,35632],{"className":122021},[1682],[212,122023,515],{"className":122024},[514],[212,122026,122028],{"className":122027},[487],[212,122029,122031],{"className":122030,"style":36606},[491],[212,122032],{},[212,122034],{"className":122035,"style":603},[354],[212,122037,122039],{"className":122038},[256],[212,122040,3096],{"className":122041},[616,9872],[212,122043,403],{"className":122044,"style":531},[256,257],[212,122046,310],{"className":122047},[343],[212,122049,800],{"className":122050},[256,257],[212,122052,317],{"className":122053},[350],[212,122055],{"className":122056,"style":2785},[354],[212,122058,5011],{"className":122059},[2789],[212,122061],{"className":122062,"style":2785},[354],[212,122064,122066,122069,122072,122075,122078,122081,122084,122087,122093],{"className":122065},[247],[212,122067],{"className":122068,"style":20763},[251],[212,122070,121291],{"className":122071,"style":121381},[256,257],[212,122073],{"className":122074,"style":603},[354],[212,122076,410],{"className":122077},[256,257],[212,122079,310],{"className":122080},[343],[212,122082,800],{"className":122083},[256,257],[212,122085,317],{"className":122086},[350],[212,122088,122090],{"className":122089},[256],[212,122091,3106],{"className":122092},[616,9872],[212,122094,4573],{"className":122095},[256],[11,122097,122098,122100,122101,122175,122176,2478,122345,122373,122374,122467],{},[1194,122099,107494],{}," 一方面，任意 ",[212,122102,122104,122126],{"className":122103,"translate":216},[215],[212,122105,122107],{"className":122106},[220],[222,122108,122109],{"xmlns":224},[226,122110,122111,122123],{},[229,122112,122113,122115,122117,122119,122121],{},[312,122114,323],{},[307,122116,10150],{},[232,122118,4356],{},[307,122120,10150],{},[312,122122,314],{},[236,122124,122125],{"encoding":238},"0\\le g\\le1",[212,122127,122129,122148,122166],{"className":122128,"ariaHidden":243},[242],[212,122130,122132,122136,122139,122142,122145],{"className":122131},[247],[212,122133],{"className":122134,"style":122135},[251],"height:0.7804em;vertical-align:-0.136em;",[212,122137,323],{"className":122138},[256],[212,122140],{"className":122141,"style":355},[354],[212,122143,10150],{"className":122144},[359],[212,122146],{"className":122147,"style":355},[354],[212,122149,122151,122154,122157,122160,122163],{"className":122150},[247],[212,122152],{"className":122153,"style":15617},[251],[212,122155,4356],{"className":122156,"style":1178},[256,257],[212,122158],{"className":122159,"style":355},[354],[212,122161,10150],{"className":122162},[359],[212,122164],{"className":122165,"style":355},[354],[212,122167,122169,122172],{"className":122168},[247],[212,122170],{"className":122171,"style":369},[251],[212,122173,314],{"className":122174},[256]," 可写为指示函数的线性组合（层叠公式），而 ",[212,122177,122179,122219],{"className":122178,"translate":216},[215],[212,122180,122182],{"className":122181},[220],[222,122183,122184],{"xmlns":224},[226,122185,122186,122216],{},[229,122187,122188,122194,122196,122198,122200,122202,122204,122210,122212,122214],{},[392,122189,122190,122192],{},[232,122191,420],{},[232,122193,403],{},[307,122195,427],{"stretchy":309},[232,122197,4356],{},[307,122199,454],{"stretchy":309},[307,122201,5011],{},[232,122203,121291],{},[392,122205,122206,122208],{},[232,122207,420],{},[232,122209,410],{},[307,122211,427],{"stretchy":309},[232,122213,4356],{},[307,122215,454],{"stretchy":309},[236,122217,122218],{"encoding":238},"E_P[g]-\\gamma E_Q[g]",[212,122220,122222,122287],{"className":122221,"ariaHidden":243},[242],[212,122223,122225,122228,122269,122272,122275,122278,122281,122284],{"className":122224},[247],[212,122226],{"className":122227,"style":336},[251],[212,122229,122231,122234],{"className":122230},[256],[212,122232,420],{"className":122233,"style":26061},[256,257],[212,122235,122237],{"className":122236},[478],[212,122238,122240,122261],{"className":122239},[482,483],[212,122241,122243,122258],{"className":122242},[487],[212,122244,122246],{"className":122245,"style":576},[491],[212,122247,122249,122252],{"style":122248},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[212,122250],{"className":122251,"style":500},[499],[212,122253,122255],{"className":122254},[504,505,506,507],[212,122256,403],{"className":122257,"style":531},[256,257,507],[212,122259,515],{"className":122260},[514],[212,122262,122264],{"className":122263},[487],[212,122265,122267],{"className":122266,"style":8166},[491],[212,122268],{},[212,122270,427],{"className":122271},[343],[212,122273,4356],{"className":122274,"style":1178},[256,257],[212,122276,454],{"className":122277},[350],[212,122279],{"className":122280,"style":2785},[354],[212,122282,5011],{"className":122283},[2789],[212,122285],{"className":122286,"style":2785},[354],[212,122288,122290,122293,122296,122336,122339,122342],{"className":122289},[247],[212,122291],{"className":122292,"style":467},[251],[212,122294,121291],{"className":122295,"style":121381},[256,257],[212,122297,122299,122302],{"className":122298},[256],[212,122300,420],{"className":122301,"style":26061},[256,257],[212,122303,122305],{"className":122304},[478],[212,122306,122308,122328],{"className":122307},[482,483],[212,122309,122311,122325],{"className":122310},[487],[212,122312,122314],{"className":122313,"style":576},[491],[212,122315,122316,122319],{"style":122248},[212,122317],{"className":122318,"style":500},[499],[212,122320,122322],{"className":122321},[504,505,506,507],[212,122323,410],{"className":122324},[256,257,507],[212,122326,515],{"className":122327},[514],[212,122329,122331],{"className":122330},[487],[212,122332,122334],{"className":122333,"style":522},[491],[212,122335],{},[212,122337,427],{"className":122338},[343],[212,122340,4356],{"className":122341,"style":1178},[256,257],[212,122343,454],{"className":122344},[350],[212,122346,122348,122361],{"className":122347,"translate":216},[215],[212,122349,122351],{"className":122350},[220],[222,122352,122353],{"xmlns":224},[226,122354,122355,122359],{},[229,122356,122357],{},[232,122358,4356],{},[236,122360,4356],{"encoding":238},[212,122362,122364],{"className":122363,"ariaHidden":243},[242],[212,122365,122367,122370],{"className":122366},[247],[212,122368],{"className":122369,"style":2474},[251],[212,122371,4356],{"className":122372,"style":1178},[256,257]," 的线性泛函，故其上确界在指示函数 ",[212,122375,122377,122399],{"className":122376,"translate":216},[215],[212,122378,122380],{"className":122379},[220],[222,122381,122382],{"xmlns":224},[226,122383,122384,122396],{},[229,122385,122386,122388,122390],{},[232,122387,4356],{},[307,122389,320],{},[392,122391,122392,122394],{},[312,122393,314],{"mathvariant":75425},[232,122395,800],{},[236,122397,122398],{"encoding":238},"g=\\mathbf1_A",[212,122400,122402,122420],{"className":122401,"ariaHidden":243},[242],[212,122403,122405,122408,122411,122414,122417],{"className":122404},[247],[212,122406],{"className":122407,"style":2474},[251],[212,122409,4356],{"className":122410,"style":1178},[256,257],[212,122412],{"className":122413,"style":355},[354],[212,122415,320],{"className":122416},[359],[212,122418],{"className":122419,"style":355},[354],[212,122421,122423,122427],{"className":122422},[247],[212,122424],{"className":122425,"style":122426},[251],"height:0.7944em;vertical-align:-0.15em;",[212,122428,122430,122433],{"className":122429},[256],[212,122431,314],{"className":122432},[256,75770],[212,122434,122436],{"className":122435},[478],[212,122437,122439,122459],{"className":122438},[482,483],[212,122440,122442,122456],{"className":122441},[487],[212,122443,122445],{"className":122444,"style":576},[491],[212,122446,122447,122450],{"style":579},[212,122448],{"className":122449,"style":500},[499],[212,122451,122453],{"className":122452},[504,505,506,507],[212,122454,800],{"className":122455},[256,257,507],[212,122457,515],{"className":122458},[514],[212,122460,122462],{"className":122461},[487],[212,122463,122465],{"className":122464,"style":8166},[491],[212,122466],{}," 上达到：",[212,122469,122471],{"className":122470,"translate":216},[377],[212,122472,122474,122576],{"className":122473,"translate":216},[215],[212,122475,122477],{"className":122476},[220],[222,122478,122479],{"xmlns":224,"display":386},[226,122480,122481,122573],{},[229,122482,122483,122503,122505,122511,122513,122515,122517,122519,122521,122527,122529,122531,122533,122535,122537,122547,122549,122551,122553,122555,122557,122559,122561,122563,122565,122567,122569,122571],{},[6214,122484,122485,122491],{},[229,122486,122487,122489],{},[232,122488,35632],{},[307,122490,4301],{},[229,122492,122493,122495,122497,122499,122501],{},[312,122494,323],{},[307,122496,10150],{},[232,122498,4356],{},[307,122500,10150],{},[312,122502,314],{},[307,122504,3096],{"stretchy":309},[392,122506,122507,122509],{},[232,122508,420],{},[232,122510,403],{},[307,122512,427],{"stretchy":309},[232,122514,4356],{},[307,122516,454],{"stretchy":309},[307,122518,5011],{},[232,122520,121291],{},[392,122522,122523,122525],{},[232,122524,420],{},[232,122526,410],{},[307,122528,427],{"stretchy":309},[232,122530,4356],{},[307,122532,454],{"stretchy":309},[307,122534,3106],{"stretchy":309},[307,122536,320],{},[6214,122538,122539,122545],{},[229,122540,122541,122543],{},[232,122542,35632],{},[307,122544,4301],{},[232,122546,800],{},[307,122548,3096],{"stretchy":309},[232,122550,403],{},[307,122552,310],{"stretchy":309},[232,122554,800],{},[307,122556,317],{"stretchy":309},[307,122558,5011],{},[232,122560,121291],{},[232,122562,410],{},[307,122564,310],{"stretchy":309},[232,122566,800],{},[307,122568,317],{"stretchy":309},[307,122570,3106],{"stretchy":309},[307,122572,748],{"separator":243},[236,122574,122575],{"encoding":238},"\\sup_{0\\le g\\le1}\\{E_P[g]-\\gamma E_Q[g]\\}\n=\\sup_{A}\\{P(A)-\\gamma Q(A)\\},",[212,122577,122579,122707,122775,122854],{"className":122578,"ariaHidden":243},[242],[212,122580,122582,122586,122646,122649,122689,122692,122695,122698,122701,122704],{"className":122581},[247],[212,122583],{"className":122584,"style":122585},[251],"height:1.7977em;vertical-align:-1.0477em;",[212,122587,122589],{"className":122588},[1682,13916],[212,122590,122592,122637],{"className":122591},[482,483],[212,122593,122595,122634],{"className":122594},[487],[212,122596,122598,122624],{"className":122597,"style":2543},[491],[212,122599,122600,122603],{"style":61132},[212,122601],{"className":122602,"style":658},[499],[212,122604,122606],{"className":122605},[504,505,506,507],[212,122607,122609,122612,122615,122618,122621],{"className":122608},[256,507],[212,122610,323],{"className":122611},[256,507],[212,122613,10150],{"className":122614},[359,507],[212,122616,4356],{"className":122617,"style":1178},[256,257,507],[212,122619,10150],{"className":122620},[359,507],[212,122622,314],{"className":122623},[256,507],[212,122625,122626,122629],{"style":12063},[212,122627],{"className":122628,"style":658},[499],[212,122630,122631],{},[212,122632,35632],{"className":122633},[1682],[212,122635,515],{"className":122636},[514],[212,122638,122640],{"className":122639},[487],[212,122641,122644],{"className":122642,"style":122643},[491],"height:1.0477em;",[212,122645],{},[212,122647,3096],{"className":122648},[343],[212,122650,122652,122655],{"className":122651},[256],[212,122653,420],{"className":122654,"style":26061},[256,257],[212,122656,122658],{"className":122657},[478],[212,122659,122661,122681],{"className":122660},[482,483],[212,122662,122664,122678],{"className":122663},[487],[212,122665,122667],{"className":122666,"style":576},[491],[212,122668,122669,122672],{"style":122248},[212,122670],{"className":122671,"style":500},[499],[212,122673,122675],{"className":122674},[504,505,506,507],[212,122676,403],{"className":122677,"style":531},[256,257,507],[212,122679,515],{"className":122680},[514],[212,122682,122684],{"className":122683},[487],[212,122685,122687],{"className":122686,"style":8166},[491],[212,122688],{},[212,122690,427],{"className":122691},[343],[212,122693,4356],{"className":122694,"style":1178},[256,257],[212,122696,454],{"className":122697},[350],[212,122699],{"className":122700,"style":2785},[354],[212,122702,5011],{"className":122703},[2789],[212,122705],{"className":122706,"style":2785},[354],[212,122708,122710,122713,122716,122756,122759,122762,122766,122769,122772],{"className":122709},[247],[212,122711],{"className":122712,"style":467},[251],[212,122714,121291],{"className":122715,"style":121381},[256,257],[212,122717,122719,122722],{"className":122718},[256],[212,122720,420],{"className":122721,"style":26061},[256,257],[212,122723,122725],{"className":122724},[478],[212,122726,122728,122748],{"className":122727},[482,483],[212,122729,122731,122745],{"className":122730},[487],[212,122732,122734],{"className":122733,"style":576},[491],[212,122735,122736,122739],{"style":122248},[212,122737],{"className":122738,"style":500},[499],[212,122740,122742],{"className":122741},[504,505,506,507],[212,122743,410],{"className":122744},[256,257,507],[212,122746,515],{"className":122747},[514],[212,122749,122751],{"className":122750},[487],[212,122752,122754],{"className":122753,"style":522},[491],[212,122755],{},[212,122757,427],{"className":122758},[343],[212,122760,4356],{"className":122761,"style":1178},[256,257],[212,122763,122765],{"className":122764},[350],"]}",[212,122767],{"className":122768,"style":355},[354],[212,122770,320],{"className":122771},[359],[212,122773],{"className":122774,"style":355},[354],[212,122776,122778,122782,122830,122833,122836,122839,122842,122845,122848,122851],{"className":122777},[247],[212,122779],{"className":122780,"style":122781},[251],"height:1.6888em;vertical-align:-0.9388em;",[212,122783,122785],{"className":122784},[1682,13916],[212,122786,122788,122821],{"className":122787},[482,483],[212,122789,122791,122818],{"className":122790},[487],[212,122792,122794,122808],{"className":122793,"style":2543},[491],[212,122795,122796,122799],{"style":36568},[212,122797],{"className":122798,"style":658},[499],[212,122800,122802],{"className":122801},[504,505,506,507],[212,122803,122805],{"className":122804},[256,507],[212,122806,800],{"className":122807},[256,257,507],[212,122809,122810,122813],{"style":12063},[212,122811],{"className":122812,"style":658},[499],[212,122814,122815],{},[212,122816,35632],{"className":122817},[1682],[212,122819,515],{"className":122820},[514],[212,122822,122824],{"className":122823},[487],[212,122825,122828],{"className":122826,"style":122827},[491],"height:0.9388em;",[212,122829],{},[212,122831,3096],{"className":122832},[343],[212,122834,403],{"className":122835,"style":531},[256,257],[212,122837,310],{"className":122838},[343],[212,122840,800],{"className":122841},[256,257],[212,122843,317],{"className":122844},[350],[212,122846],{"className":122847,"style":2785},[354],[212,122849,5011],{"className":122850},[2789],[212,122852],{"className":122853,"style":2785},[354],[212,122855,122857,122860,122863,122866,122869,122872,122875],{"className":122856},[247],[212,122858],{"className":122859,"style":336},[251],[212,122861,121291],{"className":122862,"style":121381},[256,257],[212,122864,410],{"className":122865},[256,257],[212,122867,310],{"className":122868},[343],[212,122870,800],{"className":122871},[256,257],[212,122873,61209],{"className":122874},[350],[212,122876,748],{"className":122877},[770],[11,122879,122880,122881,123054,123055,18908,123201,123316,123317,123465,123466,123752],{},"且由 ",[212,122882,122884,122926],{"className":122883,"translate":216},[215],[212,122885,122887],{"className":122886},[220],[222,122888,122889],{"xmlns":224},[226,122890,122891,122923],{},[229,122892,122893,122899,122901,122903,122905,122907,122913,122915,122917,122919,122921],{},[392,122894,122895,122897],{},[232,122896,420],{},[232,122898,403],{},[307,122900,427],{"stretchy":309},[232,122902,4356],{},[307,122904,454],{"stretchy":309},[307,122906,320],{},[392,122908,122909,122911],{},[232,122910,420],{},[232,122912,410],{},[307,122914,427],{"stretchy":309},[232,122916,4356],{},[1495,122918,1497],{},[232,122920,966],{},[307,122922,454],{"stretchy":309},[236,122924,122925],{"encoding":238},"E_P[g]=E_Q[g\\,t]",[212,122927,122929,122993],{"className":122928,"ariaHidden":243},[242],[212,122930,122932,122935,122975,122978,122981,122984,122987,122990],{"className":122931},[247],[212,122933],{"className":122934,"style":336},[251],[212,122936,122938,122941],{"className":122937},[256],[212,122939,420],{"className":122940,"style":26061},[256,257],[212,122942,122944],{"className":122943},[478],[212,122945,122947,122967],{"className":122946},[482,483],[212,122948,122950,122964],{"className":122949},[487],[212,122951,122953],{"className":122952,"style":576},[491],[212,122954,122955,122958],{"style":122248},[212,122956],{"className":122957,"style":500},[499],[212,122959,122961],{"className":122960},[504,505,506,507],[212,122962,403],{"className":122963,"style":531},[256,257,507],[212,122965,515],{"className":122966},[514],[212,122968,122970],{"className":122969},[487],[212,122971,122973],{"className":122972,"style":8166},[491],[212,122974],{},[212,122976,427],{"className":122977},[343],[212,122979,4356],{"className":122980,"style":1178},[256,257],[212,122982,454],{"className":122983},[350],[212,122985],{"className":122986,"style":355},[354],[212,122988,320],{"className":122989},[359],[212,122991],{"className":122992,"style":355},[354],[212,122994,122996,122999,123039,123042,123045,123048,123051],{"className":122995},[247],[212,122997],{"className":122998,"style":467},[251],[212,123000,123002,123005],{"className":123001},[256],[212,123003,420],{"className":123004,"style":26061},[256,257],[212,123006,123008],{"className":123007},[478],[212,123009,123011,123031],{"className":123010},[482,483],[212,123012,123014,123028],{"className":123013},[487],[212,123015,123017],{"className":123016,"style":576},[491],[212,123018,123019,123022],{"style":122248},[212,123020],{"className":123021,"style":500},[499],[212,123023,123025],{"className":123024},[504,505,506,507],[212,123026,410],{"className":123027},[256,257,507],[212,123029,515],{"className":123030},[514],[212,123032,123034],{"className":123033},[487],[212,123035,123037],{"className":123036,"style":522},[491],[212,123038],{},[212,123040,427],{"className":123041},[343],[212,123043,4356],{"className":123044,"style":1178},[256,257],[212,123046],{"className":123047,"style":603},[354],[212,123049,966],{"className":123050},[256,257],[212,123052,454],{"className":123053},[350],"，左端点态上确界为 ",[212,123056,123058,123094],{"className":123057,"translate":216},[215],[212,123059,123061],{"className":123060},[220],[222,123062,123063],{"xmlns":224},[226,123064,123065,123091],{},[229,123066,123067,123073,123075,123077,123079,123081,123083,123089],{},[392,123068,123069,123071],{},[232,123070,420],{},[232,123072,410],{},[307,123074,427],{"stretchy":309},[307,123076,310],{"stretchy":309},[232,123078,966],{},[307,123080,5011],{},[232,123082,121291],{},[7012,123084,123085,123087],{},[307,123086,317],{"stretchy":309},[307,123088,2668],{},[307,123090,454],{"stretchy":309},[236,123092,123093],{"encoding":238},"E_Q[(t-\\gamma)^+]",[212,123095,123097,123159],{"className":123096,"ariaHidden":243},[242],[212,123098,123100,123103,123143,123147,123150,123153,123156],{"className":123099},[247],[212,123101],{"className":123102,"style":467},[251],[212,123104,123106,123109],{"className":123105},[256],[212,123107,420],{"className":123108,"style":26061},[256,257],[212,123110,123112],{"className":123111},[478],[212,123113,123115,123135],{"className":123114},[482,483],[212,123116,123118,123132],{"className":123117},[487],[212,123119,123121],{"className":123120,"style":576},[491],[212,123122,123123,123126],{"style":122248},[212,123124],{"className":123125,"style":500},[499],[212,123127,123129],{"className":123128},[504,505,506,507],[212,123130,410],{"className":123131},[256,257,507],[212,123133,515],{"className":123134},[514],[212,123136,123138],{"className":123137},[487],[212,123139,123141],{"className":123140,"style":522},[491],[212,123142],{},[212,123144,123146],{"className":123145},[343],"[(",[212,123148,966],{"className":123149},[256,257],[212,123151],{"className":123152,"style":2785},[354],[212,123154,5011],{"className":123155},[2789],[212,123157],{"className":123158,"style":2785},[354],[212,123160,123162,123166,123169,123198],{"className":123161},[247],[212,123163],{"className":123164,"style":123165},[251],"height:1.0213em;vertical-align:-0.25em;",[212,123167,121291],{"className":123168,"style":121381},[256,257],[212,123170,123172,123175],{"className":123171},[350],[212,123173,317],{"className":123174},[350],[212,123176,123178],{"className":123177},[478],[212,123179,123181],{"className":123180},[482],[212,123182,123184],{"className":123183},[487],[212,123185,123187],{"className":123186,"style":21209},[491],[212,123188,123189,123192],{"style":7063},[212,123190],{"className":123191,"style":500},[499],[212,123193,123195],{"className":123194},[504,505,506,507],[212,123196,2668],{"className":123197},[2789,507],[212,123199,454],{"className":123200},[350],[212,123202,123204,123226],{"className":123203,"translate":216},[215],[212,123205,123207],{"className":123206},[220],[222,123208,123209],{"xmlns":224},[226,123210,123211,123223],{},[229,123212,123213],{},[392,123214,123215,123217],{},[232,123216,396],{},[392,123218,123219,123221],{},[232,123220,4356],{},[232,123222,121291],{},[236,123224,123225],{"encoding":238},"D_{g_\\gamma}",[212,123227,123229],{"className":123228,"ariaHidden":243},[242],[212,123230,123232,123236],{"className":123231},[247],[212,123233],{"className":123234,"style":123235},[251],"height:1.0307em;vertical-align:-0.3473em;",[212,123237,123239,123242],{"className":123238},[256],[212,123240,396],{"className":123241,"style":474},[256,257],[212,123243,123245],{"className":123244},[478],[212,123246,123248,123308],{"className":123247},[482,483],[212,123249,123251,123305],{"className":123250},[487],[212,123252,123254],{"className":123253,"style":45129},[491],[212,123255,123256,123259],{"style":495},[212,123257],{"className":123258,"style":500},[499],[212,123260,123262],{"className":123261},[504,505,506,507],[212,123263,123265],{"className":123264},[256,507],[212,123266,123268,123271],{"className":123267},[256,507],[212,123269,4356],{"className":123270,"style":1178},[256,257,507],[212,123272,123274],{"className":123273},[478],[212,123275,123277,123297],{"className":123276},[482,483],[212,123278,123280,123294],{"className":123279},[487],[212,123281,123283],{"className":123282,"style":74472},[491],[212,123284,123285,123288],{"style":121916},[212,123286],{"className":123287,"style":30406},[499],[212,123289,123291],{"className":123290},[504,30410,9872,507],[212,123292,121291],{"className":123293,"style":121381},[256,257,507],[212,123295,515],{"className":123296},[514],[212,123298,123300],{"className":123299},[487],[212,123301,123303],{"className":123302,"style":121935},[491],[212,123304],{},[212,123306,515],{"className":123307},[514],[212,123309,123311],{"className":123310},[487],[212,123312,123314],{"className":123313,"style":121947},[491],[212,123315],{},"。另一方面取 ",[212,123318,123320,123356],{"className":123319,"translate":216},[215],[212,123321,123323],{"className":123322},[220],[222,123324,123325],{"xmlns":224},[226,123326,123327,123353],{},[229,123328,123329,123335,123337],{},[7012,123330,123331,123333],{},[232,123332,4356],{},[307,123334,7771],{},[307,123336,320],{},[392,123338,123339,123341],{},[312,123340,314],{"mathvariant":75425},[229,123342,123343,123345,123347,123349,123351],{},[307,123344,3096],{"stretchy":309},[232,123346,966],{},[307,123348,3101],{},[232,123350,121291],{},[307,123352,3106],{"stretchy":309},[236,123354,123355],{"encoding":238},"g^*=\\mathbf 1_{\\{t>\\gamma\\}}",[212,123357,123359,123403],{"className":123358,"ariaHidden":243},[242],[212,123360,123362,123365,123394,123397,123400],{"className":123361},[247],[212,123363],{"className":123364,"style":64225},[251],[212,123366,123368,123371],{"className":123367},[256],[212,123369,4356],{"className":123370,"style":1178},[256,257],[212,123372,123374],{"className":123373},[478],[212,123375,123377],{"className":123376},[482],[212,123378,123380],{"className":123379},[487],[212,123381,123383],{"className":123382,"style":8697},[491],[212,123384,123385,123388],{"style":7063},[212,123386],{"className":123387,"style":500},[499],[212,123389,123391],{"className":123390},[504,505,506,507],[212,123392,7771],{"className":123393},[2789,507],[212,123395],{"className":123396,"style":355},[354],[212,123398,320],{"className":123399},[359],[212,123401],{"className":123402,"style":355},[354],[212,123404,123406,123410],{"className":123405},[247],[212,123407],{"className":123408,"style":123409},[251],"height:0.9996em;vertical-align:-0.3552em;",[212,123411,123413,123416],{"className":123412},[256],[212,123414,314],{"className":123415},[256,75770],[212,123417,123419],{"className":123418},[478],[212,123420,123422,123457],{"className":123421},[482,483],[212,123423,123425,123454],{"className":123424},[487],[212,123426,123428],{"className":123427,"style":6296},[491],[212,123429,123430,123433],{"style":75785},[212,123431],{"className":123432,"style":500},[499],[212,123434,123436],{"className":123435},[504,505,506,507],[212,123437,123439,123442,123445,123448,123451],{"className":123438},[256,507],[212,123440,3096],{"className":123441},[343,507],[212,123443,966],{"className":123444},[256,257,507],[212,123446,3101],{"className":123447},[359,507],[212,123449,121291],{"className":123450,"style":121381},[256,257,507],[212,123452,3106],{"className":123453},[350,507],[212,123455,515],{"className":123456},[514],[212,123458,123460],{"className":123459},[487],[212,123461,123463],{"className":123462,"style":6342},[491],[212,123464],{}," 恰有 ",[212,123467,123469,123533],{"className":123468,"translate":216},[215],[212,123470,123472],{"className":123471},[220],[222,123473,123474],{"xmlns":224},[226,123475,123476,123530],{},[229,123477,123478,123484,123486,123492,123494,123496,123498,123500,123502,123504,123506,123512,123514,123516,123518,123520,123522,123528],{},[392,123479,123480,123482],{},[232,123481,420],{},[232,123483,410],{},[307,123485,427],{"stretchy":309},[7012,123487,123488,123490],{},[232,123489,4356],{},[307,123491,7771],{},[307,123493,310],{"stretchy":309},[232,123495,966],{},[307,123497,5011],{},[232,123499,121291],{},[307,123501,317],{"stretchy":309},[307,123503,454],{"stretchy":309},[307,123505,320],{},[392,123507,123508,123510],{},[232,123509,420],{},[232,123511,410],{},[307,123513,427],{"stretchy":309},[307,123515,310],{"stretchy":309},[232,123517,966],{},[307,123519,5011],{},[232,123521,121291],{},[7012,123523,123524,123526],{},[307,123525,317],{"stretchy":309},[307,123527,2668],{},[307,123529,454],{"stretchy":309},[236,123531,123532],{"encoding":238},"E_Q[g^*(t-\\gamma)]=E_Q[(t-\\gamma)^+]",[212,123534,123536,123629,123650,123711],{"className":123535,"ariaHidden":243},[242],[212,123537,123539,123542,123582,123585,123614,123617,123620,123623,123626],{"className":123538},[247],[212,123540],{"className":123541,"style":467},[251],[212,123543,123545,123548],{"className":123544},[256],[212,123546,420],{"className":123547,"style":26061},[256,257],[212,123549,123551],{"className":123550},[478],[212,123552,123554,123574],{"className":123553},[482,483],[212,123555,123557,123571],{"className":123556},[487],[212,123558,123560],{"className":123559,"style":576},[491],[212,123561,123562,123565],{"style":122248},[212,123563],{"className":123564,"style":500},[499],[212,123566,123568],{"className":123567},[504,505,506,507],[212,123569,410],{"className":123570},[256,257,507],[212,123572,515],{"className":123573},[514],[212,123575,123577],{"className":123576},[487],[212,123578,123580],{"className":123579,"style":522},[491],[212,123581],{},[212,123583,427],{"className":123584},[343],[212,123586,123588,123591],{"className":123587},[256],[212,123589,4356],{"className":123590,"style":1178},[256,257],[212,123592,123594],{"className":123593},[478],[212,123595,123597],{"className":123596},[482],[212,123598,123600],{"className":123599},[487],[212,123601,123603],{"className":123602,"style":8697},[491],[212,123604,123605,123608],{"style":7063},[212,123606],{"className":123607,"style":500},[499],[212,123609,123611],{"className":123610},[504,505,506,507],[212,123612,7771],{"className":123613},[2789,507],[212,123615,310],{"className":123616},[343],[212,123618,966],{"className":123619},[256,257],[212,123621],{"className":123622,"style":2785},[354],[212,123624,5011],{"className":123625},[2789],[212,123627],{"className":123628,"style":2785},[354],[212,123630,123632,123635,123638,123641,123644,123647],{"className":123631},[247],[212,123633],{"className":123634,"style":336},[251],[212,123636,121291],{"className":123637,"style":121381},[256,257],[212,123639,20590],{"className":123640},[350],[212,123642],{"className":123643,"style":355},[354],[212,123645,320],{"className":123646},[359],[212,123648],{"className":123649,"style":355},[354],[212,123651,123653,123656,123696,123699,123702,123705,123708],{"className":123652},[247],[212,123654],{"className":123655,"style":467},[251],[212,123657,123659,123662],{"className":123658},[256],[212,123660,420],{"className":123661,"style":26061},[256,257],[212,123663,123665],{"className":123664},[478],[212,123666,123668,123688],{"className":123667},[482,483],[212,123669,123671,123685],{"className":123670},[487],[212,123672,123674],{"className":123673,"style":576},[491],[212,123675,123676,123679],{"style":122248},[212,123677],{"className":123678,"style":500},[499],[212,123680,123682],{"className":123681},[504,505,506,507],[212,123683,410],{"className":123684},[256,257,507],[212,123686,515],{"className":123687},[514],[212,123689,123691],{"className":123690},[487],[212,123692,123694],{"className":123693,"style":522},[491],[212,123695],{},[212,123697,123146],{"className":123698},[343],[212,123700,966],{"className":123701},[256,257],[212,123703],{"className":123704,"style":2785},[354],[212,123706,5011],{"className":123707},[2789],[212,123709],{"className":123710,"style":2785},[354],[212,123712,123714,123717,123720,123749],{"className":123713},[247],[212,123715],{"className":123716,"style":123165},[251],[212,123718,121291],{"className":123719,"style":121381},[256,257],[212,123721,123723,123726],{"className":123722},[350],[212,123724,317],{"className":123725},[350],[212,123727,123729],{"className":123728},[478],[212,123730,123732],{"className":123731},[482],[212,123733,123735],{"className":123734},[487],[212,123736,123738],{"className":123737,"style":21209},[491],[212,123739,123740,123743],{"style":7063},[212,123741],{"className":123742,"style":500},[499],[212,123744,123746],{"className":123745},[504,505,506,507],[212,123747,2668],{"className":123748},[2789,507],[212,123750,454],{"className":123751},[350],"，故等号可取。",[11,123754,123755,123756,123784,123785,123836,123837,123873,123874,15995,123977,124028,124029,124196,124197,124255,124256,124284],{},"几何解释：",[212,123757,123759,123772],{"className":123758,"translate":216},[215],[212,123760,123762],{"className":123761},[220],[222,123763,123764],{"xmlns":224},[226,123765,123766,123770],{},[229,123767,123768],{},[232,123769,121291],{},[236,123771,121708],{"encoding":238},[212,123773,123775],{"className":123774,"ariaHidden":243},[242],[212,123776,123778,123781],{"className":123777},[247],[212,123779],{"className":123780,"style":2474},[251],[212,123782,121291],{"className":123783,"style":121381},[256,257]," 扫过 ",[212,123786,123788,123809],{"className":123787,"translate":216},[215],[212,123789,123791],{"className":123790},[220],[222,123792,123793],{"xmlns":224},[226,123794,123795,123807],{},[229,123796,123797,123799,123801,123803,123805],{},[307,123798,427],{"stretchy":309},[312,123800,323],{},[307,123802,748],{"separator":243},[312,123804,314],{},[307,123806,454],{"stretchy":309},[236,123808,37014],{"encoding":238},[212,123810,123812],{"className":123811,"ariaHidden":243},[242],[212,123813,123815,123818,123821,123824,123827,123830,123833],{"className":123814},[247],[212,123816],{"className":123817,"style":336},[251],[212,123819,427],{"className":123820},[343],[212,123822,323],{"className":123823},[256],[212,123825,748],{"className":123826},[770],[212,123828],{"className":123829,"style":603},[354],[212,123831,314],{"className":123832},[256],[212,123834,454],{"className":123835},[350]," 时，右端就是权衡曲线（ROC 下边界）各条斜率为 ",[212,123838,123840,123858],{"className":123839,"translate":216},[215],[212,123841,123843],{"className":123842},[220],[222,123844,123845],{"xmlns":224},[226,123846,123847,123855],{},[229,123848,123849,123851,123853],{},[312,123850,314],{},[232,123852,1138],{"mathvariant":406},[232,123854,121291],{},[236,123856,123857],{"encoding":238},"1\u002F\\gamma",[212,123859,123861],{"className":123860,"ariaHidden":243},[242],[212,123862,123864,123867,123870],{"className":123863},[247],[212,123865],{"className":123866,"style":336},[251],[212,123868,8787],{"className":123869},[256],[212,123871,121291],{"className":123872,"style":121381},[256,257]," 的支撑线的截距——",[1194,123875,123876,123877,123905,123906,123976],{},"知道整条曲线 ",[212,123878,123880,123893],{"className":123879,"translate":216},[215],[212,123881,123883],{"className":123882},[220],[222,123884,123885],{"xmlns":224},[226,123886,123887,123891],{},[229,123888,123889],{},[232,123890,5590],{},[236,123892,5590],{"encoding":238},[212,123894,123896],{"className":123895,"ariaHidden":243},[242],[212,123897,123899,123902],{"className":123898},[247],[212,123900],{"className":123901,"style":861},[251],[212,123903,5590],{"className":123904,"style":531},[256,257]," 就知道全部 ",[212,123907,123909,123927],{"className":123908,"translate":216},[215],[212,123910,123912],{"className":123911},[220],[222,123913,123914],{"xmlns":224},[226,123915,123916,123924],{},[229,123917,123918],{},[392,123919,123920,123922],{},[232,123921,4356],{},[232,123923,121291],{},[236,123925,123926],{"encoding":238},"g_\\gamma",[212,123928,123930],{"className":123929,"ariaHidden":243},[242],[212,123931,123933,123936],{"className":123932},[247],[212,123934],{"className":123935,"style":93174},[251],[212,123937,123939,123942],{"className":123938},[256],[212,123940,4356],{"className":123941,"style":1178},[256,257],[212,123943,123945],{"className":123944},[478],[212,123946,123948,123968],{"className":123947},[482,483],[212,123949,123951,123965],{"className":123950},[487],[212,123952,123954],{"className":123953,"style":45129},[491],[212,123955,123956,123959],{"style":19043},[212,123957],{"className":123958,"style":500},[499],[212,123960,123962],{"className":123961},[504,505,506,507],[212,123963,121291],{"className":123964,"style":121381},[256,257,507],[212,123966,515],{"className":123967},[514],[212,123969,123971],{"className":123970},[487],[212,123972,123974],{"className":123973,"style":522},[491],[212,123975],{},"-散度",[212,123978,123980,123998],{"className":123979,"translate":216},[215],[212,123981,123983],{"className":123982},[220],[222,123984,123985],{"xmlns":224},[226,123986,123987,123995],{},[229,123988,123989,123991,123993],{},[232,123990,121291],{},[307,123992,320],{},[312,123994,314],{},[236,123996,123997],{"encoding":238},"\\gamma=1",[212,123999,124001,124019],{"className":124000,"ariaHidden":243},[242],[212,124002,124004,124007,124010,124013,124016],{"className":124003},[247],[212,124005],{"className":124006,"style":2474},[251],[212,124008,121291],{"className":124009,"style":121381},[256,257],[212,124011],{"className":124012,"style":355},[354],[212,124014,320],{"className":124015},[359],[212,124017],{"className":124018,"style":355},[354],[212,124020,124022,124025],{"className":124021},[247],[212,124023],{"className":124024,"style":369},[251],[212,124026,314],{"className":124027},[256]," 时立刻给出 ",[212,124030,124032,124084],{"className":124031,"translate":216},[215],[212,124033,124035],{"className":124034},[220],[222,124036,124037],{"xmlns":224},[226,124038,124039,124081],{},[229,124040,124041,124047,124049,124059,124061,124063,124065,124067,124069,124071,124073,124075,124077,124079],{},[229,124042,124043,124045],{},[232,124044,5590],{"mathvariant":406},[232,124046,35050],{"mathvariant":406},[307,124048,320],{},[392,124050,124051,124057],{},[229,124052,124053,124055],{},[232,124054,35632],{},[307,124056,4301],{},[232,124058,800],{},[307,124060,3096],{"stretchy":309},[232,124062,403],{},[307,124064,310],{"stretchy":309},[232,124066,800],{},[307,124068,317],{"stretchy":309},[307,124070,5011],{},[232,124072,410],{},[307,124074,310],{"stretchy":309},[232,124076,800],{},[307,124078,317],{"stretchy":309},[307,124080,3106],{"stretchy":309},[236,124082,124083],{"encoding":238},"\\mathrm{TV}=\\sup_A\\{P(A)-Q(A)\\}",[212,124085,124087,124108,124178],{"className":124086,"ariaHidden":243},[242],[212,124088,124090,124093,124099,124102,124105],{"className":124089},[247],[212,124091],{"className":124092,"style":861},[251],[212,124094,124096],{"className":124095},[256],[212,124097,86976],{"className":124098,"style":4355},[256,32862],[212,124100],{"className":124101,"style":355},[354],[212,124103,320],{"className":124104},[359],[212,124106],{"className":124107,"style":355},[354],[212,124109,124111,124114,124154,124157,124160,124163,124166,124169,124172,124175],{"className":124110},[247],[212,124112],{"className":124113,"style":336},[251],[212,124115,124117,124120],{"className":124116},[1682],[212,124118,35632],{"className":124119},[1682],[212,124121,124123],{"className":124122},[478],[212,124124,124126,124146],{"className":124125},[482,483],[212,124127,124129,124143],{"className":124128},[487],[212,124130,124132],{"className":124131,"style":35775},[491],[212,124133,124134,124137],{"style":35778},[212,124135],{"className":124136,"style":500},[499],[212,124138,124140],{"className":124139},[504,505,506,507],[212,124141,800],{"className":124142},[256,257,507],[212,124144,515],{"className":124145},[514],[212,124147,124149],{"className":124148},[487],[212,124150,124152],{"className":124151,"style":37220},[491],[212,124153],{},[212,124155,3096],{"className":124156},[343],[212,124158,403],{"className":124159,"style":531},[256,257],[212,124161,310],{"className":124162},[343],[212,124164,800],{"className":124165},[256,257],[212,124167,317],{"className":124168},[350],[212,124170],{"className":124171,"style":2785},[354],[212,124173,5011],{"className":124174},[2789],[212,124176],{"className":124177,"style":2785},[354],[212,124179,124181,124184,124187,124190,124193],{"className":124180},[247],[212,124182],{"className":124183,"style":336},[251],[212,124185,410],{"className":124186},[256,257],[212,124188,310],{"className":124189},[343],[212,124191,800],{"className":124192},[256,257],[212,124194,61209],{"className":124195},[350],"）。反过来，知道单个标量散度（如 KL 或 ",[212,124198,124200,124217],{"className":124199,"translate":216},[215],[212,124201,124203],{"className":124202},[220],[222,124204,124205],{"xmlns":224},[226,124206,124207,124215],{},[229,124208,124209],{},[7012,124210,124211,124213],{},[232,124212,37649],{},[312,124214,2661],{},[236,124216,40594],{"encoding":238},[212,124218,124220],{"className":124219,"ariaHidden":243},[242],[212,124221,124223,124226],{"className":124222},[247],[212,124224],{"className":124225,"style":40604},[251],[212,124227,124229,124232],{"className":124228},[256],[212,124230,37649],{"className":124231},[256,257],[212,124233,124235],{"className":124234},[478],[212,124236,124238],{"className":124237},[482],[212,124239,124241],{"className":124240},[487],[212,124242,124244],{"className":124243,"style":20228},[491],[212,124245,124246,124249],{"style":7063},[212,124247],{"className":124248,"style":500},[499],[212,124250,124252],{"className":124251},[504,505,506,507],[212,124253,2661],{"className":124254},[256,507],"）只对 ",[212,124257,124259,124272],{"className":124258,"translate":216},[215],[212,124260,124262],{"className":124261},[220],[222,124263,124264],{"xmlns":224},[226,124265,124266,124270],{},[229,124267,124268],{},[232,124269,5590],{},[236,124271,5590],{"encoding":238},[212,124273,124275],{"className":124274,"ariaHidden":243},[242],[212,124276,124278,124281],{"className":124277},[247],[212,124279],{"className":124280,"style":861},[251],[212,124282,5590],{"className":124283,"style":531},[256,257]," 施加一个切向约束（4.7 节的不等式网络），信息严格更少；",[10225,124286,124287,124519],{},[6863,124288,124289,124290,20166],{},"在「小隐私预算」下，所有 f-DP 都由**高斯差分隐私（GDP）**统一逼近，其权衡函数 ",[212,124291,124293,124351],{"className":124292,"translate":216},[215],[212,124294,124296],{"className":124295},[220],[222,124297,124298],{"xmlns":224},[226,124299,124300,124348],{},[229,124301,124302,124309,124311,124313,124315,124317,124320,124322,124332,124334,124336,124338,124340,124342,124344,124346],{},[392,124303,124304,124307],{},[232,124305,124306],{},"G",[232,124308,2562],{},[307,124310,310],{"stretchy":309},[232,124312,44954],{},[307,124314,317],{"stretchy":309},[307,124316,320],{},[232,124318,124319],{"mathvariant":406},"Φ",[307,124321,310],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[7012,124323,124324,124326],{},[232,124325,124319],{"mathvariant":406},[229,124327,124328,124330],{},[307,124329,5011],{},[312,124331,314],{},[307,124333,310],{"stretchy":309},[312,124335,314],{},[307,124337,5011],{},[232,124339,44954],{},[307,124341,317],{"stretchy":309},[307,124343,5011],{},[232,124345,2562],{},[307,124347,317],{"fence":309,"stretchy":243,"minsize":9648,"maxsize":9648},[236,124349,124350],{"encoding":238},"G_\\mu(\\alpha)=\\Phi\\big(\\Phi^{-1}(1-\\alpha)-\\mu\\big)",[212,124352,124354,124418,124483,124504],{"className":124353,"ariaHidden":243},[242],[212,124355,124357,124360,124400,124403,124406,124409,124412,124415],{"className":124356},[247],[212,124358],{"className":124359,"style":467},[251],[212,124361,124363,124366],{"className":124362},[256],[212,124364,124306],{"className":124365},[256,257],[212,124367,124369],{"className":124368},[478],[212,124370,124372,124392],{"className":124371},[482,483],[212,124373,124375,124389],{"className":124374},[487],[212,124376,124378],{"className":124377,"style":45129},[491],[212,124379,124380,124383],{"style":579},[212,124381],{"className":124382,"style":500},[499],[212,124384,124386],{"className":124385},[504,505,506,507],[212,124387,2562],{"className":124388},[256,257,507],[212,124390,515],{"className":124391},[514],[212,124393,124395],{"className":124394},[487],[212,124396,124398],{"className":124397,"style":522},[491],[212,124399],{},[212,124401,310],{"className":124402},[343],[212,124404,44954],{"className":124405,"style":44984},[256,257],[212,124407,317],{"className":124408},[350],[212,124410],{"className":124411,"style":355},[354],[212,124413,320],{"className":124414},[359],[212,124416],{"className":124417,"style":355},[354],[212,124419,124421,124424,124427,124433,124468,124471,124474,124477,124480],{"className":124420},[247],[212,124422],{"className":124423,"style":20763},[251],[212,124425,124319],{"className":124426},[256],[212,124428,124430],{"className":124429},[256],[212,124431,310],{"className":124432},[616,9872],[212,124434,124436,124439],{"className":124435},[256],[212,124437,124319],{"className":124438},[256],[212,124440,124442],{"className":124441},[478],[212,124443,124445],{"className":124444},[482],[212,124446,124448],{"className":124447},[487],[212,124449,124451],{"className":124450,"style":20228},[491],[212,124452,124453,124456],{"style":7063},[212,124454],{"className":124455,"style":500},[499],[212,124457,124459],{"className":124458},[504,505,506,507],[212,124460,124462,124465],{"className":124461},[256,507],[212,124463,5011],{"className":124464},[256,507],[212,124466,314],{"className":124467},[256,507],[212,124469,310],{"className":124470},[343],[212,124472,314],{"className":124473},[256],[212,124475],{"className":124476,"style":2785},[354],[212,124478,5011],{"className":124479},[2789],[212,124481],{"className":124482,"style":2785},[354],[212,124484,124486,124489,124492,124495,124498,124501],{"className":124485},[247],[212,124487],{"className":124488,"style":336},[251],[212,124490,44954],{"className":124491,"style":44984},[256,257],[212,124493,317],{"className":124494},[350],[212,124496],{"className":124497,"style":2785},[354],[212,124499,5011],{"className":124500},[2789],[212,124502],{"className":124503,"style":2785},[354],[212,124505,124507,124510,124513],{"className":124506},[247],[212,124508],{"className":124509,"style":20763},[251],[212,124511,2562],{"className":124512},[256,257],[212,124514,124516],{"className":124515},[256],[212,124517,317],{"className":124518},[616,9872],[6863,124520,124521,124522,124525,124526,124554],{},"权衡函数族在",[1194,124523,124524],{},"组合","（post-processing、串联）下封闭，并装备了一个与 f-散度\"散度序\"同构的偏序——这与 f-散度族的\"",[212,124527,124529,124542],{"className":124528,"translate":216},[215],[212,124530,124532],{"className":124531},[220],[222,124533,124534],{"xmlns":224},[226,124535,124536,124540],{},[229,124537,124538],{},[307,124539,7126],{},[236,124541,55690],{"encoding":238},[212,124543,124545],{"className":124544,"ariaHidden":243},[242],[212,124546,124548,124551],{"className":124547},[247],[212,124549],{"className":124550,"style":43388},[251],[212,124552,7126],{"className":124553},[359]," 比较\"在结构上完全平行。",[11,124556,124557],{},"这说明 f-散度不仅统一了信息论度量，也统一了现代隐私的定义框架：用一条凸曲线代替一个标量数字。",[725,124559,124561],{"id":124560},"_9-计算实例","9. 计算实例",[2509,124563,124565],{"id":124564},"_91-正态分布","9.1 正态分布",[11,124567,731,124568,5843,124743,10378],{},[212,124569,124571,124609],{"className":124570,"translate":216},[215],[212,124572,124574],{"className":124573},[220],[222,124575,124576],{"xmlns":224},[226,124577,124578,124606],{},[229,124579,124580,124582,124584,124586,124588,124594,124596,124604],{},[232,124581,403],{},[307,124583,320],{},[232,124585,38484],{},[307,124587,310],{"stretchy":309},[392,124589,124590,124592],{},[232,124591,2562],{},[312,124593,314],{},[307,124595,748],{"separator":243},[7751,124597,124598,124600,124602],{},[232,124599,2530],{},[312,124601,314],{},[312,124603,2661],{},[307,124605,317],{"stretchy":309},[236,124607,124608],{"encoding":238},"P=N(\\mu_1,\\sigma_1^2)",[212,124610,124612,124630],{"className":124611,"ariaHidden":243},[242],[212,124613,124615,124618,124621,124624,124627],{"className":124614},[247],[212,124616],{"className":124617,"style":861},[251],[212,124619,403],{"className":124620,"style":531},[256,257],[212,124622],{"className":124623,"style":355},[354],[212,124625,320],{"className":124626},[359],[212,124628],{"className":124629,"style":355},[354],[212,124631,124633,124636,124639,124642,124682,124685,124688,124740],{"className":124632},[247],[212,124634],{"className":124635,"style":20203},[251],[212,124637,38484],{"className":124638,"style":25801},[256,257],[212,124640,310],{"className":124641},[343],[212,124643,124645,124648],{"className":124644},[256],[212,124646,2562],{"className":124647},[256,257],[212,124649,124651],{"className":124650},[478],[212,124652,124654,124674],{"className":124653},[482,483],[212,124655,124657,124671],{"className":124656},[487],[212,124658,124660],{"className":124659,"style":11333},[491],[212,124661,124662,124665],{"style":579},[212,124663],{"className":124664,"style":500},[499],[212,124666,124668],{"className":124667},[504,505,506,507],[212,124669,314],{"className":124670},[256,507],[212,124672,515],{"className":124673},[514],[212,124675,124677],{"className":124676},[487],[212,124678,124680],{"className":124679,"style":8166},[491],[212,124681],{},[212,124683,748],{"className":124684},[770],[212,124686],{"className":124687,"style":603},[354],[212,124689,124691,124694],{"className":124690},[256],[212,124692,2530],{"className":124693,"style":1178},[256,257],[212,124695,124697],{"className":124696},[478],[212,124698,124700,124732],{"className":124699},[482,483],[212,124701,124703,124729],{"className":124702},[487],[212,124704,124706,124718],{"className":124705,"style":20228},[491],[212,124707,124709,124712],{"style":124708},"top:-2.4519em;margin-left:-0.0359em;margin-right:0.05em;",[212,124710],{"className":124711,"style":500},[499],[212,124713,124715],{"className":124714},[504,505,506,507],[212,124716,314],{"className":124717},[256,507],[212,124719,124720,124723],{"style":7063},[212,124721],{"className":124722,"style":500},[499],[212,124724,124726],{"className":124725},[504,505,506,507],[212,124727,2661],{"className":124728},[256,507],[212,124730,515],{"className":124731},[514],[212,124733,124735],{"className":124734},[487],[212,124736,124738],{"className":124737,"style":52323},[491],[212,124739],{},[212,124741,317],{"className":124742},[350],[212,124744,124746,124784],{"className":124745,"translate":216},[215],[212,124747,124749],{"className":124748},[220],[222,124750,124751],{"xmlns":224},[226,124752,124753,124781],{},[229,124754,124755,124757,124759,124761,124763,124769,124771,124779],{},[232,124756,410],{},[307,124758,320],{},[232,124760,38484],{},[307,124762,310],{"stretchy":309},[392,124764,124765,124767],{},[232,124766,2562],{},[312,124768,2661],{},[307,124770,748],{"separator":243},[7751,124772,124773,124775,124777],{},[232,124774,2530],{},[312,124776,2661],{},[312,124778,2661],{},[307,124780,317],{"stretchy":309},[236,124782,124783],{"encoding":238},"Q=N(\\mu_2,\\sigma_2^2)",[212,124785,124787,124805],{"className":124786,"ariaHidden":243},[242],[212,124788,124790,124793,124796,124799,124802],{"className":124789},[247],[212,124791],{"className":124792,"style":763},[251],[212,124794,410],{"className":124795},[256,257],[212,124797],{"className":124798,"style":355},[354],[212,124800,320],{"className":124801},[359],[212,124803],{"className":124804,"style":355},[354],[212,124806,124808,124811,124814,124817,124857,124860,124863,124914],{"className":124807},[247],[212,124809],{"className":124810,"style":20203},[251],[212,124812,38484],{"className":124813,"style":25801},[256,257],[212,124815,310],{"className":124816},[343],[212,124818,124820,124823],{"className":124819},[256],[212,124821,2562],{"className":124822},[256,257],[212,124824,124826],{"className":124825},[478],[212,124827,124829,124849],{"className":124828},[482,483],[212,124830,124832,124846],{"className":124831},[487],[212,124833,124835],{"className":124834,"style":11333},[491],[212,124836,124837,124840],{"style":579},[212,124838],{"className":124839,"style":500},[499],[212,124841,124843],{"className":124842},[504,505,506,507],[212,124844,2661],{"className":124845},[256,507],[212,124847,515],{"className":124848},[514],[212,124850,124852],{"className":124851},[487],[212,124853,124855],{"className":124854,"style":8166},[491],[212,124856],{},[212,124858,748],{"className":124859},[770],[212,124861],{"className":124862,"style":603},[354],[212,124864,124866,124869],{"className":124865},[256],[212,124867,2530],{"className":124868,"style":1178},[256,257],[212,124870,124872],{"className":124871},[478],[212,124873,124875,124906],{"className":124874},[482,483],[212,124876,124878,124903],{"className":124877},[487],[212,124879,124881,124892],{"className":124880,"style":20228},[491],[212,124882,124883,124886],{"style":124708},[212,124884],{"className":124885,"style":500},[499],[212,124887,124889],{"className":124888},[504,505,506,507],[212,124890,2661],{"className":124891},[256,507],[212,124893,124894,124897],{"style":7063},[212,124895],{"className":124896,"style":500},[499],[212,124898,124900],{"className":124899},[504,505,506,507],[212,124901,2661],{"className":124902},[256,507],[212,124904,515],{"className":124905},[514],[212,124907,124909],{"className":124908},[487],[212,124910,124912],{"className":124911,"style":52323},[491],[212,124913],{},[212,124915,317],{"className":124916},[350],[11,124918,124919],{},[1194,124920,124921],{},"KL（经典公式）。",[212,124923,124925],{"className":124924,"translate":216},[377],[212,124926,124928,125040],{"className":124927,"translate":216},[215],[212,124929,124931],{"className":124930},[220],[222,124932,124933],{"xmlns":224,"display":386},[226,124934,124935,125037],{},[229,124936,124937,124947,124949,124951,124953,124955,124957,124959,124961,124963,124977,124979,125027,125029,125035],{},[392,124938,124939,124941],{},[232,124940,396],{},[229,124942,124943,124945],{},[232,124944,10894],{},[232,124946,22093],{},[307,124948,310],{"stretchy":309},[232,124950,403],{},[232,124952,407],{"mathvariant":406},[232,124954,410],{},[307,124956,317],{"stretchy":309},[307,124958,320],{},[232,124960,4298],{},[307,124962,4301],{},[435,124964,124965,124971],{},[392,124966,124967,124969],{},[232,124968,2530],{},[312,124970,2661],{},[392,124972,124973,124975],{},[232,124974,2530],{},[312,124976,314],{},[307,124978,2668],{},[435,124980,124981,125015],{},[229,124982,124983,124991,124993,124995,125001,125003,125009],{},[7751,124984,124985,124987,124989],{},[232,124986,2530],{},[312,124988,314],{},[312,124990,2661],{},[307,124992,2668],{},[307,124994,310],{"stretchy":309},[392,124996,124997,124999],{},[232,124998,2562],{},[312,125000,314],{},[307,125002,5011],{},[392,125004,125005,125007],{},[232,125006,2562],{},[312,125008,2661],{},[7012,125010,125011,125013],{},[307,125012,317],{"stretchy":309},[312,125014,2661],{},[229,125016,125017,125019],{},[312,125018,2661],{},[7751,125020,125021,125023,125025],{},[232,125022,2530],{},[312,125024,2661],{},[312,125026,2661],{},[307,125028,5011],{},[435,125030,125031,125033],{},[312,125032,314],{},[312,125034,2661],{},[232,125036,4573],{"mathvariant":406},[236,125038,125039],{"encoding":238},"D_{KL}(P\\|Q)=\\log\\frac{\\sigma_2}{\\sigma_1}\n+\\frac{\\sigma_1^2+(\\mu_1-\\mu_2)^2}{2\\sigma_2^2}\n-\\frac12 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计算 ",[212,126037,126039,126063],{"className":126038,"translate":216},[215],[212,126040,126042],{"className":126041},[220],[222,126043,126044],{"xmlns":224},[226,126045,126046,126060],{},[229,126047,126048,126050,126056,126058],{},[307,126049,1485],{},[7012,126051,126052,126054],{},[232,126053,11],{},[312,126055,2661],{},[232,126057,1138],{"mathvariant":406},[232,126059,1141],{},[236,126061,126062],{"encoding":238},"\\int p^2\u002Fq",[212,126064,126066],{"className":126065,"ariaHidden":243},[242],[212,126067,126069,126072,126075,126078,126107,126110],{"className":126068},[247],[212,126070],{"className":126071,"style":50527},[251],[212,126073,1485],{"className":126074,"style":5815},[1682,1683,5814],[212,126076],{"className":126077,"style":603},[354],[212,126079,126081,126084],{"className":126080},[256],[212,126082,11],{"className":126083},[256,257],[212,126085,126087],{"className":126086},[478],[212,126088,126090],{"className":126089},[482],[212,126091,126093],{"className":126092},[487],[212,126094,126096],{"className":126095,"style":20228},[491],[212,126097,126098,126101],{"style":7063},[212,126099],{"className":126100,"style":500},[499],[212,126102,126104],{"className":126103},[504,505,506,507],[212,126105,2661],{"className":126106},[256,507],[212,126108,1138],{"className":126109},[256],[212,126111,1141],{"className":126112,"style":1178},[256,257],"：由配方可得",[212,126115,126117],{"className":126116,"translate":216},[377],[212,126118,126120,126181],{"className":126119,"translate":216},[215],[212,126121,126123],{"className":126122},[220],[222,126124,126125],{"xmlns":224,"display":386},[226,126126,126127,126178],{},[229,126128,126129,126131,126141,126143,126145,126147,126149,126152,126154,126156,126176],{},[307,126130,1485],{},[435,126132,126133,126139],{},[7012,126134,126135,126137],{},[232,126136,11],{},[312,126138,2661],{},[232,126140,1141],{},[1495,126142,1497],{},[232,126144,441],{},[232,126146,971],{},[307,126148,320],{},[232,126150,126151],{},"exp",[307,126153,4301],{},[1495,126155,1502],{},[229,126157,126158,126160,126174],{},[307,126159,310],{"fence":243},[435,126161,126162,126168],{},[7012,126163,126164,126166],{},[232,126165,125893],{"mathvariant":406},[312,126167,2661],{},[7012,126169,126170,126172],{},[232,126171,2530],{},[312,126173,2661],{},[307,126175,317],{"fence":243},[307,126177,748],{"separator":243},[236,126179,126180],{"encoding":238},"\\int \\frac{p^2}{q}\\,dx\n=\\exp\\!\\left(\\frac{\\Delta^2}{\\sigma^2}\\right),",[212,126182,126184,126302],{"className":126183,"ariaHidden":243},[242],[212,126185,126187,126190,126193,126196,126284,126287,126290,126293,126296,126299],{"className":126186},[247],[212,126188],{"className":126189,"style":37898},[251],[212,126191,1485],{"className":126192,"style":1685},[1682,1683,1684],[212,126194],{"className":126195,"style":603},[354],[212,126197,126199,126202,126281],{"className":126198},[256],[212,126200],{"className":126201},[343,638],[212,126203,126205],{"className":126204},[435],[212,126206,126208,126273],{"className":126207},[482,483],[212,126209,126211,126270],{"className":126210},[487],[212,126212,126214,126225,126233],{"className":126213,"style":37923},[491],[212,126215,126216,126219],{"style":654},[212,126217],{"className":126218,"style":658},[499],[212,126220,126222],{"className":126221},[256],[212,126223,1141],{"className":126224,"style":1178},[256,257],[212,126226,126227,126230],{"style":670},[212,126228],{"className":126229,"style":658},[499],[212,126231],{"className":126232,"style":678},[677],[212,126234,126235,126238],{"style":681},[212,126236],{"className":126237,"style":658},[499],[212,126239,126241],{"className":126240},[256],[212,126242,126244,126247],{"className":126243},[256],[212,126245,11],{"className":126246},[256,257],[212,126248,126250],{"className":126249},[478],[212,126251,126253],{"className":126252},[482],[212,126254,126256],{"className":126255},[487],[212,126257,126259],{"className":126258,"style":20228},[491],[212,126260,126261,126264],{"style":7063},[212,126262],{"className":126263,"style":500},[499],[212,126265,126267],{"className":126266},[504,505,506,507],[212,126268,2661],{"className":126269},[256,507],[212,126271,515],{"className":126272},[514],[212,126274,126276],{"className":126275},[487],[212,126277,126279],{"className":126278,"style":703},[491],[212,126280],{},[212,126282],{"className":126283},[350,638],[212,126285],{"className":126286,"style":603},[354],[212,126288,441],{"className":126289},[256,257],[212,126291,971],{"className":126292},[256,257],[212,126294],{"className":126295,"style":355},[354],[212,126297,320],{"className":126298},[359],[212,126300],{"className":126301,"style":355},[354],[212,126303,126305,126308,126311,126314,126317,126446,126449],{"className":126304},[247],[212,126306],{"className":126307,"style":87472},[251],[212,126309,126151],{"className":126310},[1682],[212,126312],{"className":126313,"style":1710},[354],[212,126315],{"className":126316,"style":603},[354],[212,126318,126320,126326,126440],{"className":126319},[607],[212,126321,126323],{"className":126322,"style":612},[343,611],[212,126324,310],{"className":126325},[616,506],[212,126327,126329,126332,126437],{"className":126328},[256],[212,126330],{"className":126331},[343,638],[212,126333,126335],{"className":126334},[435],[212,126336,126338,126429],{"className":126337},[482,483],[212,126339,126341,126426],{"className":126340},[487],[212,126342,126344,126381,126389],{"className":126343,"style":37923},[491],[212,126345,126346,126349],{"style":654},[212,126347],{"className":126348,"style":658},[499],[212,126350,126352],{"className":126351},[256],[212,126353,126355,126358],{"className":126354},[256],[212,126356,2530],{"className":126357,"style":1178},[256,257],[212,126359,126361],{"className":126360},[478],[212,126362,126364],{"className":126363},[482],[212,126365,126367],{"className":126366},[487],[212,126368,126370],{"className":126369,"style":45232},[491],[212,126371,126372,126375],{"style":45235},[212,126373],{"className":126374,"style":500},[499],[212,126376,126378],{"className":126377},[504,505,506,507],[212,126379,2661],{"className":126380},[256,507],[212,126382,126383,126386],{"style":670},[212,126384],{"className":126385,"style":658},[499],[212,126387],{"className":126388,"style":678},[677],[212,126390,126391,126394],{"style":681},[212,126392],{"className":126393,"style":658},[499],[212,126395,126397],{"className":126396},[256],[212,126398,126400,126403],{"className":126399},[256],[212,126401,125893],{"className":126402},[256],[212,126404,126406],{"className":126405},[478],[212,126407,126409],{"className":126408},[482],[212,126410,126412],{"className":126411},[487],[212,126413,126415],{"className":126414,"style":20228},[491],[212,126416,126417,126420],{"style":7063},[212,126418],{"className":126419,"style":500},[499],[212,126421,126423],{"className":126422},[504,505,506,507],[212,126424,2661],{"className":126425},[256,507],[212,126427,515],{"className":126428},[514],[212,126430,126432],{"className":126431},[487],[212,126433,126435],{"className":126434,"style":3976},[491],[212,126436],{},[212,126438],{"className":126439},[350,638],[212,126441,126443],{"className":126442,"style":612},[350,611],[212,126444,317],{"className":126445},[616,506],[212,126447],{"className":126448,"style":603},[354],[212,126450,748],{"className":126451},[770],[11,126453,48358],{},[212,126455,126457],{"className":1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.",[212,126569,126571,126630,126766,126875,126893,127046],{"className":126570,"ariaHidden":243},[242],[212,126572,126574,126577,126606,126609,126612,126615,126618,126621,126624,126627],{"className":126573},[247],[212,126575],{"className":126576,"style":37451},[251],[212,126578,126580,126583],{"className":126579},[256],[212,126581,37649],{"className":126582},[256,257],[212,126584,126586],{"className":126585},[478],[212,126587,126589],{"className":126588},[482],[212,126590,126592],{"className":126591},[487],[212,126593,126595],{"className":126594,"style":19935},[491],[212,126596,126597,126600],{"style":8475},[212,126598],{"className":126599,"style":500},[499],[212,126601,126603],{"className":126602},[504,505,506,507],[212,126604,2661],{"className":126605},[256,507],[212,126607,310],{"className":126608},[343],[212,126610,403],{"className":126611,"style":531},[256,257],[212,126613,407],{"className":126614},[256],[212,126616,410],{"className":126617},[256,257],[212,126619,317],{"className":126620},[350],[212,126622],{"className":126623,"style":355},[354],[212,126625,320],{"className":126626},[359],[212,126628],{"className":126629,"style":355},[354],[212,126631,126633,126636,126639,126642,126748,126751,126754,126757,126760,126763],{"className":126632},[247],[212,126634],{"className":126635,"style":37898},[251],[212,126637,1485],{"className":126638,"style":1685},[1682,1683,1684],[212,126640],{"className":126641,"style":603},[354],[212,126643,126645,126648,126745],{"className":126644},[256],[212,126646],{"className":126647},[343,638],[212,126649,126651],{"className":126650},[435],[212,126652,126654,126737],{"className":126653},[482,483],[212,126655,126657,126734],{"className":126656},[487],[212,126658,126660,126671,126679],{"className":126659,"style":37923},[491],[212,126661,126662,126665],{"style":654},[212,126663],{"className":126664,"style":658},[499],[212,126666,126668],{"className":126667},[256],[212,126669,1141],{"className":126670,"style":1178},[256,257],[212,126672,126673,126676],{"style":670},[212,126674],{"className":126675,"style":658},[499],[212,126677],{"className":126678,"style":678},[677],[212,126680,126681,126684],{"style":681},[212,126682],{"className":126683,"style":658},[499],[212,126685,126687,126690,126693,126696,126699,126702,126705],{"className":126686},[256],[212,126688,310],{"className":126689},[343],[212,126691,11],{"className":126692},[256,257],[212,126694],{"className":126695,"style":2785},[354],[212,126697,5011],{"className":126698},[2789],[212,126700],{"className":126701,"style":2785},[354],[212,126703,1141],{"className":126704,"style":1178},[256,257],[212,126706,126708,126711],{"className":126707},[350],[212,126709,317],{"className":126710},[350],[212,126712,126714],{"className":126713},[478],[212,126715,126717],{"className":126716},[482],[212,126718,126720],{"className":126719},[487],[212,126721,126723],{"className":126722,"style":20228},[491],[212,126724,126725,126728],{"style":7063},[212,126726],{"className":126727,"style":500},[499],[212,126729,126731],{"className":126730},[504,505,506,507],[212,126732,2661],{"className":126733},[256,507],[212,126735,515],{"className":126736},[514],[212,126738,126740],{"className":126739},[487],[212,126741,126743],{"className":126742,"style":703},[491],[212,126744],{},[212,126746],{"className":126747},[350,638],[212,126749],{"className":126750,"style":603},[354],[212,126752,441],{"className":126753},[256,257],[212,126755,971],{"className":126756},[256,257],[212,126758],{"className":126759,"style":355},[354],[212,126761,320],{"className":126762},[359],[212,126764],{"className":126765,"style":355},[354],[212,126767,126769,126772,126775,126778,126866,126869,126872],{"className":126768},[247],[212,126770],{"className":126771,"style":37898},[251],[212,126773,1485],{"className":126774,"style":1685},[1682,1683,1684],[212,126776],{"className":126777,"style":603},[354],[212,126779,126781,126784,126863],{"className":126780},[256],[212,126782],{"className":126783},[343,638],[212,126785,126787],{"className":126786},[435],[212,126788,126790,126855],{"className":126789},[482,483],[212,126791,126793,126852],{"className":126792},[487],[212,126794,126796,126807,126815],{"className":126795,"style":37923},[491],[212,126797,126798,126801],{"style":654},[212,126799],{"className":126800,"style":658},[499],[212,126802,126804],{"className":126803},[256],[212,126805,1141],{"className":126806,"style":1178},[256,257],[212,126808,126809,126812],{"style":670},[212,126810],{"className":126811,"style":658},[499],[212,126813],{"className":126814,"style":678},[677],[212,126816,126817,126820],{"style":681},[212,126818],{"className":126819,"style":658},[499],[212,126821,126823],{"className":126822},[256],[212,126824,126826,126829],{"className":126825},[256],[212,126827,11],{"className":126828},[256,257],[212,126830,126832],{"className":126831},[478],[212,126833,126835],{"className":126834},[482],[212,126836,126838],{"className":126837},[487],[212,126839,126841],{"className":126840,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也会随 ",[212,127118,127120,127146],{"className":127119,"translate":216},[215],[212,127121,127123],{"className":127122},[220],[222,127124,127125],{"xmlns":224},[226,127126,127127,127143],{},[229,127128,127129,127135,127137],{},[7012,127130,127131,127133],{},[232,127132,125893],{"mathvariant":406},[312,127134,2661],{},[232,127136,1138],{"mathvariant":406},[7012,127138,127139,127141],{},[232,127140,2530],{},[312,127142,2661],{},[236,127144,127145],{"encoding":238},"\\Delta^2\u002F\\sigma^2",[212,127147,127149],{"className":127148,"ariaHidden":243},[242],[212,127150,127152,127155,127184,127187],{"className":127151},[247],[212,127153],{"className":127154,"style":20203},[251],[212,127156,127158,127161],{"className":127157},[256],[212,127159,125893],{"className":127160},[256],[212,127162,127164],{"className":127163},[478],[212,127165,127167],{"className":127166},[482],[212,127168,127170],{"className":127169},[487],[212,127171,127173],{"className":127172,"style":20228},[491],[212,127174,127175,127178],{"style":7063},[212,127176],{"className":127177,"style":500},[499],[212,127179,127181],{"className":127180},[504,505,506,507],[212,127182,2661],{"className":127183},[256,507],[212,127185,1138],{"className":127186},[256],[212,127188,127190,127193],{"className":127189},[256],[212,127191,2530],{"className":127192,"style":1178},[256,257],[212,127194,127196],{"className":127195},[478],[212,127197,127199],{"className":127198},[482],[212,127200,127202],{"className":127201},[487],[212,127203,127205],{"className":127204,"style":20228},[491],[212,127206,127207,127210],{"style":7063},[212,127208],{"className":127209,"style":500},[499],[212,127211,127213],{"className":127212},[504,505,506,507],[212,127214,2661],{"className":127215},[256,507]," 指数爆炸。",[11,127218,127219,127222],{},[1194,127220,127221],{},"Hellinger²（等方差）。"," Bhattacharyya 系数",[212,127224,127226],{"className":127225,"translate":216},[377],[212,127227,127229,127303],{"className":127228,"translate":216},[215],[212,127230,127232],{"className":127231},[220],[222,127233,127234],{"xmlns":224,"display":386},[226,127235,127236,127300],{},[229,127237,127238,127240,127242,127244,127246,127248,127250,127252,127254,127256,127264,127266,127268,127270,127272,127298],{},[232,127239,39491],{},[232,127241,39494],{},[307,127243,310],{"stretchy":309},[232,127245,403],{},[307,127247,748],{"separator":243},[232,127249,410],{},[307,127251,317],{"stretchy":309},[307,127253,320],{},[307,127255,1485],{},[34539,127257,127258],{},[229,127259,127260,127262],{},[232,127261,11],{},[232,127263,1141],{},[307,127265,320],{},[232,127267,126151],{},[307,127269,4301],{},[1495,127271,1502],{},[229,127273,127274,127276,127278,127296],{},[307,127275,310],{"fence":243},[307,127277,5011],{},[435,127279,127280,127286],{},[7012,127281,127282,127284],{},[232,127283,125893],{"mathvariant":406},[312,127285,2661],{},[229,127287,127288,127290],{},[312,127289,39503],{},[7012,127291,127292,127294],{},[232,127293,2530],{},[312,127295,2661],{},[307,127297,317],{"fence":243},[307,127299,748],{"separator":243},[236,127301,127302],{"encoding":238},"BC(P,Q)=\\int\\sqrt{pq}\n=\\exp\\!\\left(-\\frac{\\Delta^2}{8\\sigma^2}\\right),",[212,127304,127306,127345,127413],{"className":127305,"ariaHidden":243},[242],[212,127307,127309,127312,127315,127318,127321,127324,127327,127330,127333,127336,127339,127342],{"className":127308},[247],[212,127310],{"className":127311,"style":336},[251],[212,127313,39491],{"className":127314,"style":39587},[256,257],[212,127316,39494],{"className":127317,"style":10982},[256,257],[212,127319,310],{"className":127320},[343],[212,127322,403],{"className":127323,"style":531},[256,257],[212,127325,748],{"className":127326},[770],[212,127328],{"className":127329,"style":603},[354],[212,127331,410],{"className":127332},[256,257],[212,127334,317],{"className":127335},[350],[212,127337],{"className":127338,"style":355},[354],[212,127340,320],{"className":127341},[359],[212,127343],{"className":127344,"style":355},[354],[212,127346,127348,127351,127354,127357,127404,127407,127410],{"className":127347},[247],[212,127349],{"className":127350,"style":5975},[251],[212,127352,1485],{"className":127353,"style":1685},[1682,1683,1684],[212,127355],{"className":127356,"style":603},[354],[212,127358,127360],{"className":127359},[256,34567],[212,127361,127363,127396],{"className":127362},[482,483],[212,127364,127366,127393],{"className":127365},[487],[212,127367,127369,127381],{"className":127368,"style":7060},[491],[212,127370,127372,127375],{"className":127371,"style":12063},[6505],[212,127373],{"className":127374,"style":658},[499],[212,127376,127378],{"className":127377,"style":34587},[256],[212,127379,41805],{"className":127380,"style":1178},[256,257],[212,127382,127383,127386],{"style":41550},[212,127384],{"className":127385,"style":658},[499],[212,127387,127389],{"className":127388,"style":34644},[34643],[6521,127390,127391],{"xmlns":6523,"width":6524,"height":34647,"viewBox":34648,"preserveAspectRatio":6527},[6529,127392],{"d":34651},[212,127394,515],{"className":127395},[514],[212,127397,127399],{"className":127398},[487],[212,127400,127402],{"className":127401,"style":41570},[491],[212,127403],{},[212,127405],{"className":127406,"style":355},[354],[212,127408,320],{"className":127409},[359],[212,127411],{"className":127412,"style":355},[354],[212,127414,127416,127419,127422,127425,127428,127563,127566],{"className":127415},[247],[212,127417],{"className":127418,"style":87472},[251],[212,127420,126151],{"className":127421},[1682],[212,127423],{"className":127424,"style":1710},[354],[212,127426],{"className":127427,"style":603},[354],[212,127429,127431,127437,127440,127557],{"className":127430},[607],[212,127432,127434],{"className":127433,"style":612},[343,611],[212,127435,310],{"className":127436},[616,506],[212,127438,5011],{"className":127439},[256],[212,127441,127443,127446,127554],{"className":127442},[256],[212,127444],{"className":127445},[343,638],[212,127447,127449],{"className":127448},[435],[212,127450,127452,127546],{"className":127451},[482,483],[212,127453,127455,127543],{"className":127454},[487],[212,127456,127458,127498,127506],{"className":127457,"style":37923},[491],[212,127459,127460,127463],{"style":654},[212,127461],{"className":127462,"style":658},[499],[212,127464,127466,127469],{"className":127465},[256],[212,127467,39503],{"className":127468},[256],[212,127470,127472,127475],{"className":127471},[256],[212,127473,2530],{"className":127474,"style":1178},[256,257],[212,127476,127478],{"className":127477},[478],[212,127479,127481],{"className":127480},[482],[212,127482,127484],{"className":127483},[487],[212,127485,127487],{"className":127486,"style":45232},[491],[212,127488,127489,127492],{"style":45235},[212,127490],{"className":127491,"style":500},[499],[212,127493,127495],{"className":12749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由 3.6 节",[212,128092,128094],{"className":128093,"translate":216},[377],[212,128095,128097,128205],{"className":128096,"translate":216},[215],[212,128098,128100],{"className":128099},[220],[222,128101,128102],{"xmlns":224,"display":386},[226,128103,128104,128202],{},[229,128105,128106,128112,128114,128132,128134,128136,128138,128178,128180,128182,128184,128186,128188,128200],{},[392,128107,128108,128110],{},[232,128109,396],{},[232,128111,44954],{},[307,128113,320],{},[435,128115,128116,128118],{},[312,128117,314],{},[229,128119,128120,128122,128124,128126,128128,128130],{},[232,128121,15],{},[307,128123,310],{"stretchy":309},[312,128125,314],{},[307,128127,5011],{},[232,128129,15],{},[307,128131,317],{"stretchy":309},[307,128133,310],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[312,128135,314],{},[307,128137,5011],{},[7012,128139,128140,128142],{},[232,128141,7765],{},[229,128143,128144,128146],{},[307,128145,5011],{},[435,128147,128148,128168],{},[229,128149,128150,128152,128154,128156,128158,128160,128162],{},[232,128151,15],{},[307,128153,310],{"stretchy":309},[312,128155,314],{},[307,128157,5011],{},[232,128159,15],{},[307,128161,317],{"stretchy":309},[7012,128163,128164,128166],{},[232,128165,125893],{"mathvariant":406},[312,128167,2661],{},[229,128169,128170,128172],{},[312,128171,2661],{},[7012,128173,128174,128176],{},[232,128175,2530],{},[312,128177,2661],{},[307,128179,317],{"fence":309,"stretchy":243,"minsize":17639,"maxsize":17639},[307,128181,748],{"separator":243},[354,128183],{"width":3460},[232,128185,15],{},[307,128187,320],{},[435,128189,128190,128198],{},[229,128191,128192,128194,128196],{},[312,128193,314],{},[307,128195,2668],{},[232,128197,44954],{},[312,128199,2661],{},[307,128201,748],{"separator":243},[236,128203,128204],{"encoding":238},"D_\\alpha=\\frac{1}{a(1-a)}\n\\Big(1-\ne^{-\\frac{a(1-a)\\Delta^2}{2\\sigma^2}}\\Big),\n\\qquad a=\\frac{1+\\alpha}{2},",[212,128206,128208,128263,128370,128582],{"className":128207,"ariaHidden":243},[242],[212,128209,128211,128214,128254,128257,128260],{"className":128210},[247],[212,128212],{"className":128213,"style":16161},[251],[212,128215,128217,128220],{"className":128216},[256],[212,128218,396],{"className":128219,"style":474},[256,257],[212,128221,128223],{"className":128222},[478],[212,128224,128226,128246],{"className":128225},[482,483],[212,128227,128229,128243],{"className":128228},[487],[212,128230,128232],{"className":128231,"style":45129},[491],[212,128233,128234,128237],{"style":495},[212,128235],{"className":128236,"style":500},[499],[212,128238,128240],{"className":128239},[504,505,506,507],[212,128241,44954],{"className":128242,"style":44984},[256,257,507],[212,128244,515],{"className":128245},[514],[212,128247,128249],{"className":128248},[487],[212,128250,128252],{"className":128251,"style":8166},[491],[212,128253],{},[212,128255],{"className":128256,"style":355},[354],[212,128258,320],{"className":128259},[359],[212,128261],{"className":128262,"style":355},[354],[212,128264,128266,128269,128352,128358,128361,128364,128367],{"className":128265},[247],[212,128267],{"className":128268,"style":68779},[251],[212,128270,128272,128275,128349],{"className":128271},[256],[212,128273],{"className":128274},[343,638],[212,128276,128278],{"className":128277},[435],[212,128279,128281,128341],{"className":128280},[482,483],[212,128282,128284,128338],{"className":128283},[487],[212,128285,128287,128319,128327],{"className":128286,"style":23089},[491],[212,128288,128289,128292],{"style":654},[212,128290],{"className":128291,"style":658},[499],[212,128293,128295,128298,128301,128304,128307,128310,128313,128316],{"className":128294},[256],[212,128296,15],{"className":128297},[256,257],[212,128299,310],{"className":128300},[343],[212,128302,314],{"className":128303},[256],[212,128305],{"className":128306,"style":2785},[354],[212,128308,5011],{"className":128309},[2789],[212,128311],{"className":128312,"style":2785},[354],[212,128314,15],{"className":128315},[256,257],[212,128317,317],{"className":128318},[350],[212,128320,128321,128324],{"style":670},[212,128322],{"className":128323,"style":658},[499],[212,128325],{"className":128326,"style":678},[677],[212,128328,128329,128332],{"style":681},[212,128330],{"className":128331,"style":658},[499],[212,128333,128335],{"className":128334},[256],[212,128336,314],{"className":128337},[256],[212,128339,515],{"className":128340},[514],[212,128342,128344],{"className":128343},[487],[212,128345,128347],{"className":128346,"style":1799},[491],[212,128348],{},[212,128350],{"className":128351},[350,638],[212,128353,128355],{"className":128354},[256],[212,128356,310],{"className":128357},[616,3918],[212,128359,314],{"className":128360},[256],[212,128362],{"className":128363,"style":2785},[354],[212,128365,5011],{"className":128366},[2789],[212,128368],{"className":128369,"style":2785},[354],[212,128371,128373,128377,128555,128561,128564,128567,128570,128573,128576,128579],{"className":128372},[247],[212,128374],{"className":128375,"style":128376},[251],"height:1.9791em;vertical-align:-0.65em;",[212,128378,128380,128383],{"className":128379},[256],[212,128381,7765],{"className":128382},[256,257],[212,128384,128386],{"className":128385},[478],[212,128387,128389],{"className":128388},[482],[212,128390,128392],{"className":128391},[487],[212,128393,128396],{"className":128394,"style":128395},[491],"height:1.3291em;",[212,128397,128399,128402],{"style":128398},"top:-3.4534em;margin-right:0.05em;",[212,128400],{"className":128401,"style":658},[499],[212,128403,128405],{"className":128404},[504,505,506,507],[212,128406,128408,128411],{"className":128407},[256,507],[212,128409,5011],{"className":128410},[256,507],[212,128412,128414,128417,128552],{"className":128413},[256,507],[212,128415],{"className":128416},[343,638,504,30410,111540],[212,128418,128420],{"className":128419},[435],[212,128421,128423,128543],{"className":128422},[482,483],[212,128424,128426,128540],{"className":128425},[487],[212,128427,128430,128474,128482],{"className":128428,"style":128429},[491],"height:1.251em;",[212,128431,128433,128436],{"style":128432},"top:-2.5062em;",[212,128434],{"className":128435,"style":658},[499],[212,128437,128439],{"className":128438},[504,30410,9872,507],[212,128440,128442,128445],{"className":128441},[256,507],[212,128443,2661],{"className":128444},[256,507],[212,128446,128448,128451],{"className":128447},[256,507],[212,128449,2530],{"className":128450,"style":1178},[256,257,507],[212,128452,128454],{"className":128453},[478],[212,128455,128457],{"className":128456},[482],[212,128458,128460],{"className":128459},[487],[212,128461,128464],{"className":128462,"style":128463},[491],"height:0.9384em;",[212,128465,128467,128471],{"style":128466},"top:-2.9384em;margin-right:0.1em;",[212,128468],{"className":128469,"style":128470},[499],"height:2.6444em;",[212,128472,2661],{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",[212,128669,128671,128685],{"className":128670,"translate":216},[215],[212,128672,128674],{"className":128673},[220],[222,128675,128676],{"xmlns":224},[226,128677,128678,128682],{},[229,128679,128680],{},[232,128681,125893],{"mathvariant":406},[236,128683,128684],{"encoding":238},"\\Delta",[212,128686,128688],{"className":128687,"ariaHidden":243},[242],[212,128689,128691,128694],{"className":128690},[247],[212,128692],{"className":128693,"style":861},[251],[212,128695,125893],{"className":128696},[256],[212,128698,128700,128732],{"className":128699,"translate":216},[215],[212,128701,128703],{"className":128702},[220],[222,128704,128705],{"xmlns":224},[226,128706,128707,128729],{},[229,128708,128709,128711],{},[307,128710,33159],{},[435,128712,128713,128719],{},[7012,128714,128715,128717],{},[232,128716,125893],{"mathvariant":406},[312,128718,2661],{},[229,128720,128721,128723],{},[312,128722,2661],{},[7012,128724,128725,128727],{},[232,128726,2530],{},[312,128728,2661],{},[236,128730,128731],{"encoding":238},"\\approx\\frac{\\Delta^2}{2\\sigma^2}",[212,128733,128735,128747],{"className":128734,"ariaHidden":243},[242],[212,128736,128738,128741,128744],{"className":128737},[247],[212,128739],{"className":128740,"style":117378},[251],[212,128742,33159],{"className":128743},[359],[212,128745],{"className":128746,"style":355},[354],[212,128748,128750,128754],{"className":128749},[247],[212,128751],{"className":128752,"style":128753},[251],"height:1.3629em;vertical-align:-0.345em;",[212,128755,128757,128760,128874],{"className":128756},[256],[212,128758],{"className":128759},[343,638],[212,128761,128763],{"className":128762},[435],[212,128764,128766,128866],{"className":128765},[482,483],[212,128767,128769,128863],{"className":128768},[487],[212,128770,128772,128815,128823],{"className":128771,"style":113989},[491],[212,128773,128774,128777],{"style":2725},[212,128775],{"className":128776,"style":658},[499],[212,128778,128780],{"className":128779},[504,505,506,507],[212,128781,128783,128786],{"className":128782},[256,507],[212,128784,2661],{"className":128785},[256,507],[212,128787,128789,128792],{"className":128788},[256,507],[212,128790,2530],{"className":128791,"style":1178},[256,257,507],[212,128793,128795],{"className":128794},[478],[212,128796,128798],{"className":128797},[482],[212,128799,128801],{"className":128800},[487],[212,128802,128804],{"className":128803,"style":45658},[491],[212,128805,128806,128809],{"style":45661},[212,128807],{"className":128808,"style":30406},[499],[212,128810,128812],{"className":128811},[504,30410,9872,507],[212,128813,2661],{"className":128814},[256,507],[212,128816,128817,128820],{"style":670},[212,128818],{"className":128819,"style":658},[499],[212,128821],{"className":128822,"style":678},[677],[212,128824,128825,128828],{"style":2748},[212,128826],{"className":128827,"style":658},[499],[212,128829,128831],{"className":128830},[504,505,506,507],[212,128832,128834],{"className":128833},[256,507],[212,128835,128837,128840],{"className":128836},[256,507],[212,128838,125893],{"className":128839},[256,507],[212,128841,128843],{"className":128842},[478],[212,128844,128846],{"className":128845},[482],[212,128847,128849],{"className":128848},[487],[212,128850,128852],{"className":128851,"style":38712},[491],[212,128853,128854,128857],{"style":38715},[212,128855],{"className":128856,"style":30406},[499],[212,128858,128860],{"className":128859},[504,30410,9872,507],[212,128861,2661],{"className":128862},[256,507],[212,128864,515],{"className":128865},[514],[212,128867,128869],{"className":128868},[487],[212,128870,128872],{"className":128871,"style":2770},[491],[212,128873],{},[212,128875],{"className":128876},[350,638],"，与 4.6 节的局部展开一致（且此时与 ",[212,128879,128881,128894],{"className":128880,"translate":216},[215],[212,128882,128884],{"className":128883},[220],[222,128885,128886],{"xmlns":224},[226,128887,128888,128892],{},[229,128889,128890],{},[232,128891,44954],{},[236,128893,49289],{"encoding":238},[212,128895,128897],{"className":128896,"ariaHidden":243},[242],[212,128898,128900,128903],{"className":128899},[247],[212,128901],{"className":128902,"style":2543},[251],[212,128904,44954],{"className":128905,"style":44984},[256,257]," 无关）。",[2509,128908,128910],{"id":128909},"_92-伯努利分布","9.2 伯努利分布",[11,128912,731,128913,5843,128990,15995,129067,129154,129155,129257,129258,129286,129287,129257,129453,1188],{},[212,128914,128916,128948],{"className":128915,"translate":216},[215],[212,128917,128919],{"className":128918},[220],[222,128920,128921],{"xmlns":224},[226,128922,128923,128945],{},[229,128924,128925,128927,128929,128939,128941,128943],{},[232,128926,403],{},[307,128928,320],{},[229,128930,128931,128933,128935,128937],{},[232,128932,39491],{"mathvariant":406},[232,128934,7765],{"mathvariant":406},[232,128936,16650],{"mathvariant":406},[232,128938,82510],{"mathvariant":406},[307,128940,310],{"stretchy":309},[232,128942,11],{},[307,128944,317],{"stretchy":309},[236,128946,128947],{"encoding":238},"P=\\mathrm{Bern}(p)",[212,128949,128951,128969],{"className":128950,"ariaHidden":243},[242],[212,128952,128954,128957,128960,128963,128966],{"className":128953},[247],[212,128955],{"className":128956,"style":861},[251],[212,128958,403],{"className":128959,"style":531},[256,257],[212,128961],{"className":128962,"style":355},[354],[212,128964,320],{"className":128965},[359],[212,128967],{"className":128968,"style":355},[354],[212,128970,128972,128975,128981,128984,128987],{"className":128971},[247],[212,128973],{"className":128974,"style":336},[251],[212,128976,128978],{"className":128977},[256],[212,128979,84522],{"className":128980},[256,32862],[212,128982,310],{"className":128983},[343],[212,128985,11],{"className":128986},[256,257],[212,128988,317],{"className":128989},[350],[212,128991,128993,129025],{"className":128992,"translate":216},[215],[212,128994,128996],{"className":128995},[220],[222,128997,128998],{"xmlns":224},[226,128999,129000,129022],{},[229,129001,129002,129004,129006,129016,129018,129020],{},[232,129003,410],{},[307,129005,320],{},[229,129007,129008,129010,129012,129014],{},[232,129009,39491],{"mathvariant":406},[232,129011,7765],{"mathvariant":406},[232,129013,16650],{"mathvariant":406},[232,129015,82510],{"mathvariant":406},[307,129017,310],{"stretchy":309},[232,129019,1141],{},[307,129021,317],{"stretchy":309},[236,129023,129024],{"encoding":238},"Q=\\mathrm{Bern}(q)",[212,129026,129028,129046],{"className":129027,"ariaHidden":243},[242],[212,129029,129031,129034,129037,129040,129043],{"className":129030},[247],[212,129032],{"className":129033,"style":763},[251],[212,129035,410],{"className":129036},[256,257],[212,129038],{"className":129039,"style":355},[354],[212,129041,320],{"className":129042},[359],[212,129044],{"className":129045,"style":355},[354],[212,129047,129049,129052,129058,129061,129064],{"className":129048},[247],[212,129050],{"className":129051,"style":336},[251],[212,129053,129055],{"className":129054},[256],[212,129056,84522],{"className":129057},[256,32862],[212,129059,310],{"className":129060},[343],[212,129062,1141],{"className":129063,"style":1178},[256,257],[212,129065,317],{"className":129066},[350],[212,129068,129070,129100],{"className":129069,"translate":216},[215],[212,129071,129073],{"className":129072},[220],[222,129074,129075],{"xmlns":224},[226,129076,129077,129097],{},[229,129078,129079,129081,129083,129085,129087,129089,129091,129093,129095],{},[232,129080,11],{},[307,129082,748],{"separator":243},[232,129084,1141],{},[307,129086,6107],{},[307,129088,310],{"stretchy":309},[312,129090,323],{},[307,129092,748],{"separator":243},[312,129094,314],{},[307,129096,317],{"stretchy":309},[236,129098,129099],{"encoding":238},"p,q\\in(0,1)",[212,129101,129103,129130],{"className":129102,"ariaHidden":243},[242],[212,129104,129106,129109,129112,129115,129118,129121,129124,129127],{"className":129105},[247],[212,129107],{"className":129108,"style":31892},[251],[212,129110,11],{"className":129111},[256,257],[212,129113,748],{"className":129114},[770],[212,129116],{"className":129117,"style":603},[354],[212,129119,1141],{"className":129120,"style":1178},[256,257],[212,129122],{"className":129123,"style":355},[354],[212,129125,6107],{"className":129126},[359],[212,129128],{"className":129129,"style":355},[354],[212,129131,129133,129136,129139,129142,129145,129148,129151],{"className":129132},[247],[212,129134],{"className":129135,"style":336},[251],[212,129137,310],{"className":129138},[343],[212,129140,323],{"className":129141},[256],[212,129143,748],{"className":129144},[770],[212,129146],{"className":129147,"style":603},[354],[212,129149,314],{"className":129150},[256],[212,129152,317],{"className":129153},[350],"），似然比取值 ",[212,129156,129158,129184],{"className":129157,"translate":216},[215],[212,129159,129161],{"className":129160},[220],[222,129162,129163],{"xmlns":224},[226,129164,129165,129181],{},[229,129166,129167,129173,129175,129177,129179],{},[392,129168,129169,129171],{},[232,129170,966],{},[312,129172,314],{},[307,129174,320],{},[232,129176,11],{},[232,129178,1138],{"mathvariant":406},[232,129180,1141],{},[236,129182,129183],{"encoding":238},"t_1=p\u002Fq",[212,129185,129187,129242],{"className":129186,"ariaHidden":243},[242],[212,129188,129190,129193,129233,129236,129239],{"className":129189},[247],[212,129191],{"className":129192,"style":96141},[251],[212,129194,129196,129199],{"className":129195},[256],[212,129197,966],{"className":129198},[256,257],[212,129200,129202],{"className":129201},[478],[212,129203,129205,129225],{"className":129204},[482,483],[212,129206,129208,129222],{"className":129207},[487],[212,129209,129211],{"className":129210,"style":11333},[491],[212,129212,129213,129216],{"style":579},[212,129214],{"className":129215,"style":500},[499],[212,129217,129219],{"className":129218},[504,505,506,507],[212,129220,314],{"className":129221},[256,507],[212,129223,515],{"className":129224},[514],[212,129226,129228],{"className":129227},[487],[212,129229,129231],{"className":129230,"style":8166},[491],[212,129232],{},[212,129234],{"className":129235,"style":355},[354],[212,129237,320],{"className":129238},[359],[212,129240],{"className":129241,"style":355},[354],[212,129243,129245,129248,129251,129254],{"className":129244},[247],[212,129246],{"className":129247,"style":336},[251],[212,129249,11],{"className":129250},[256,257],[212,129252,1138],{"className":129253},[256],[212,129255,1141],{"className":129256,"style":1178},[256,257],"（概率 ",[212,129259,129261,129274],{"className":129260,"translate":216},[215],[212,129262,129264],{"className":129263},[220],[222,129265,129266],{"xmlns":224},[226,129267,129268,129272],{},[229,129269,129270],{},[232,129271,1141],{},[236,129273,1141],{"encoding":238},[212,129275,129277],{"className":129276,"ariaHidden":243},[242],[212,129278,129280,129283],{"className":129279},[247],[212,129281],{"className":129282,"style":2474},[251],[212,129284,1141],{"className":129285,"style":1178},[256,257],"）与 ",[212,129288,129290,129332],{"className":129289,"translate":216},[215],[212,129291,129293],{"className":129292},[220],[222,129294,129295],{"xmlns":224},[226,129296,129297,129329],{},[229,129298,129299,129305,129307,129309,129311,129313,129315,129317,129319,129321,129323,129325,129327],{},[392,129300,129301,129303],{},[232,129302,966],{},[312,129304,323],{},[307,129306,320],{},[307,129308,310],{"stretchy":309},[312,129310,314],{},[307,129312,5011],{},[232,129314,11],{},[307,129316,317],{"stretchy":309},[232,129318,1138],{"mathvariant":406},[307,129320,310],{"stretchy":309},[312,129322,314],{},[307,129324,5011],{},[232,129326,1141],{},[307,129328,317],{"stretchy":309},[236,129330,129331],{"encoding":238},"t_0=(1-p)\u002F(1-q)",[212,129333,129335,129390,129411,129441],{"className":129334,"ariaHidden":243},[242],[212,129336,129338,129341,129381,129384,129387],{"className":129337},[247],[212,129339],{"className":129340,"style":96141},[251],[212,129342,129344,129347],{"className":129343},[256],[212,129345,966],{"className":129346},[256,257],[212,129348,129350],{"className":129349},[478],[212,129351,129353,129373],{"className":129352},[482,483],[212,129354,129356,129370],{"className":129355},[487],[212,129357,129359],{"className":129358,"style":11333},[491],[212,129360,129361,129364],{"style":579},[212,129362],{"className":129363,"style":500},[499],[212,129365,129367],{"className":129366},[504,505,506,507],[212,129368,323],{"className":129369},[256,507],[212,129371,515],{"className":129372},[514],[212,129374,129376],{"className":129375},[487],[212,129377,129379],{"className":129378,"style":8166},[491],[212,129380],{},[212,129382],{"className":129383,"style":355},[354],[212,129385,320],{"className":129386},[359],[212,129388],{"className":129389,"style":355},[354],[212,129391,129393,129396,129399,129402,129405,129408],{"className":129392},[247],[212,129394],{"className":129395,"style":336},[251],[212,129397,310],{"className":129398},[343],[212,129400,314],{"className":129401},[256],[212,129403],{"className":129404,"style":2785},[354],[212,129406,5011],{"className":129407},[2789],[212,129409],{"className":129410,"style":2785},[354],[212,129412,129414,129417,129420,129423,129426,129429,129432,129435,129438],{"className":129413},[247],[212,129415],{"className":129416,"style":336},[251],[212,129418,11],{"className":129419},[256,257],[212,129421,317],{"className":129422},[350],[212,129424,1138],{"className":129425},[256],[212,129427,310],{"className":129428},[343],[212,129430,314],{"className":129431},[256],[212,129433],{"className":129434,"style":2785},[354],[212,129436,5011],{"className":129437},[2789],[212,129439],{"className":129440,"style":2785},[354],[212,129442,129444,129447,129450],{"className":129443},[247],[212,129445],{"className":129446,"style":336},[251],[212,129448,1141],{"className":129449,"style":1178},[256,257],[212,129451,317],{"className":129452},[350],[212,129454,129456,129474],{"className":129455,"translate":216},[215],[212,129457,129459],{"className":129458},[220],[222,129460,129461],{"xmlns":224},[226,129462,129463,129471],{},[229,129464,129465,129467,129469],{},[312,129466,314],{},[307,129468,5011],{},[232,129470,1141],{},[236,129472,129473],{"encoding":238},"1-q",[212,129475,129477,129495],{"className":129476,"ariaHidden":243},[242],[212,129478,129480,129483,129486,129489,129492],{"className":129479},[247],[212,129481],{"className":129482,"style":12778},[251],[212,129484,314],{"className":129485},[256],[212,129487],{"className":129488,"style":2785},[354],[212,129490,5011],{"className":129491},[2789],[212,129493],{"className":129494,"style":2785},[354],[212,129496,129498,129501],{"className":129497},[247],[212,129499],{"className":129500,"style":2474},[251],[212,129502,1141],{"className":129503,"style":1178},[256,257],[212,129505,129507],{"className":129506,"translate":216},[377],[212,129508,129510,129592],{"className":129509,"translate":216},[215],[212,129511,129513],{"className":129512},[220],[222,129514,129515],{"xmlns":224,"display":386},[226,129516,129517,129589],{},[229,129518,129519,129529,129531,129533,129535,129537,129539,129541,129543,129545,129547,129553,129555,129557,129559,129561,129563,129565,129567,129569,129587],{},[392,129520,129521,129523],{},[232,129522,396],{},[229,129524,129525,129527],{},[232,129526,10894],{},[232,129528,22093],{},[307,129530,310],{"stretchy":309},[232,129532,403],{},[232,129534,407],{"mathvariant":406},[232,129536,410],{},[307,129538,317],{"stretchy":309},[307,129540,320],{},[232,129542,11],{},[232,129544,4298],{},[307,129546,4301],{},[435,129548,129549,129551],{},[232,129550,11],{},[232,129552,1141],{},[307,129554,2668],{},[307,129556,310],{"stretchy":309},[312,129558,314],{},[307,129560,5011],{},[232,129562,11],{},[307,129564,317],{"stretchy":309},[232,129566,4298],{},[307,129568,4301],{},[435,129570,129571,129579],{},[229,129572,129573,129575,129577],{},[312,129574,314],{},[307,129576,5011],{},[232,129578,11],{},[229,129580,129581,129583,129585],{},[312,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",[212,130667,130669,130691],{"className":130668,"translate":216},[215],[212,130670,130672],{"className":130671},[220],[222,130673,130674],{"xmlns":224},[226,130675,130676,130688],{},[229,130677,130678],{},[392,130679,130680,130682],{},[232,130681,396],{},[229,130683,130684,130686],{},[232,130685,10894],{},[232,130687,22093],{},[236,130689,130690],{"encoding":238},"D_{KL}",[212,130692,130694],{"className":130693,"ariaHidden":243},[242],[212,130695,130697,130700],{"className":130696},[247],[212,130698],{"className":130699,"style":16161},[251],[212,130701,130703,130706],{"className":130702},[256],[212,130704,396],{"className":130705,"style":474},[256,257],[212,130707,130709],{"className":130708},[478],[212,130710,130712,130738],{"className":130711},[482,483],[212,130713,130715,130735],{"className":130714},[487],[212,130716,130718],{"className":130717,"style":576},[491],[212,130719,130720,130723],{"style":495},[212,130721],{"className":130722,"style":500},[499],[212,130724,130726],{"className":130725},[504,505,506,507],[212,130727,130729,130732],{"className":130728},[256,507],[212,130730,10894],{"className":130731,"style":10982},[256,257,507],[212,130733,22093],{"className":130734},[256,257,507],[212,130736,515],{"className":130737},[514],[212,130739,130741],{"className":130740},[487],[212,130742,130744],{"className":130743,"style":8166},[491],[212,130745],{},[212,130747,130749,130762],{"className":130748,"translate":216},[215],[212,130750,130752],{"className":130751},[220],[222,130753,130754],{"xmlns":224},[226,130755,130756,130760],{},[229,130757,130758],{},[232,130759,11],{},[236,130761,11],{"encoding":238},[212,130763,130765],{"className":130764,"ariaHidden":243},[242],[212,130766,130768,130771],{"className":130767},[247],[212,130769],{"className":130770,"style":2474},[251],[212,130772,11],{"className":130773},[256,257],[212,130775,130777,130795],{"className":130776,"translate":216},[215],[212,130778,130780],{"className":130779},[220],[222,130781,130782],{"xmlns":224},[226,130783,130784,130792],{},[229,130785,130786,130788,130790],{},[232,130787,11],{},[307,130789,320],{},[232,130791,1141],{},[236,130793,130794],{"encoding":238},"p=q",[212,130796,130798,130816],{"className":130797,"ariaHidden":243},[242],[212,130799,130801,130804,130807,130810,130813],{"className":130800},[247],[212,130802],{"className":130803,"style":2474},[251],[212,130805,11],{"className":130806},[256,257],[212,130808],{"className":130809,"style":355},[354],[212,130811,320],{"className":130812},[359],[212,130814],{"className":130815,"style":355},[354],[212,130817,130819,130822],{"className":130818},[247],[212,130820],{"className":130821,"style":2474},[251],[212,130823,1141],{"className":130824,"style":1178},[256,257]," 处做二阶展开，应回到 ",[212,130827,130829,130889],{"className":130828,"translate":216},[215],[212,130830,130832],{"className":130831},[220],[222,130833,130834],{"xmlns":224},[226,130835,130836,130886],{},[229,130837,130838,130872,130874,130880],{},[435,130839,130840,130856],{},[229,130841,130842,130844,130846,130848,130850],{},[307,130843,310],{"stretchy":309},[232,130845,11],{},[307,130847,5011],{},[232,130849,1141],{},[7012,130851,130852,130854],{},[307,130853,317],{"stretchy":309},[312,130855,2661],{},[229,130857,130858,130860,130862,130864,130866,130868,130870],{},[312,130859,2661],{},[232,130861,1141],{},[307,130863,310],{"stretchy":309},[312,130865,314],{},[307,130867,5011],{},[232,130869,1141],{},[307,130871,317],{"stretchy":309},[307,130873,320],{},[435,130875,130876,130878],{},[312,130877,314],{},[312,130879,2661],{},[7012,130881,130882,130884],{},[232,130883,37649],{},[312,130885,2661],{},[236,130887,130888],{"encoding":238},"\\frac{(p-q)^2}{2q(1-q)}=\\frac12\\chi^2",[212,130890,130892,131032],{"className":130891,"ariaHidden":243},[242],[212,130893,130895,130899,131023,131026,131029],{"className":130894},[247],[212,130896],{"className":130897,"style":130898},[251],"height:1.6289em;vertical-align:-0.52em;",[212,130900,130902,130905,131020],{"className":130901},[256],[212,130903],{"className":130904},[343,638],[212,130906,130908],{"className":130907},[435],[212,130909,130911,131012],{"className":130910},[482,483],[212,130912,130914,131009],{"className":130913},[487],[212,130915,130917,130949,130957],{"className":130916,"style":38648},[491],[212,130918,130919,130922],{"style":2725},[212,130920],{"className":130921,"style":658},[499],[212,130923,130925],{"className":130924},[504,505,506,507],[212,130926,130928,130931,130934,130937,130940,130943,130946],{"className":130927},[256,507],[212,130929,2661],{"className":130930},[256,507],[212,130932,1141],{"className":130933,"style":1178},[256,257,507],[212,130935,310],{"className":130936},[343,507],[212,130938,314],{"className":130939},[256,507],[212,130941,5011],{"className":130942},[2789,507],[212,130944,1141],{"className":130945,"style":1178},[256,257,507],[212,130947,317],{"className":130948},[350,507],[212,130950,130951,130954],{"style":670},[212,130952],{"className":130953,"style":658},[499],[212,130955],{"className":130956,"style":678},[677],[212,130958,130959,130962],{"style":26618},[212,130960],{"className":130961,"style":658},[499],[212,130963,130965],{"className":130964},[504,505,506,507],[212,130966,130968,130971,130974,130977,130980],{"className":130967},[256,507],[212,130969,310],{"className":130970},[343,507],[212,130972,11],{"className":130973},[256,257,507],[212,130975,5011],{"className":130976},[2789,507],[212,130978,1141],{"className":130979,"style":1178},[256,257,507],[212,130981,130983,130986],{"className":130982},[350,507],[212,130984,317],{"className":130985},[350,507],[212,130987,130989],{"className":130988},[478],[212,130990,130992],{"className":130991},[482],[212,130993,130995],{"className":130994},[487],[212,130996,130998],{"className":130997,"style":38712},[491],[212,130999,131000,131003],{"style":38715},[212,131001],{"className":131002,"style":30406},[499],[212,131004,131006],{"className":131005},[504,30410,9872,507],[212,131007,2661],{"className":131008},[256,507],[212,131010,515],{"className":131011},[514],[212,131013,131015],{"className":131014},[487],[212,131016,131018],{"className":131017,"style":45801},[491],[212,131019],{},[212,131021],{"className":131022},[350,638],[212,131024],{"className":131025,"style":355},[354],[212,131027,320],{"className":131028},[359],[212,131030],{"className":131031,"style":355},[354],[212,131033,131035,131038,131106],{"className":131034},[247],[212,131036],{"className":131037,"style":2703},[251],[212,131039,131041,131044,131103],{"className":131040},[256],[212,131042],{"className":131043},[343,638],[212,131045,131047],{"className":131046},[435],[212,131048,131050,131095],{"className":131049},[482,483],[212,131051,131053,131092],{"className":131052},[487],[212,131054,131056,131070,131078],{"className":131055,"style":2722},[491],[212,131057,131058,131061],{"style":2725},[212,131059],{"className":131060,"style":658},[499],[212,131062,131064],{"className":131063},[504,505,506,507],[212,131065,131067],{"className":131066},[256,507],[212,131068,2661],{"className":131069},[256,507],[212,131071,131072,131075],{"style":670},[212,131073],{"className":131074,"style":658},[499],[212,131076],{"className":131077,"style":678},[677],[212,131079,131080,131083],{"style":2748},[212,131081],{"className":131082,"style":658},[499],[212,131084,131086],{"className":131085},[504,505,506,507],[212,131087,131089],{"className":131088},[256,507],[212,131090,314],{"className":131091},[256,507],[212,131093,515],{"className":131094},[514],[212,131096,131098],{"className":131097},[487],[212,131099,131101],{"className":131100,"style":2770},[491],[212,131102],{},[212,131104],{"className":131105},[350,638],[212,131107,131109,131112],{"className":131108},[256],[212,131110,37649],{"className":131111},[256,257],[212,131113,131115],{"className":131114},[478],[212,131116,131118],{"className":131117},[482],[212,131119,131121],{"className":131120},[487],[212,131122,131124],{"className":131123,"style":20228},[491],[212,131125,131126,131129],{"style":7063},[212,131127],{"className":131128,"style":500},[499],[212,131130,131132],{"className":131131},[504,505,506,507],[212,131133,2661],{"className":131134},[256,507],"，与 4.6 节吻合。",[2509,131137,131139],{"id":131138},"_93-用对偶表示反推-kl","9.3 用对偶表示反推 KL",[11,131141,131142,131143,5843,131228,131369,131370,9598],{},"取 ",[212,131144,131146,131175],{"className":131145,"translate":216},[215],[212,131147,131149],{"className":131148},[220],[222,131150,131151],{"xmlns":224},[226,131152,131153,131173],{},[229,131154,131155,131157,131159,131161,131163,131165,131167,131169,131171],{},[232,131156,234],{},[307,131158,310],{"stretchy":309},[232,131160,966],{},[307,131162,317],{"stretchy":309},[307,131164,320],{},[232,131166,966],{},[232,131168,4298],{},[307,131170,4301],{},[232,131172,966],{},[236,131174,4306],{"encoding":238},[212,131176,131178,131205],{"className":131177,"ariaHidden":243},[242],[212,131179,131181,131184,131187,131190,131193,131196,131199,131202],{"className":131180},[247],[212,131182],{"className":131183,"style":336},[251],[212,131185,234],{"className":131186,"style":258},[256,257],[212,131188,310],{"className":131189},[343],[212,131191,966],{"className":131192},[256,257],[212,131194,317],{"className":131195},[350],[212,131197],{"className":131198,"style":355},[354],[212,131200,320],{"className":131201},[359],[212,131203],{"className":131204,"style":355},[354],[212,131206,131208,131211,131214,131217,131222,131225],{"className":131207},[247],[212,131209],{"className":131210,"style":252},[251],[212,131212,966],{"className":131213},[256,257],[212,131215],{"className":131216,"style":603},[354],[212,131218,4352,131220],{"className":131219},[1682],[212,131221,4356],{"style":4355},[212,131223],{"className":131224,"style":603},[354],[212,131226,966],{"className":131227},[256,257],[212,131229,131231,131269],{"className":131230,"translate":216},[215],[212,131232,131234],{"className":131233},[220],[222,131235,131236],{"xmlns":224},[226,131237,131238,131266],{},[229,131239,131240,131246,131248,131250,131252,131254],{},[7012,131241,131242,131244],{},[232,131243,234],{},[307,131245,7771],{},[307,131247,310],{"stretchy":309},[232,131249,40437],{},[307,131251,317],{"stretchy":309},[307,131253,320],{},[7012,131255,131256,131258],{},[232,131257,7765],{},[229,131259,131260,131262,131264],{},[232,131261,40437],{},[307,131263,5011],{},[312,131265,314],{},[236,131267,131268],{"encoding":238},"f^*(y)=e^{y-1}",[212,131270,131272,131325],{"className":131271,"ariaHidden":243},[242],[212,131273,131275,131278,131307,131310,131313,131316,131319,131322],{"className":131274},[247],[212,131276],{"className":131277,"style":336},[251],[212,131279,131281,131284],{"className":131280},[256],[212,131282,234],{"className":131283,"style":258},[256,257],[212,131285,131287],{"className":131286},[478],[212,131288,131290],{"className":131289},[482],[212,131291,131293],{"className":131292},[487],[212,131294,131296],{"className":131295,"style":8697},[491],[212,131297,131298,131301],{"style":7063},[212,131299],{"className":131300,"style":500},[499],[212,131302,131304],{"className":131303},[504,505,506,507],[212,131305,7771],{"className":131306},[2789,507],[212,131308,310],{"className":131309},[343],[212,131311,40437],{"className":131312,"style":1178},[256,257],[212,131314,317],{"className":131315},[350],[212,131317],{"className":131318,"style":355},[354],[212,131320,320],{"className":131321},[359],[212,131323],{"className":131324,"style":355},[354],[212,131326,131328,131331],{"className":131327},[247],[212,131329],{"className":131330,"style":20228},[251],[212,131332,131334,131337],{"className":131333},[256],[212,131335,7765],{"className":131336},[256,257],[212,131338,131340],{"className":131339},[478],[212,131341,131343],{"className":131342},[482],[212,131344,131346],{"className":131345},[487],[212,131347,131349],{"className":131348,"style":20228},[491],[212,131350,131351,131354],{"style":7063},[212,131352],{"className":131353,"style":500},[499],[212,131355,131357],{"className":131356},[504,505,506,507],[212,131358,131360,131363,131366],{"className":131359},[256,507],[212,131361,40437],{"className":131362,"style":1178},[256,257,507],[212,131364,5011],{"className":131365},[2789,507],[212,131367,314],{"className":131368},[256,507],"，则对任意 ",[212,131371,131373,131386],{"className":131372,"translate":216},[215],[212,131374,131376],{"className":131375},[220],[222,131377,131378],{"xmlns":224},[226,131379,131380,131384],{},[229,131381,131382],{},[232,131383,4356],{},[236,131385,4356],{"encoding":238},[212,131387,131389],{"className":131388,"ariaHidden":243},[242],[212,131390,131392,131395],{"className":131391},[247],[212,131393],{"className":131394,"style":2474},[251],[212,131396,4356],{"className":131397,"style":1178},[256,257],[212,131399,131401],{"className":131400,"translate":216},[377],[212,131402,131404,131476],{"className":131403,"translate":216},[215],[212,131405,131407],{"className":131406},[220],[222,131408,131409],{"xmlns":224,"display":386},[226,131410,131411,131473],{},[229,131412,131413,131423,131425,131427,131429,131431,131433,131435,131441,131443,131445,131447,131449,131455,131457,131469,131471],{},[392,131414,131415,131417],{},[232,131416,396],{},[229,131418,131419,131421],{},[232,131420,10894],{},[232,131422,22093],{},[307,131424,310],{"stretchy":309},[232,131426,403],{},[232,131428,407],{"mathvariant":406},[232,131430,410],{},[307,131432,317],{"stretchy":309},[307,131434,7126],{},[392,131436,131437,131439],{},[232,131438,420],{"mathvariant":419},[232,131440,403],{},[307,131442,427],{"stretchy":309},[232,131444,4356],{},[307,131446,454],{"stretchy":309},[307,131448,5011],{},[392,131450,131451,131453],{},[232,131452,420],{"mathvariant":419},[232,131454,410],{},[307,131456,427],{"stretchy":309},[7012,131458,131459,131461],{},[232,131460,7765],{},[229,131462,131463,131465,131467],{},[232,131464,4356],{},[307,131466,5011],{},[312,131468,314],{},[307,131470,454],{"stretchy":309},[307,131472,748],{"separator":243},[236,131474,131475],{"encoding":238},"D_{KL}(P\\|Q)\\ge \\mathbb E_P[g]\n-\\mathbb E_Q[e^{g-1}],",[212,131477,131479,131555,131619],{"className":131478,"ariaHidden":243},[242],[212,131480,131482,131485,131531,131534,131537,131540,131543,131546,131549,131552],{"className":131481},[247],[212,131483],{"className":131484,"style":336},[251],[212,131486,131488,131491],{"className":131487},[256],[212,131489,396],{"className":131490,"style":474},[256,257],[212,131492,131494],{"className":131493},[478],[212,131495,131497,131523],{"className":131496},[482,483],[212,131498,131500,131520],{"className":131499},[487],[212,131501,131503],{"className":131502,"style":576},[491],[212,131504,131505,131508],{"style":495},[212,131506],{"className":131507,"style":500},[499],[212,131509,131511],{"className":131510},[504,505,506,507],[212,131512,131514,131517],{"className":131513},[256,507],[212,131515,10894],{"className":131516,"style":10982},[256,257,507],[212,131518,22093],{"className":131519},[256,257,507],[212,131521,515],{"className":131522},[514],[212,131524,131526],{"className":131525},[487],[212,131527,131529],{"className":131528,"style":8166},[491],[212,131530],{},[212,131532,310],{"className":131533},[343],[212,131535,403],{"className":131536,"style":531},[256,257],[212,131538,407],{"className":131539},[256],[212,131541,410],{"className":131542},[256,257],[212,131544,317],{"className":131545},[350],[212,131547],{"className":131548,"style":355},[354],[212,131550,7126],{"className":131551},[359],[212,131553],{"className":131554,"style":355},[354],[212,131556,131558,131561,131601,131604,131607,131610,131613,131616],{"className":131557},[247],[212,131559],{"className":131560,"style":336},[251],[212,131562,131564,131567],{"className":131563},[256],[212,131565,420],{"className":131566},[256,563],[212,131568,131570],{"className":131569},[478],[212,131571,131573,131593],{"className":131572},[482,483],[212,131574,131576,131590],{"className":131575},[487],[212,131577,131579],{"className":131578,"style":576},[491],[212,131580,131581,131584],{"style":579},[212,131582],{"className":131583,"style":500},[499],[212,131585,131587],{"className":131586},[504,505,506,507],[212,131588,403],{"className":131589,"style":531},[256,257,507],[212,131591,515],{"className":131592},[514],[212,131594,131596],{"className":131595},[487],[212,131597,131599],{"className":131598,"style":8166},[491],[212,131600],{},[212,131602,427],{"className":131603},[343],[212,131605,4356],{"className":131606,"style":1178},[256,257],[212,131608,454],{"className":131609},[350],[212,131611],{"className":131612,"style":2785},[354],[212,131614,5011],{"className":131615},[2789],[212,131617],{"className":131618,"style":2785},[354],[212,131620,131622,131626,131666,131669,131707,131710],{"className":131621},[247],[212,131623],{"className":131624,"style":131625},[251],"height:1.1502em;vertical-align:-0.2861em;",[212,131627,131629,131632],{"className":131628},[256],[212,131630,420],{"className":131631},[256,563],[212,131633,131635],{"className":131634},[478],[212,131636,131638,131658],{"className":131637},[482,483],[212,131639,131641,131655],{"className":131640},[487],[212,131642,131644],{"className":131643,"style":576},[491],[212,131645,131646,131649],{"style":579},[212,131647],{"className":131648,"style":500},[499],[212,131650,131652],{"className":131651},[504,505,506,507],[212,131653,410],{"className":131654},[256,257,507],[212,131656,515],{"className":131657},[514],[212,131659,131661],{"className":131660},[487],[212,131662,131664],{"className":131663,"style":522},[491],[212,131665],{},[212,131667,427],{"className":131668},[343],[212,131670,131672,131675],{"className":131671},[256],[212,131673,7765],{"className":131674},[256,257],[212,131676,131678],{"className":131677},[478],[212,131679,131681],{"className":131680},[482],[212,131682,131684],{"className":131683},[487],[212,131685,131687],{"className":131686,"style":19935},[491],[212,131688,131689,131692],{"style":8475},[212,131690],{"className":131691,"style":500},[499],[212,131693,131695],{"className":131694},[504,505,506,507],[212,131696,131698,131701,131704],{"className":131697},[256,507],[212,131699,4356],{"className":131700,"style":1178},[256,257,507],[212,131702,5011],{"className":131703},[2789,507],[212,131705,314],{"className":131706},[256,507],[212,131708,454],{"className":131709},[350],[212,131711,748],{"className":131712},[770],[11,131714,131715,131716,131818],{},"等号在 ",[212,131717,131719,131753],{"className":131718,"translate":216},[215],[212,131720,131722],{"className":131721},[220],[222,131723,131724],{"xmlns":224},[226,131725,131726,131750],{},[229,131727,131728,131730,131732,131734,131736,131738,131740,131742,131744,131746,131748],{},[232,131729,4356],{},[307,131731,320],{},[232,131733,4298],{},[307,131735,4301],{},[307,131737,310],{"stretchy":309},[232,131739,11],{},[232,131741,1138],{"mathvariant":406},[232,131743,1141],{},[307,131745,317],{"stretchy":309},[307,131747,2668],{},[312,131749,314],{},[236,131751,131752],{"encoding":238},"g=\\log(p\u002Fq)+1",[212,131754,131756,131774,131809],{"className":131755,"ariaHidden":243},[242],[212,131757,131759,131762,131765,131768,131771],{"className":131758},[247],[212,131760],{"className":131761,"style":2474},[251],[212,131763,4356],{"className":131764,"style":1178},[256,257],[212,131766],{"className":131767,"style":355},[354],[212,131769,320],{"className":131770},[359],[212,131772],{"className":131773,"style":355},[354],[212,131775,131777,131780,131785,131788,131791,131794,131797,131800,131803,131806],{"className":131776},[247],[212,131778],{"className":131779,"style":336},[251],[212,131781,4352,131783],{"className":131782},[1682],[212,131784,4356],{"style":4355},[212,131786,310],{"className":131787},[343],[212,131789,11],{"className":131790},[256,257],[212,131792,1138],{"className":131793},[256],[212,131795,1141],{"className":131796,"style":1178},[256,257],[212,131798,317],{"className":131799},[350],[212,131801],{"className":131802,"style":2785},[354],[212,131804,2668],{"className":131805},[2789],[212,131807],{"className":131808,"style":2785},[354],[212,131810,131812,131815],{"className":131811},[247],[212,131813],{"className":131814,"style":369},[251],[212,131816,314],{"className":131817},[256]," 处取到。代回：",[212,131820,131822],{"className":131821,"translate":216},[377],[212,131823,131825,131951],{"className":131824,"translate":216},[215],[212,131826,131828],{"className":131827},[220],[222,131829,131830],{"xmlns":224,"display":386},[226,131831,131832,131948],{},[229,131833,131834,131840,131842,131844,131846,131848,131850,131852,131854,131856,131858,131860,131862,131864,131870,131872,131892,131894,131896,131906,131908,131910,131912,131914,131916,131918,131920,131922,131924,131926,131936,131938,131940,131942,131944,131946],{},[392,131835,131836,131838],{},[232,131837,420],{"mathvariant":419},[232,131839,403],{},[307,131841,427],{"stretchy":309},[232,131843,4298],{},[307,131845,4301],{},[307,131847,310],{"stretchy":309},[232,131849,11],{},[232,131851,1138],{"mathvariant":406},[232,131853,1141],{},[307,131855,317],{"stretchy":309},[307,131857,2668],{},[312,131859,314],{},[307,131861,454],{"stretchy":309},[307,131863,5011],{},[392,131865,131866,131868],{},[232,131867,420],{"mathvariant":419},[232,131869,410],{},[307,131871,427],{"stretchy":309},[7012,131873,131874,131876],{},[232,131875,7765],{},[229,131877,131878,131880,131882,131884,131886,131888,131890],{},[232,131879,4298],{},[307,131881,4301],{},[307,131883,310],{"stretchy":309},[232,131885,11],{},[232,131887,1138],{"mathvariant":406},[232,131889,1141],{},[307,131891,317],{"stretchy":309},[307,131893,454],{"stretchy":309},[307,131895,320],{},[392,131897,131898,131900],{},[232,131899,396],{},[229,131901,131902,131904],{},[232,131903,10894],{},[232,131905,22093],{},[307,131907,310],{"stretchy":309},[232,131909,403],{},[232,131911,407],{"mathvariant":406},[232,131913,410],{},[307,131915,317],{"stretchy":309},[307,131917,2668],{},[312,131919,314],{},[307,131921,5011],{},[312,131923,314],{},[307,131925,320],{},[392,131927,131928,131930],{},[232,131929,396],{},[229,131931,131932,131934],{},[232,131933,10894],{},[232,131935,22093],{},[307,131937,310],{"stretchy":309},[232,131939,403],{},[232,131941,407],{"mathvariant":406},[232,131943,410],{},[307,131945,317],{"stretchy":309},[307,131947,748],{"separator":243},[236,131949,131950],{"encoding":238},"\\mathbb E_P[\\log(p\u002Fq)+1]\n-\\mathbb E_Q[e^{\\log(p\u002Fq)}]\n=D_{KL}(P\\|Q)+1-1=D_{KL}(P\\|Q),",[212,131952,131954,132032,132053,132171,132247,132265,132283],{"className":131953,"ariaHidden":243},[242],[212,131955,131957,131960,132000,132003,132008,132011,132014,132017,132020,132023,132026,132029],{"className":131956},[247],[212,131958],{"className":131959,"style":336},[251],[212,131961,131963,131966],{"className":131962},[256],[212,131964,420],{"className":131965},[256,563],[212,131967,131969],{"className":131968},[478],[212,131970,131972,131992],{"className":131971},[482,483],[212,131973,131975,131989],{"className":131974},[487],[212,131976,131978],{"className":131977,"style":576},[491],[212,131979,131980,131983],{"style":579},[212,131981],{"className":131982,"style":500},[499],[212,131984,131986],{"className":131985},[504,505,506,507],[212,131987,403],{"className":131988,"style":531},[256,257,507],[212,131990,515],{"className":131991},[514],[212,131993,131995],{"className":131994},[487],[212,131996,131998],{"className":131997,"style":8166},[491],[212,131999],{},[212,132001,427],{"className":132002},[343],[212,132004,4352,132006],{"className":132005},[1682],[212,132007,4356],{"style":4355},[212,132009,310],{"className":132010},[343],[212,132012,11],{"className":132013},[256,257],[212,132015,1138],{"className":132016},[256],[212,132018,1141],{"className":132019,"style":1178},[256,257],[212,132021,317],{"className":132022},[350],[212,132024],{"className":132025,"style":2785},[354],[212,132027,2668],{"className":132028},[2789],[212,132030],{"className":132031,"style":2785},[354],[212,132033,132035,132038,132041,132044,132047,132050],{"className":132034},[247],[212,132036],{"className":132037,"style":336},[251],[212,132039,314],{"className":132040},[256],[212,132042,454],{"className":132043},[350],[212,132045],{"className":132046,"style":2785},[354],[212,132048,5011],{"className":132049},[2789],[212,132051],{"className":132052,"style":2785},[354],[212,132054,132056,132060,132100,132103,132159,132162,132165,132168],{"className":132055},[247],[212,132057],{"className":132058,"style":132059},[251],"height:1.2241em;vertical-align:-0.2861em;",[212,132061,132063,132066],{"className":132062},[256],[212,132064,420],{"className":132065},[256,563],[212,132067,132069],{"className":132068},[478],[212,132070,132072,132092],{"className":132071},[482,483],[212,132073,132075,132089],{"className":132074},[487],[212,132076,132078],{"className":132077,"style":576},[491],[212,132079,132080,132083],{"style":579},[212,132081],{"className":132082,"style":500},[499],[212,132084,132086],{"className":132085},[504,505,506,507],[212,132087,410],{"className":132088},[256,257,507],[212,132090,515],{"className":132091},[514],[212,132093,132095],{"className":132094},[487],[212,132096,132098],{"className":132097,"style":522},[491],[212,132099],{},[212,132101,427],{"className":132102},[343],[212,132104,132106,132109],{"className":132105},[256],[212,132107,7765],{"className":132108},[256,257],[212,132110,132112],{"className":132111},[478],[212,132113,132115],{"className":132114},[482],[212,132116,132118],{"className":132117},[487],[212,132119,132121],{"className":132120,"style":45320},[491],[212,132122,132123,132126],{"style":8475},[212,132124],{"className":132125,"style":500},[499],[212,132127,132129],{"className":132128},[504,505,506,507],[212,132130,132132,132144,132147,132150,132153,132156],{"className":132131},[256,507],[212,132133,132135,132138,132141],{"className":132134},[1682,507],[212,132136,47857],{"className":132137},[507],[212,132139,47861],{"className":132140},[507],[212,132142,4356],{"className":132143,"style":4355},[507],[212,132145,310],{"className":132146},[343,507],[212,132148,11],{"className":132149},[256,257,507],[212,132151,1138],{"className":132152},[256,507],[212,132154,1141],{"className":132155,"style":1178},[256,257,507],[212,132157,317],{"className":132158},[350,507],[212,132160,454],{"className":132161},[350],[212,132163],{"className":132164,"style":355},[354],[212,132166,320],{"className":132167},[359],[212,132169],{"className":132170,"style":355},[354],[212,132172,132174,132177,132223,132226,132229,132232,132235,132238,132241,132244],{"className":132173},[247],[212,132175],{"className":132176,"style":336},[251],[212,132178,132180,132183],{"className":132179},[256],[212,132181,396],{"className":132182,"style":474},[256,257],[212,132184,132186],{"className":132185},[478],[212,132187,132189,132215],{"className":132188},[482,483],[212,132190,132192,132212],{"className":132191},[487],[212,132193,132195],{"className":132194,"style":576},[491],[212,132196,132197,132200],{"style":495},[212,132198],{"className":132199,"style":500},[499],[212,132201,132203],{"className":132202},[504,505,506,507],[212,132204,132206,132209],{"className":132205},[256,507],[212,132207,10894],{"className":132208,"style":10982},[256,257,507],[212,132210,22093],{"className":132211},[256,257,507],[212,132213,515],{"className":132214},[514],[212,132216,132218],{"className":132217},[487],[212,132219,132221],{"className":132220,"style":8166},[491],[212,132222],{},[212,132224,310],{"className":132225},[343],[212,132227,403],{"className":132228,"style":531},[256,257],[212,132230,407],{"className":132231},[256],[212,132233,410],{"className":132234},[256,257],[212,132236,317],{"className":132237},[350],[212,132239],{"className":132240,"style":2785},[354],[212,132242,2668],{"className":132243},[2789],[212,132245],{"className":132246,"style":2785},[354],[212,132248,132250,132253,132256,132259,132262],{"className":132249},[247],[212,132251],{"className":132252,"style":12778},[251],[212,132254,314],{"className":132255},[256],[212,132257],{"className":132258,"style":2785},[354],[212,132260,5011],{"className":132261},[2789],[212,132263],{"className":132264,"style":2785},[354],[212,132266,132268,132271,132274,132277,132280],{"className":132267},[247],[212,132269],{"className":132270,"style":369},[251],[212,132272,314],{"className":132273},[256],[212,132275],{"className":132276,"style":355},[354],[212,132278,320],{"className":132279},[359],[212,132281],{"className":132282,"style":355},[354],[212,132284,132286,132289,132335,132338,132341,132344,132347,132350],{"className":132285},[247],[212,132287],{"className":132288,"style":336},[251],[212,132290,132292,132295],{"className":132291},[256],[212,132293,396],{"className":132294,"style":474},[256,257],[212,132296,132298],{"className":132297},[478],[212,132299,132301,132327],{"className":132300},[482,483],[212,132302,132304,132324],{"className":132303},[487],[212,132305,132307],{"className":132306,"style":576},[491],[212,132308,132309,132312],{"style":495},[212,132310],{"className":132311,"style":500},[499],[212,132313,132315],{"className":132314},[504,505,506,507],[212,132316,132318,132321],{"className":132317},[256,507],[212,132319,10894],{"className":132320,"style":10982},[256,257,507],[212,132322,22093],{"className":132323},[256,257,507],[212,132325,515],{"className":132326},[514],[212,132328,132330],{"className":132329},[487],[212,132331,132333],{"className":132332,"style":8166},[491],[212,132334],{},[212,132336,310],{"className":132337},[343],[212,132339,403],{"className":132340,"style":531},[256,257],[212,132342,407],{"className":132343},[256],[212,132345,410],{"className":132346},[256,257],[212,132348,317],{"className":132349},[350],[212,132351,748],{"className":132352},[770],[11,132354,132355],{},"完全自洽。这给出了一个「可验证」的对偶表示练习。",[725,132357,132359],{"id":132358},"_10-结论","10. 结论",[11,132361,132362],{},"f-散度族的故事可以浓缩成三句话：",[6860,132364,132365,132668,132834],{},[6863,132366,132367,9598,132370,2943,132575,92685,132603,10378],{},[1194,132368,132369],{},"一个模板",[212,132371,132373,132429],{"className":132372,"translate":216},[215],[212,132374,132376],{"className":132375},[220],[222,132377,132378],{"xmlns":224},[226,132379,132380,132426],{},[229,132381,132382,132388,132390,132392,132394,132396,132398,132400,132406,132408,132410,132412,132414,132416,132418,132420,132422,132424],{},[392,132383,132384,132386],{},[232,132385,396],{},[232,132387,234],{},[307,132389,310],{"stretchy":309},[232,132391,403],{},[232,132393,407],{"mathvariant":406},[232,132395,410],{},[307,132397,317],{"stretchy":309},[307,132399,320],{},[392,132401,132402,132404],{},[232,132403,420],{"mathvariant":419},[232,132405,410],{},[307,132407,427],{"stretchy":309},[232,132409,234],{},[307,132411,310],{"stretchy":309},[232,132413,441],{},[232,132415,403],{},[232,132417,1138],{"mathvariant":406},[232,132419,441],{},[232,132421,410],{},[307,132423,317],{"stretchy":309},[307,132425,454],{"stretchy":309},[236,132427,132428],{"encoding":238},"D_f(P\\|Q)=\\mathbb E_Q[f(dP\u002FdQ)]",[212,132430,132432,132502],{"className":132431,"ariaHidden":243},[242],[212,132433,132435,132438,132478,132481,132484,132487,132490,132493,132496,132499],{"className":132434},[247],[212,132436],{"className":132437,"style":467},[251],[212,132439,132441,132444],{"className":132440},[256],[212,132442,396],{"className":132443,"style":474},[256,257],[212,132445,132447],{"className":132446},[478],[212,132448,132450,132470],{"className":132449},[482,483],[212,132451,132453,132467],{"className":132452},[487],[212,132454,132456],{"className":132455,"style":492},[491],[212,132457,132458,132461],{"style":495},[212,132459],{"className":132460,"style":500},[499],[212,132462,132464],{"className":132463},[504,505,506,507],[212,132465,234],{"className":132466,"style":258},[256,257,507],[212,132468,515],{"className":132469},[514],[212,132471,132473],{"className":132472},[487],[212,132474,132476],{"className":132475,"style":522},[491],[212,132477],{},[212,132479,310],{"className":132480},[343],[212,132482,403],{"className":132483,"style":531},[256,257],[212,132485,407],{"className":132486},[256],[212,132488,410],{"className":132489},[256,257],[212,132491,317],{"className":132492},[350],[212,132494],{"className":132495,"style":355},[354],[212,132497,320],{"className":132498},[359],[212,132500],{"className":132501,"style":355},[354],[212,132503,132505,132508,132548,132551,132554,132557,132560,132563,132566,132569,132572],{"className":132504},[247],[212,132506],{"className":132507,"style":467},[251],[212,132509,132511,132514],{"className":132510},[256],[212,132512,420],{"className":132513},[256,563],[212,132515,132517],{"className":132516},[478],[212,132518,132520,132540],{"className":132519},[482,483],[212,132521,132523,132537],{"className":132522},[487],[212,132524,132526],{"className":132525,"style":576},[491],[212,132527,132528,132531],{"style":579},[212,132529],{"className":132530,"style":500},[499],[212,132532,132534],{"className":132533},[504,505,506,507],[212,132535,410],{"className":132536},[256,257,507],[212,132538,515],{"className":132539},[514],[212,132541,132543],{"className":132542},[487],[212,132544,132546],{"className":132545,"style":522},[491],[212,132547],{},[212,132549,427],{"className":132550},[343],[212,132552,234],{"className":132553,"style":258},[256,257],[212,132555,310],{"className":132556},[343],[212,132558,441],{"className":132559},[256,257],[212,132561,403],{"className":132562,"style":531},[256,257],[212,132564,1138],{"className":132565},[256],[212,132567,441],{"className":132568},[256,257],[212,132570,410],{"className":132571},[256,257],[212,132573,20590],{"className":132574},[350],[212,132576,132578,132591],{"className":132577,"translate":216},[215],[212,132579,132581],{"className":132580},[220],[222,132582,132583],{"xmlns":224},[226,132584,132585,132589],{},[229,132586,132587],{},[232,132588,234],{},[236,132590,234],{"encoding":238},[212,132592,132594],{"className":132593,"ariaHidden":243},[242],[212,132595,132597,132600],{"className":132596},[247],[212,132598],{"className":132599,"style":252},[251],[212,132601,234],{"className":132602,"style":258},[256,257],[212,132604,132606,132629],{"className":132605,"translate":216},[215],[212,132607,132609],{"className":132608},[220],[222,132610,132611],{"xmlns":224},[226,132612,132613,132627],{},[229,132614,132615,132617,132619,132621,132623,132625],{},[232,132616,234],{},[307,132618,310],{"stretchy":309},[312,132620,314],{},[307,132622,317],{"stretchy":309},[307,132624,320],{},[312,132626,323],{},[236,132628,326],{"encoding":238},[212,132630,132632,132659],{"className":132631,"ariaHidden":243},[242],[212,132633,132635,132638,132641,132644,132647,132650,132653,132656],{"className":132634},[247],[212,132636],{"className":132637,"style":336},[251],[212,132639,234],{"className":132640,"style":258},[256,257],[212,132642,310],{"className":132643},[343],[212,132645,314],{"className":132646},[256],[212,132648,317],{"className":132649},[350],[212,132651],{"className":132652,"style":355},[354],[212,132654,320],{"className":132655},[359],[212,132657],{"className":132658,"style":355},[354],[212,132660,132662,132665],{"className":132661},[247],[212,132663],{"className":132664,"style":369},[251],[212,132666,323],{"className":132667},[256],[6863,132669,132670,9598,132673,132754,132755,132833],{},[1194,132671,132672],{},"两组对偶",[212,132674,132676,132698],{"className":132675,"translate":216},[215],[212,132677,132679],{"className":132678},[220],[222,132680,132681],{"xmlns":224},[226,132682,132683,132695],{},[229,132684,132685,132687,132689],{},[232,132686,234],{},[307,132688,21559],{},[7012,132690,132691,132693],{},[232,132692,234],{},[307,132694,7771],{},[236,132696,132697],{"encoding":238},"f\\leftrightarrow f^*",[212,132699,132701,132719],{"className":132700,"ariaHidden":243},[242],[212,132702,132704,132707,132710,132713,132716],{"className":132703},[247],[212,132705],{"className":132706,"style":252},[251],[212,132708,234],{"className":132709,"style":258},[256,257],[212,132711],{"className":132712,"style":355},[354],[212,132714,21559],{"className":132715},[359],[212,132717],{"className":132718,"style":355},[354],[212,132720,132722,132725],{"className":132721},[247],[212,132723],{"className":132724,"style":252},[251],[212,132726,132728,132731],{"className":132727},[256],[212,132729,234],{"className":132730,"style":258},[256,257],[212,132732,132734],{"className":132733},[478],[212,132735,132737],{"className":132736},[482],[212,132738,132740],{"className":132739},[487],[212,132741,132743],{"className":132742,"style":8697},[491],[212,132744,132745,132748],{"style":7063},[212,132746],{"className":132747,"style":500},[499],[212,132749,132751],{"className":132750},[504,505,506,507],[212,132752,7771],{"className":132753},[2789,507]," 给出变分表示（可用于估计与对抗训练）；",[212,132756,132758,132788],{"className":132757,"translate":216},[215],[212,132759,132761],{"className":132760},[220],[222,132762,132763],{"xmlns":224},[226,132764,132765,132785],{},[229,132766,132767,132769,132771,132773,132775,132777,132779,132781,132783],{},[232,132768,234],{},[307,132770,21559],{},[232,132772,966],{},[232,132774,234],{},[307,132776,310],{"stretchy":309},[312,132778,314],{},[232,132780,1138],{"mathvariant":406},[232,132782,966],{},[307,132784,317],{"stretchy":309},[236,132786,132787],{"encoding":238},"f\\leftrightarrow t f(1\u002Ft)",[212,132789,132791,132809],{"className":132790,"ariaHidden":243},[242],[212,132792,132794,132797,132800,132803,132806],{"className":132793},[247],[212,132795],{"className":132796,"style":252},[251],[212,132798,234],{"className":132799,"style":258},[256,257],[212,132801],{"className":132802,"style":355},[354],[212,132804,21559],{"className":132805},[359],[212,132807],{"className":132808,"style":355},[354],[212,132810,132812,132815,132818,132821,132824,132827,132830],{"className":132811},[247],[212,132813],{"className":132814,"style":336},[251],[212,132816,966],{"className":132817},[256,257],[212,132819,234],{"className":132820,"style":258},[256,257],[212,132822,310],{"className":132823},[343],[212,132825,8787],{"className":132826},[256],[212,132828,966],{"className":132829},[256,257],[212,132831,317],{"className":132832},[350]," 给出方向对称性（可用于构造对称散度）。",[6863,132835,132836,132839],{},[1194,132837,132838],{},"一个不变量","：数据处理不等式，说明它是「信息量」而非「几何量」。正因如此，它与 Wasserstein\u002FMMD 在支撑分离时行为迥异。",[11,132841,132842],{},"经典文献可参考：Csiszár (1967)、Ali–Silvey (1966) 的原始定义；Liese–Vajda 的专著对 f-散度的对偶、拓扑与充分性做了系统处理；Amari 的信息几何给出 α-族与 Fisher 度量；Nowozin 等 (2016) 的 f-GAN、Belghazi 等 (2018) 的 MINE 把对偶表示变成可训练算法；Dong–Roth–Su (2022) 说明 f-散度的语言如何统一差分隐私。把这几条线索接起来，读者就能在「定义—性质—估计—应用」四个层面上自由穿梭。",{"title":186,"searchDepth":187,"depth":187,"links":132844},[132845,132852,132857,132867,132877,132884,132889,132897,132898,132903],{"id":727,"depth":187,"text":728,"children":132846},[132847,132849,132850,132851],{"id":2511,"depth":132848,"text":2512},3,{"id":5402,"depth":132848,"text":5403},{"id":5771,"depth":132848,"text":5772},{"id":7559,"depth":132848,"text":7560},{"id":8949,"depth":187,"text":132853,"children":132854},"2. 为何 fff 凸且 f(1)=0f(1)=0f(1)=0",[132855,132856],{"id":9047,"depth":132848,"text":9048},{"id":10758,"depth":132848,"text":10759},{"id":21607,"depth":187,"text":21608,"children":132858},[132859,132860,132861,132862,132863,132864,132865,132866],{"id":21669,"depth":132848,"text":21670},{"id":25748,"depth":132848,"text":25749},{"id":34709,"depth":132848,"text":34710},{"id":37348,"depth":132848,"text":37349},{"id":40637,"depth":132848,"text":40638},{"id":44936,"depth":132848,"text":44937},{"id":49574,"depth":132848,"text":49575},{"id":52688,"depth":132848,"text":52689},{"id":55111,"depth":187,"text":55112,"children":132868},[132869,132870,132871,132872,132873,132874,132875,132876],{"id":55410,"depth":132848,"text":55411},{"id":56337,"depth":132848,"text":56338},{"id":58493,"depth":132848,"text":58494},{"id":60889,"depth":132848,"text":60890},{"id":74660,"depth":132848,"text":74661},{"id":78243,"depth":132848,"text":78244},{"id":82271,"depth":132848,"text":82272},{"id":97165,"depth":132848,"text":97166},{"id":99512,"depth":187,"text":99513,"children":132878},[132879,132880,132881,132882,132883],{"id":99516,"depth":132848,"text":99517},{"id":101560,"depth":132848,"text":101561},{"id":103404,"depth":132848,"text":103405},{"id":105566,"depth":132848,"text":105567},{"id":108458,"depth":132848,"text":108459},{"id":108799,"depth":187,"text":108800,"children":132885},[132886,132887,132888],{"id":108803,"depth":132848,"text":108804},{"id":114829,"depth":132848,"text":114830},{"id":116611,"depth":132848,"text":116612},{"id":117655,"depth":187,"text":117656,"children":132890},[132891,132892,132893,132894,132895,132896],{"id":117724,"depth":132848,"text":117725},{"id":117918,"depth":132848,"text":117919},{"id":118809,"depth":132848,"text":118810},{"id":119508,"depth":132848,"text":119509},{"id":119966,"depth":132848,"text":119967},{"id":120035,"depth":132848,"text":120036},{"id":120399,"depth":187,"text":120400},{"id":124560,"depth":187,"text":124561,"children":132899},[132900,132901,132902],{"id":124564,"depth":132848,"text":124565},{"id":128909,"depth":132848,"text":128910},{"id":131138,"depth":132848,"text":131139},{"id":132358,"depth":187,"text":132359},"f-散度族是概率分布之间差异的一大类度量，它用一个凸函数 fff 来统一描述 KL 散度、JS 散度、全变差、卡方散度等许多常见散度。可以把它理解为「散度」的通用模板。",{},"\u002Fblog\u002F2026\u002F0011-about-the-f-divergence",{"title":205,"description":132904},"blog\u002F2026\u002F0011-about-the-f-divergence","f-散度族（f-divergence）用一个凸函数 f 统一刻画两个概率分布之间的差异，KL、JS、全变差、卡方、Hellinger、α-散度都是它的特例。",[132911,132912],"statistics","mathematics","2026-10-17T04:47:08+08:00","GHo-ixgq8dzLCdMARQXci-0vuQRiORPDjOvtm081mYg",1792921284129]