人工智能08不確定性-wenkub.com
2025-02-17 12:32 本頁面
【正文】 Correct answer: 50% Bayes’ rule with 多重證據(jù)和條件獨立性 P(Cavity | toothache ∧ catch) = αP(toothache ∧ catch | Cavity) P(Cavity) = αP(toothache | Cavity) P(catch | Cavity) P(Cavity) This is an example of a na239。cavity) = P(catch | 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（未觀測變量） 通過枚舉的推理 Typically, we are interested in the posterior joint distribution of the query variables（查詢變量） Y given specific values e for the evidence variables（證據(jù)變量） E Let the hidden variables（未觀測變量） be H = X Y – E Then the required summation of joint entries is done by summing out the hidden variables: P(Y | E = e) = αP(Y,E = e) = αΣhP(Y,E= e, H = h) The terms in the summation are joint entries because Y, E and H together exhaust the set of random variables（ Y, E, H構(gòu)成了域中所有變量的完整集合） Obvious problems: 1. Worstcase time plexity O(dn) where d is the largest arity 2. Space plexity O(dn) to store the joint distribution 3. How to find the numbers for O(dn) entries? Independence（獨立性） A and B are independent iff P(A| B) = P(A) or P(B| A) = P(B) or P(A, B) = P(A) P(B) : roll of 2 die: P({1},{3}) = 1/6*1/6 = 1/36 P(Toothache, Catch, Cavity, Weather) = P(Toothache, Catch, Cavity) P(Weather) 32 entries reduced to 12。 also allow, ., Temp Syntax Elementary proposition（命題） constructed by assignment of a value to a random variable: ., Weather = sunny, Cavity = false (簡寫為 172。filling（補(bǔ)牙） and ... then problem = cavity ? 以上規(guī)則是復(fù)雜的 。因此其必須在不確定的環(huán)境下行動。 ? 概率推理 得到了某一證據(jù)，那么有多大的幾率結(jié)論為真？ 例如：我頸部痛 。 更好的方法 : if toothache then problem is cavity with probability or P(cavity | toothache) = the probability of cavity is given toothache is observed 不確定性 Let action At = 離起飛時間提前 t分鐘動身去機(jī)場 At 會使我準(zhǔn)時到達(dá)機(jī)場嗎 ? Problems: 1. partial observability/部分可觀察性 (road state, other drivers‘ plans) 2. noisy sensors (traffic reports) 3. 行動結(jié)果的不確定性 (flat tire, etc.) 4. immense plexity of modeling and predicting traffic 因此一個純粹的邏輯描述方法： 1. risks falsehood（錯誤風(fēng)險） : “A25 will get me there on time”, or 2. leads to conclusions that are too weak for decision making: “A25 will get me there on time if there’s no accident on the bridge and it doesn‘t rain and my tires remain intact etc etc.” (A1440 might reasonably be said to get me there on time but I’d have to stay overnight in the airport …) 世界與模型中的不確定性 ? True uncertainty: rules are probabilistic in nature 擲骰子，拋硬幣 ? 惰性 : 把所有意外的規(guī)則都列舉出來是很困難的 花費太多時間來確定所有的相關(guān)因素 這些規(guī)則過于繁雜而難以使用 ? 理論的無知 : 某些領(lǐng)域中還沒有完整的理論 (.,medical diagnosis) ? 實踐的無知 : 掌握了所有規(guī)則 但是 并不是所有的相關(guān)信息都能被收集到 處理不確定性的方法 ? 概率理論作為一種正式的方法 for： 不確定知識的表示和推理 命題中的模型信度 (event, conclusion, diagnosis, etc.) 給定可獲得的證據(jù) , A25 will get me there on time with probability ? 概率是不確定性的語言 現(xiàn)代 AI的中心支柱 Probability概率 概率理論提供了一種方法以概括來自我們的惰性和無知的不確定性。cavity) Complex propositions formed from elementary propositions and standard logical connectives
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