人工智能09貝葉斯網(wǎng)絡(luò)(編輯修改稿)
2025-03-09 12:56 本頁(yè)面
【文章內(nèi)容簡(jiǎn)介】 more than k parents, the plete work requires O(n 2k) numbers ., grows linearly with n, vs. O(2n) for the full joint distribution For burglary , 1 + 1 + 4 + 2 + 2 = 10 numbers (vs. 251 = 31) Global semantics（全局語(yǔ)義） The full joint distribution is defined as the product of the local conditional distributions: 全聯(lián)合概率分布可以表示為貝葉斯網(wǎng)絡(luò)中的條件概率分布的乘積 Global semantics（全局語(yǔ)義） The full joint distribution is defined as the product of the local conditional distributions: 全聯(lián)合概率分布可以表示為貝葉斯網(wǎng)絡(luò)中的條件概率分布的乘積 Local semantics Local semantics: each node is conditionally independent of its nondescendants（非后代） given its parents 給定父節(jié)點(diǎn)，一個(gè)節(jié)點(diǎn)與它的非后代節(jié)點(diǎn)是條件獨(dú)立 的 Theorem: Local semantics global semantics Causal Chains因果鏈 ? 一個(gè)基本形式： – Is X independent of Z given Y? – Evidence along the chain “blocks” the influence Common Cause共同原因 ? 另一個(gè)基礎(chǔ)的形態(tài) : two effects of the same cause – Are X and Z independent? – Are X and Z independent given Y? – Observing the cause blocks influence between effects. Common Effect共同影響 ? 最后一種配置形態(tài) : two causes of one effect (vstructures) – Are X and Z independent? ? Yes: remember the ballgame and the rain causing traffic, no correlation? – Are X and Z independent given Y? ? No: remember that seeing traffic put the rain and the ballgame in petition? – This is backwards from the other cases ? Observing the effect enables influence between causes. 構(gòu)造貝葉斯網(wǎng)絡(luò) Need a method such that a series of locally testable assertions of conditional independence guarantees the required global semantics 需要一種方法使得局部的條件獨(dú)立關(guān)系能夠保證全局語(yǔ)義得以成立 1. Choose an ordering of variables X1, … ,Xn 2. For i = 1 to n add Xi to the work select parents from X1, … ,Xi1 such that P (Xi | Parents(Xi)) = P (Xi | X1, ... Xi1) 該父親選擇保證了全局語(yǔ)義 : 構(gòu)造貝葉斯網(wǎng)絡(luò) 要求網(wǎng)絡(luò)的拓?fù)浣Y(jié)構(gòu)確實(shí)反映了合適的父節(jié)點(diǎn)集對(duì)每個(gè)變量的那些直接影響。 添加節(jié)點(diǎn)的正確次序是首先添加“根本原因”節(jié)點(diǎn)，然后加入受它們直接影響的變量，以此類推。 Example Example Example Example Example Example contd. 在非因果方向決定條件獨(dú)立性是很難的 (Causal models and conditional independence seem hardwired for humans!) Network is less p
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