人工智能08不確定性-在線瀏覽
2025-03-23 12:32本頁(yè)面
【正文】 gent39。 also allow, ., Temp Syntax Elementary proposition（命題） constructed by assignment of a value to a random variable: ., Weather = sunny, Cavity = false (簡(jiǎn)寫(xiě)為 172。 ., if the world consists of only two Boolean variables Cavity and Toothache, then there are 4 distinct atomic events: Cavity = false ∧ Toothache = false Cavity = false ∧ Toothache = true Cavity = true ∧ Toothache = false Cavity = true ∧ Toothache = true Atomic events are mutually exclusive and exhaustive 窮盡和互斥 概率公理 對(duì)任意命題 A, B 0 ≤ P(A) ≤ 1 P(true) = 1 and P(false) = 0 P(A ∨ B) = P(A) + P(B) P(A ∧ B) Prior probability（先驗(yàn)概率） Prior or unconditional probabilities（無(wú)條件概率） of propositions 在沒(méi)有任何其它信息存在的情況下關(guān)于命題的信度 ., P(Cavity = true) = and P(Weather = sunny) = correspond to belief prior to arrival of any (new) evidence Probability distribution gives values for all possible assignments: 概率分布 給出一個(gè)隨機(jī)變量所有可能取值的概率 P(Weather) = , (normalized（歸一化的） , ., sums to 1) Joint probability distribution for a set of random variables gives the probability of every atomic event on those random variables (., every sample point) 聯(lián)合概率分布給出一個(gè)隨機(jī)變量集的值的全部組合的概率 P(Weather,Cavity) = a 4 2 matrix of values: Every question about a domain can be answered by the joint distribution because every event is a sum of sample points 連續(xù)變量的概率 Express distribution as a parameterized（參數(shù)化的） function of value: P(X =x) = U[18, 26](x) = uniform（均勻分布） density between 18 and 26 連續(xù)變量的概率 Marginal Distributions（邊緣概率分布） ? Marginal distributions are subtables which eliminate variables ? Marginalization (summing out): Combine collapsed rows by adding Conditional probability（條件概率） Conditional or posterior probabilities（后驗(yàn)概率） P(a|b) 證據(jù)累積過(guò)程的形式化和發(fā)現(xiàn)新證據(jù)后的概率更新 當(dāng)一個(gè)命題為真的條件下，指定命題的概率 ., P(cavity | toothache) = ., 鑒于牙疼是已知證據(jù) (Notation for conditional distributions（條件概率分布） : P(cavity | toothache) = a single number P(Cavity, Toothache) = 2x2 table summing to 1 P(Cavity | Toothache) = 2element vector of 2element vectors If we know more, ., cavity is also given, then we have P(cavity | toothache, cavity) = 1 新證據(jù)可能是不相關(guān)的，可以簡(jiǎn)化 , ., P(cavity | toothache, sunny) = P(cavity | toothache) = 條件概率 定義 條件概率為 : P(a | b) = P(a ∧ b) / P(b) if P(b) 0 Product rule（乘法規(guī)則） gives an alternative formulation: P(a ∧ b) = P(a | b) P(b) = P(b | a) P(a) A general version holds for whole distributions, ., P(Weather, Cavity) = P(Weather | Cavity) P(Cavity) (View as a set of 4 2 equations, not matrix multiplication) Chain rule（鏈?zhǔn)椒▌t） is derived by successive application of product rule: 條件概率 條件概率跟標(biāo)準(zhǔn)概率一樣 , for example: 0 = P(a | e) = 1 conditional probabilities are between 0 and 1 inclusive P(a1 | e) + P(a2 | e) + ... + P(ak | e) = 1 conditional probabilities sum to 1 where a1, …, ak are all values in the domain of random variable A P(172。 catch)] = α *, + ,+ = α , = , General idea: pute distribution on query variable by fixing evidence variables（證據(jù)變量） and summing over hidden variables（未觀測(cè)變量）
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