Yip Man 4 Free Movie 2019 release Solar Movies gomovies 
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Abstract Yip Man 4 is a movie starring Donnie Yen, Scott Adkins, and Kwok-Kwan Chan. The Kung Fu master travels to the U.S. where his student has upset the local martial arts community by opening a Wing Chun school. Country China. &ref(https://m.media-amazon.com/images/M/MV5BY2FkY2QzOTctNmViZi00YTU5LTk5ZmQtMTJhMzFiOTIyZDc2XkEyXkFqcGdeQXVyNzQ2NTQzMDk@._V1_UY190_CR0,0,128,190_AL_.jpg). 7,9 / 10. Vanness Wu. Writer Tai-lee Chan.
Why i have bad feeling about steve in this movie, i mean he dies when his plane explode right and this steve probally enemy disguise and if this steve enemy in disguise i gonna feel so sad to her or this steve probally illusion that diana have because she still cant forget steve ?. Lol bts recommended suga ip man 1,2,3. No thanks, I can watch it for free all the movies. Guapo Donni Yen el mejor. Undisputed last stand yuri vs iceman rematch. Dois mitos no mesmo filme.
Ip Man One of the best Movies EVER! ??
Ip man city. Ip Man 4.2. Ip man 4 2017. Yip Man 4 Online Watch TV Series… Watch Yip Man Online Independent Yip~Man~4~in~hindi~download. Voice ip phone system. Cheap ip phone service. Wow, wow, wow. amazing trailer, i love the series, and the actor. such an amazing talent. Ip man 4 pelicula completa en espanol. Well being that the rise of Skywalker is probably going to suck I expect this to be the top movie ?????. Going to see IP MAN 4. Ip man of steel. 
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0 引言 ? 事?上，介??叶斯定理?叶斯方法?叶斯推断的?料?籍不少，比如《数理??学?史》，以及《??决策?及?叶斯分析 James rger著》等等，然介??叶斯网?的中文?料?非常少，中文?籍?共也没几本，有的多是英文?料，但初学者一上来就扔?他一堆英文?文，因无基?和?言的障碍而?得异常吃力?致无法???下去?是非常可惜的（当然，有了一定的基?后，便可??更多的英文?料）. ? 11月9日上午， 机器学?班 ?第9次???叶斯网?，帮助大家提?了?叶斯网?的几个??点：?叶斯网?的定?3??构形式因子?以及Summary-Product算法等等，知道了?叶斯网?是?，怎?做，目?是?之后，相信看英文?文也更好看懂了. ? 故本文?合?程??及相?参考?料写就，从?叶斯方法?起，重点?述?叶斯网?，依然可以定??一篇??笔?或学?笔?，有任何??，?迎随?不吝指出，thanks. 1 ?叶斯方法 ? ?久以来，人??一件事情?生或不?生的概率 ，只有固定的0和1，即要??生，要?不?生，从来不会去考?某件事情?生的概率有多大，不?生的概率又是多大.而且概率 ?然未知，但最起?是一个确定的?.比如如果?那?的人?一个??：“有一个袋子，里面装着若干个白球和?球，??从袋子中取得白球的概率 是多少？”他?会想都不用想，会立?告?你，取出白球的概率 就是1/2，要?取到白球，要?取不到白球，即θ只能有一个?，而且不?你取了多少次，取得白球的概率θ始?都是1/2，即不随?察?果X 的?化而?化. ? ???率派的?点?期?治着人?的?念，直到后来一个名叫Thomas Bayes的人物出?. 1. 1 ?叶斯方法的提出 ? 托?斯?叶斯Thomas Bayes（1702-1763）在世?，并不?当?的人?所熟知，很少?表?文或出版著作，与当?学?界的人沟通交流也很少，用?在的?来?，?叶斯就是活生生一民?学?“??”，可?个“??”最??表了一篇名?“An essay towards solving a problem in the doctrine of chances”，翻??来?是：机遇理?中一个??的解.你可能?得我要?：?篇?文的?表随机?生??效?，从而奠定?叶斯在学?史上的地位. ? ? ? ? ? 事?上，上篇?文?表后，在当?并未?生多少影响，在20世?后，?篇?文才逐?被人?所重?.?此，与梵高何其?似，画的画生前一文不?，死后价??城. ? 回到上面的例子：“有一个袋子，里面装着若干个白球和?球，??从袋子中取得白球的概率θ是多少？”?叶斯??取得白球的概率 是个不确定的?，因?其中含有机遇的成分.比如，一个朋友??，你明明知道??的?果就两?，即要?成功要?失?，但你依然会忍不住去估?他??成功的几率有多大？你如果?他?人比?了解，而且有方法思路清晰有毅力且能??周?的人，你会不由自主的估?他??成功的几率可能在80%以上.??不同于最?始的“非?即白非0即1”的思考方式，便是?叶斯式的思考方式. ? ??深入?解?叶斯方法之前，先????下?率派与?叶斯派各自不同的思考方式： ? 相?来?，?率派的?点容易理解，所以下文重点?述?叶斯派的?点. ? ?叶斯派既然把 看做是一个随机?量，所以要?算 的分布，便得事先知道 的无条件分布，即在有?本之前（或?察到X之前）， 有着怎?的分布呢？ ? 比如往台球桌上扔一个球，?个球落会落在何?呢？如果是不偏不倚的把球抛出去，那?此球落在台球桌上的任一位置都有着相同的机会，即球落在台球桌上某一位置的概率 服从均�擁�布.??在??之前定下的属于基本前提性?的分布称?先?分布，或 的无条件分布. ? 至此，?叶斯及?叶斯派提出了一个思考??的固定模式： ? 上述思考模式意味着，新?察到的?本信息将修正人?以前?事物的?知.?言之，在得到新的?本信息之前，人?? 的?知是先?分布 ，在得到新的?本信息 后，人?? 的?知?. 其中，先?信息一般来源于??跟?史?料.比如林丹跟某?手?决，解?一般会根据林丹?次比?的成??此次比?的??做个大致的判断.再比如，某工厂?天都要??品?行??，以?估?品的不合格率θ，??一段??后便会?累大量的?史?料，?些?史?料便是先?知?，有了?些先?知?，便在决定?一个?品是否需要?天???便有了依据，如果以往的?史?料?示，某?品的不合格率只有0. 01%，便可??信得??品或免??品，只?月抽?一两次，从而省去大量的人力物力. ? 而后?分布 一般也??是在?定?本 的情况下 的条件分布，而使 达到最大的? 称?最大后?估?，?似于?典??学中的极大似然估?. ? ?合起来看，?好比是人???始??大自然只有少得可怜的先?知?，但随着不断?察???得更多的?本?果，使得人??自然界的?律摸得越来越透?.所以，?叶斯方法既符合人?日常生活的思考方式，也符合人???自然的?律，??不断的?展，最?占据??学?域的半壁江山，与?典??学分庭抗礼. ? 此外，?叶斯除了提出上述思考模式之外，?特?提出了?世?名的?叶斯定理. 1. 2 ?叶斯定理 ? 在引出?叶斯定理之前，先学?几个定?： 条件概率 （又称后?概率）就是事件A在另外一个事件B已??生条件下的?生概率.条件概率表示?P(A,B)，?作“在B条件下A的概率”. 比如，在同一个?本空?Ω中的事件或者子集A与B，如果随机从Ω中?出的一个素属于B，那??个随机??的素?属于A的概率就定??在B的前提下A的条件概率，所以：P(A,B) A∩B, B,，接着分子分母都除以,Ω,得到 ? 接着，考?一个??：P(A,B)是在B?生的情况下A?生的可能性. 首先，事件B?生之前，我??事件A的?生有一个基本的概率判断，称?A的先?概率，用P(A)表示； 其次，事件B?生之后，我??事件A的?生概率重新?估，称?A的后?概率，用P(A,B)表示； ?似的，事件A?生之前，我??事件B的?生有一个基本的概率判断，称?B的先?概率，用P(B)表示； 同?，事件A?生之后，我??事件B的?生概率重新?估，称?B的后?概率，用P(B,A)表示. ? ?叶斯定理便是基于下述?叶斯公式： ? 上述公式的推?其?非常??，就是从条件概率推出. ? 根据条件概率的定?，在事件B?生的条件下事件A?生的概率是 ? 同?地，在事件A?生的条件下事件B?生的概率 ? 整理与合并上述两个方程式，便可以得到： ? 接着，上式两?同除以P(B)，若P(B)是非零的，我?便可以得到 ?叶斯定理 的公式表达式： ? 所以，?叶斯公式可以直接根据条件概率的定?直接推出.即因?P(A, B. P(A)P(B,A. P(B)P(A,B)，所以P(A,B. P(A)P(B,A) P(B. 1. 3 ?用：拼写?? ? ?常在网上搜索?西的朋友知道，当你不小心?入一个不存在的???，搜索引�臆馗鷦�你是不是要?入某一个正确的??，比如当你在Google中?入“ Julw ”?，系?会猜?你的意?：是不是要搜索“July”，如下?所示： ? ?叫做拼写??.根据谷歌一?工写的 文章 ?示，Google的拼写??基于?叶斯方法.下面我?就来看看，怎?利用?叶斯方法，??"拼写??"的功能. ? 用??入一个???，可能拼写正确，也可能拼写??.如果把拼写正确的情况?做c（代表correct），拼写??的情况?做w（代表wrong），那?"拼写??"要做的事情就是：在?生w的情况下，??推断出c.?言之：已知w，然后在若干个??方案中，找出可能性最大的那个c，也就是求 的最大?. ? 而根据?叶斯定理，有： ? 由于?于所有??的c来?，??的都是同一个w，所以它?的P(w)是相同的，因此我?只要最大化 ? 即可.其中： P(c)表示某个正确的?的出?"概率"，它可以用"?率"代替.如果我?有一个足?大的文本?，那??个文本?中?个??的出??率，就相当于它的?生概率.某个?的出??率越高，P(c)就越大.比如在你?入一个??的?“Julw”?，系?更?向于去猜?你可能想?入的?是“July”，而不是“Jult”，因?“July”更常?. P(w,c)表示在??拼写c的情况下，出?拼写??w的概率.?了?化??，假定两个??在字形上越接近，就有越可能拼?，P(w,c)就越大.?例来?，相差一个字母的拼法，就比相差两个字母的拼法，?生概率更高.你想拼写??July，那???拼成Julw（相差一个字母）的可能性，就比拼成Jullw高（相差两个字母）.?得一提的是，一般把????称?“??距离”，参?博客中的 ?篇 文章. ? 所以，我?比?所有拼写相近的?在文本?中的出??率，再从中挑出出??率最高的一个，即是用?最想?入的那个?.具体的?算?程及此方法的缺陷?参? ?里. 2 ?叶斯网? 2. 1 ?叶斯网?的定? ? ?叶斯网?(Bayesian?network)，又称信念网?(Belief Network)，或有向无??模型(directed?acyclic?graphical?model)，是一?概率?模型，于1985年由Judea Pearl首先提出.它是一?模?人?推理?程中因果?系的不确定性?理模型，其网?拓朴?构是一个有向无??(DAG. ? ?叶斯网?的有向无??中的?点表示随机?量 ，它?可以是可?察到的?量，或??量未知参数等.??有因果?系（或非条件独立）的?量或命??用箭?来?接.若两个?点?以一个?箭??接在一起，表示其中一个?点是“因(parents)”，另一个是“果(children)”，两?点就会?生一个条件概率?. ? ?而言之， ?接两个?点的箭?代表此两个随机?量是具有因果?系，或非条件独立. 例如，假??点E直接影响到?点H，即E→H，?用从E指向H的箭?建立?点E到?点H的有向弧(E, H)，??(即?接?度)用条件概率P(H,E)来表示，如下?所示： ???言之，把某个研究系?中?及的随机?量，根据是否条件独立?制在一个有向?中，就形成了?叶斯网?.其主要用来描述随机?量之?的条件依?，用圈表示随机?量(random variables)，用箭?表示条件依?(conditional dependencies. ??令G. I, E)表示一个有向无??(DAG)，其中I代表?形中所有的?点的集合，而E代表有向?接?段的集合，且令X. Xi)i ∈ I?其有向无??中的某一?点i所代表的随机?量，若?点X的?合概率可以表示成： ? ?称X?相?于一有向无??G?的?叶斯网?，其中， 表示?点i之“因”，或称pa(i)是i的parents（父母）. ? 此外，?于任意的随机?量，其?合概率可由各自的局部条件概率分布相乘而得出： ? 如下?所示，便是一个??的?叶斯网?： ? 因?a?致b，a和b?致c，所以有 2. 2 ?叶斯网?的3??构形式 ? ?定如下?所示的一个?叶斯网?： ? 从?上可以比?直?的看出： 1. x1, x2, …x7的?合分布? 2. x1和x2独立（??head-to-head）； 3. x6和x7在x4?定的条件下独立（??tail-to-tail）. ? 根据上?，第1点可能很容易理解，但第23点中所述的条件独立是?意思呢？其?第23点是?叶斯网?中3??构形式中的其中二?.?了?清楚?个??，需要引入D-Separation（D-分离）?个概念. ? D-Separation是一?用来判断?量是否条件独立的?形化方法.?言之，?于一个DAG(有向无??)E，D-Separation方法可以快速的判断出两个?点之?是否是条件独立的. 2. 2. 1 形式1：head-to-head ? ?叶斯网?的第一??构形式如下?所示： ? 所以有：P(a, b, c. P(a) P(b) P(c,a, b)成立，化?后可得： ? 即在 c未知的条件下，ab被阻断(blocked)，是独立的 ，称之?head-to-head条件独立，??本?中最?始那??中的“x1x2独立”. 2. 2 形式2：tail-to-tail ? ?叶斯网?的第二??构形式如下?所示 ? 考?c未知，跟c已知?两?情况： 在c未知的?候，有：P(a, b, c) P(c) P(a,c) P(b,c)，此?，没法得出P(a, b. P(a)P(b)，即c未知?，ab不独立. 在c已知的?候，有：P(a, b,c) P(a, b, c) P(c)，然后将P(a, b, c) P(c) P(a,c) P(b,c)?入式子中，得到：P(a, b,c) P(a, b, c) P(c) P(c) P(a,c) P(b,c) P(c) P(a,c) P(b,c)，即c已知?，ab独立. ? 所以， 在c?定的条件下，a，b被阻断(blocked)，是独立的 ，称之?tail-to-tail条件独立，??本?中最?始那??中的“x6和x7在x4?定的条件下独立”. 2. 3 形式3：head-to-tail ? ?叶斯网?的第三??构形式如下?所示： ? ?是分c未知跟c已知?两?情况： c未知?，有：P(a, b, c) P(a) P(c,a) P(b,c)，但无法推出P(a, b. P(a)P(b)，即c未知?，ab不独立. c已知?，有：P(a, b,c) P(a, b, c) P(c)，且根据P(a, c. P(a) P(c,a. P(c) P(a,c)，可化?得到： ? 所以， 在c?定的条件下，a，b被阻断(blocked)，是独立的 ，称之?head-to-tail条件独立. ? 插一句 ：?个head-to-tail其?就是一个?式网?，如下?所示： ? 根据之前?head-to-tail的?解，我?已?知道，在xi?定的条件下，xi+1的分布和x1, x2…xi-1条件独立.意味着?呢？意味着：xi+1的分布状?只和xi有?，和其他?量条件独立.通俗点?，当前状?只跟上一状?有?，跟上上或上上之前的状?无?.???次演?的随机?程，就叫做??科夫?（Markov chain）.且有： ? 接着，将上述?点推广到?点集，?是：?于任意的?点集A，B，C，考察�
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0 引言 ? 事?上，介??叶斯定理?叶斯方法?叶斯推断的?料?籍不少，比如《数理??学?史》，以及《??决策?及?叶斯分析 James rger著》等等，然介??叶斯网?的中文?料?非常少，中文?籍?共也没几本，有的多是英文?料，但初学者一上来就扔?他一堆英文?文，因无基?和?言的障碍而?得异常吃力?致无法???下去?是非常可惜的（当然，有了一定的基?后，便可??更多的英文?料）. ? 11月9日上午， 机器学?班 ?第9次???叶斯网?，帮助大家提?了?叶斯网?的几个??点：?叶斯网?的定?3??构形式因子?以及Summary-Product算法等等，知道了?叶斯网?是?，怎?做，目?是?之后，相信看英文?文也更好看懂了. ? 故本文?合?程??及相?参考?料写就，从?叶斯方法?起，重点?述?叶斯网?，依然可以定??一篇??笔?或学?笔?，有任何??，?迎随?不吝指出，thanks. 1 ?叶斯方法 ? ?久以来，人??一件事情?生或不?生的概率 ，只有固定的0和1，即要??生，要?不?生，从来不会去考?某件事情?生的概率有多大，不?生的概率又是多大.而且概率 ?然未知，但最起?是一个确定的?.比如如果?那?的人?一个??：“有一个袋子，里面装着若干个白球和?球，??从袋子中取得白球的概率 是多少？”他?会想都不用想，会立?告?你，取出白球的概率 就是1/2，要?取到白球，要?取不到白球，即θ只能有一个?，而且不?你取了多少次，取得白球的概率θ始?都是1/2，即不随?察?果X 的?化而?化. ? ???率派的?点?期?治着人?的?念，直到后来一个名叫Thomas Bayes的人物出?. 1. 1 ?叶斯方法的提出 ? 托?斯?叶斯Thomas Bayes（1702-1763）在世?，并不?当?的人?所熟知，很少?表?文或出版著作，与当?学?界的人沟通交流也很少，用?在的?来?，?叶斯就是活生生一民?学?“??”，可?个“??”最??表了一篇名?“An essay towards solving a problem in the doctrine of chances”，翻??来?是：机遇理?中一个??的解.你可能?得我要?：?篇?文的?表随机?生??效?，从而奠定?叶斯在学?史上的地位. ? ? ? ? ? 事?上，上篇?文?表后，在当?并未?生多少影响，在20世?后，?篇?文才逐?被人?所重?.?此，与梵高何其?似，画的画生前一文不?，死后价??城. ? 回到上面的例子：“有一个袋子，里面装着若干个白球和?球，??从袋子中取得白球的概率θ是多少？”?叶斯??取得白球的概率 是个不确定的?，因?其中含有机遇的成分.比如，一个朋友??，你明明知道??的?果就两?，即要?成功要?失?，但你依然会忍不住去估?他??成功的几率有多大？你如果?他?人比?了解，而且有方法思路清晰有毅力且能??周?的人，你会不由自主的估?他??成功的几率可能在80%以上.??不同于最?始的“非?即白非0即1”的思考方式，便是?叶斯式的思考方式. ? ??深入?解?叶斯方法之前，先????下?率派与?叶斯派各自不同的思考方式： ? 相?来?，?率派的?点容易理解，所以下文重点?述?叶斯派的?点. ? ?叶斯派既然把 看做是一个随机?量，所以要?算 的分布，便得事先知道 的无条件分布，即在有?本之前（或?察到X之前）， 有着怎?的分布呢？ ? 比如往台球桌上扔一个球，?个球落会落在何?呢？如果是不偏不倚的把球抛出去，那?此球落在台球桌上的任一位置都有着相同的机会，即球落在台球桌上某一位置的概率 服从均�擁�布.??在??之前定下的属于基本前提性?的分布称?先?分布，或 的无条件分布. ? 至此，?叶斯及?叶斯派提出了一个思考??的固定模式： ? 上述思考模式意味着，新?察到的?本信息将修正人?以前?事物的?知.?言之，在得到新的?本信息之前，人?? 的?知是先?分布 ，在得到新的?本信息 后，人?? 的?知?. 其中，先?信息一般来源于??跟?史?料.比如林丹跟某?手?决，解?一般会根据林丹?次比?的成??此次比?的??做个大致的判断.再比如，某工厂?天都要??品?行??，以?估?品的不合格率θ，??一段??后便会?累大量的?史?料，?些?史?料便是先?知?，有了?些先?知?，便在决定?一个?品是否需要?天???便有了依据，如果以往的?史?料?示，某?品的不合格率只有0. 01%，便可??信得??品或免??品，只?月抽?一两次，从而省去大量的人力物力. ? 而后?分布 一般也??是在?定?本 的情况下 的条件分布，而使 达到最大的? 称?最大后?估?，?似于?典??学中的极大似然估?. ? ?合起来看，?好比是人???始??大自然只有少得可怜的先?知?，但随着不断?察???得更多的?本?果，使得人??自然界的?律摸得越来越透?.所以，?叶斯方法既符合人?日常生活的思考方式，也符合人???自然的?律，??不断的?展，最?占据??学?域的半壁江山，与?典??学分庭抗礼. ? 此外，?叶斯除了提出上述思考模式之外，?特?提出了?世?名的?叶斯定理. 1. 2 ?叶斯定理 ? 在引出?叶斯定理之前，先学?几个定?： 条件概率 （又称后?概率）就是事件A在另外一个事件B已??生条件下的?生概率.条件概率表示?P(A,B)，?作“在B条件下A的概率”. 比如，在同一个?本空?Ω中的事件或者子集A与B，如果随机从Ω中?出的一个素属于B，那??个随机??的素?属于A的概率就定??在B的前提下A的条件概率，所以：P(A,B) A∩B, B,，接着分子分母都除以,Ω,得到 ? 接着，考?一个??：P(A,B)是在B?生的情况下A?生的可能性. 首先，事件B?生之前，我??事件A的?生有一个基本的概率判断，称?A的先?概率，用P(A)表示； 其次，事件B?生之后，我??事件A的?生概率重新?估，称?A的后?概率，用P(A,B)表示； ?似的，事件A?生之前，我??事件B的?生有一个基本的概率判断，称?B的先?概率，用P(B)表示； 同?，事件A?生之后，我??事件B的?生概率重新?估，称?B的后?概率，用P(B,A)表示. ? ?叶斯定理便是基于下述?叶斯公式： ? 上述公式的推?其?非常??，就是从条件概率推出. ? 根据条件概率的定?，在事件B?生的条件下事件A?生的概率是 ? 同?地，在事件A?生的条件下事件B?生的概率 ? 整理与合并上述两个方程式，便可以得到： ? 接着，上式两?同除以P(B)，若P(B)是非零的，我?便可以得到 ?叶斯定理 的公式表达式： ? 所以，?叶斯公式可以直接根据条件概率的定?直接推出.即因?P(A, B. P(A)P(B,A. P(B)P(A,B)，所以P(A,B. P(A)P(B,A) P(B. 1. 3 ?用：拼写?? ? ?常在网上搜索?西的朋友知道，当你不小心?入一个不存在的???，搜索引�臆馗鷦�你是不是要?入某一个正确的??，比如当你在Google中?入“ Julw ”?，系?会猜?你的意?：是不是要搜索“July”，如下?所示： ? ?叫做拼写??.根据谷歌一?工写的 文章 ?示，Google的拼写??基于?叶斯方法.下面我?就来看看，怎?利用?叶斯方法，??"拼写??"的功能. ? 用??入一个???，可能拼写正确，也可能拼写??.如果把拼写正确的情况?做c（代表correct），拼写??的情况?做w（代表wrong），那?"拼写??"要做的事情就是：在?生w的情况下，??推断出c.?言之：已知w，然后在若干个??方案中，找出可能性最大的那个c，也就是求 的最大?. ? 而根据?叶斯定理，有： ? 由于?于所有??的c来?，??的都是同一个w，所以它?的P(w)是相同的，因此我?只要最大化 ? 即可.其中： P(c)表示某个正确的?的出?"概率"，它可以用"?率"代替.如果我?有一个足?大的文本?，那??个文本?中?个??的出??率，就相当于它的?生概率.某个?的出??率越高，P(c)就越大.比如在你?入一个??的?“Julw”?，系?更?向于去猜?你可能想?入的?是“July”，而不是“Jult”，因?“July”更常?. P(w,c)表示在??拼写c的情况下，出?拼写??w的概率.?了?化??，假定两个??在字形上越接近，就有越可能拼?，P(w,c)就越大.?例来?，相差一个字母的拼法，就比相差两个字母的拼法，?生概率更高.你想拼写??July，那???拼成Julw（相差一个字母）的可能性，就比拼成Jullw高（相差两个字母）.?得一提的是，一般把????称?“??距离”，参?博客中的 ?篇 文章. ? 所以，我?比?所有拼写相近的?在文本?中的出??率，再从中挑出出??率最高的一个，即是用?最想?入的那个?.具体的?算?程及此方法的缺陷?参? ?里. 2 ?叶斯网? 2. 1 ?叶斯网?的定? ? ?叶斯网?(Bayesian?network)，又称信念网?(Belief Network)，或有向无??模型(directed?acyclic?graphical?model)，是一?概率?模型，于1985年由Judea Pearl首先提出.它是一?模?人?推理?程中因果?系的不确定性?理模型，其网?拓朴?构是一个有向无??(DAG. ? ?叶斯网?的有向无??中的?点表示随机?量 ，它?可以是可?察到的?量，或??量未知参数等.??有因果?系（或非条件独立）的?量或命??用箭?来?接.若两个?点?以一个?箭??接在一起，表示其中一个?点是“因(parents)”，另一个是“果(children)”，两?点就会?生一个条件概率?. ? ?而言之， ?接两个?点的箭?代表此两个随机?量是具有因果?系，或非条件独立. 例如，假??点E直接影响到?点H，即E→H，?用从E指向H的箭?建立?点E到?点H的有向弧(E, H)，??(即?接?度)用条件概率P(H,E)来表示，如下?所示： ???言之，把某个研究系?中?及的随机?量，根据是否条件独立?制在一个有向?中，就形成了?叶斯网?.其主要用来描述随机?量之?的条件依?，用圈表示随机?量(random variables)，用箭?表示条件依?(conditional dependencies. ??令G. I, E)表示一个有向无??(DAG)，其中I代表?形中所有的?点的集合，而E代表有向?接?段的集合，且令X. Xi)i ∈ I?其有向无??中的某一?点i所代表的随机?量，若?点X的?合概率可以表示成： ? ?称X?相?于一有向无??G?的?叶斯网?，其中， 表示?点i之“因”，或称pa(i)是i的parents（父母）. ? 此外，?于任意的随机?量，其?合概率可由各自的局部条件概率分布相乘而得出： ? 如下?所示，便是一个??的?叶斯网?： ? 因?a?致b，a和b?致c，所以有 2. 2 ?叶斯网?的3??构形式 ? ?定如下?所示的一个?叶斯网?： ? 从?上可以比?直?的看出： 1. x1, x2, …x7的?合分布? 2. x1和x2独立（??head-to-head）； 3. x6和x7在x4?定的条件下独立（??tail-to-tail）. ? 根据上?，第1点可能很容易理解，但第23点中所述的条件独立是?意思呢？其?第23点是?叶斯网?中3??构形式中的其中二?.?了?清楚?个??，需要引入D-Separation（D-分离）?个概念. ? D-Separation是一?用来判断?量是否条件独立的?形化方法.?言之，?于一个DAG(有向无??)E，D-Separation方法可以快速的判断出两个?点之?是否是条件独立的. 2. 2. 1 形式1：head-to-head ? ?叶斯网?的第一??构形式如下?所示： ? 所以有：P(a, b, c. P(a) P(b) P(c,a, b)成立，化?后可得： ? 即在 c未知的条件下，ab被阻断(blocked)，是独立的 ，称之?head-to-head条件独立，??本?中最?始那??中的“x1x2独立”. 2. 2 形式2：tail-to-tail ? ?叶斯网?的第二??构形式如下?所示 ? 考?c未知，跟c已知?两?情况： 在c未知的?候，有：P(a, b, c) P(c) P(a,c) P(b,c)，此?，没法得出P(a, b. P(a)P(b)，即c未知?，ab不独立. 在c已知的?候，有：P(a, b,c) P(a, b, c) P(c)，然后将P(a, b, c) P(c) P(a,c) P(b,c)?入式子中，得到：P(a, b,c) P(a, b, c) P(c) P(c) P(a,c) P(b,c) P(c) P(a,c) P(b,c)，即c已知?，ab独立. ? 所以， 在c?定的条件下，a，b被阻断(blocked)，是独立的 ，称之?tail-to-tail条件独立，??本?中最?始那??中的“x6和x7在x4?定的条件下独立”. 2. 3 形式3：head-to-tail ? ?叶斯网?的第三??构形式如下?所示： ? ?是分c未知跟c已知?两?情况： c未知?，有：P(a, b, c) P(a) P(c,a) P(b,c)，但无法推出P(a, b. P(a)P(b)，即c未知?，ab不独立. c已知?，有：P(a, b,c) P(a, b, c) P(c)，且根据P(a, c. P(a) P(c,a. P(c) P(a,c)，可化?得到： ? 所以， 在c?定的条件下，a，b被阻断(blocked)，是独立的 ，称之?head-to-tail条件独立. ? 插一句 ：?个head-to-tail其?就是一个?式网?，如下?所示： ? 根据之前?head-to-tail的?解，我?已?知道，在xi?定的条件下，xi+1的分布和x1, x2…xi-1条件独立.意味着?呢？意味着：xi+1的分布状?只和xi有?，和其他?量条件独立.通俗点?，当前状?只跟上一状?有?，跟上上或上上之前的状?无?.???次演?的随机?程，就叫做??科夫?（Markov chain）.且有： ? 接着，将上述?点推广到?点集，?是：?于任意的?点集A，B，C，考察�
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