人工智能08不确定性（PPT54页)

手写数字识别文本分类图像分割第八章Uncertainty不确定性对应教材第13章本章大纲•Uncertainty不确定性•Probability概率•SyntaxandSemantics语法与语义•Inference推理•IndependenceandBayes‘Rule—独立性及贝叶斯法则不确定性•智能体几乎从来无法了解关于其环境的全部事实。因此其必须在不确定的环境下行动。•概率推理得到了某一证据，那么有多大的几率结论为真？例如：我颈部痛;我得脑膜炎的可能有多大?不确定性•假如有如下规则:iftoothache（牙疼）then原因是cavity（牙齿有洞）•但并不是所有牙疼的病人都是因为牙齿有洞，所以我们可以建立如下规则:iftoothacheand¬gum-disease（牙龈疾病）and¬filling（补牙）and...thenproblem=cavity•以上规则是复杂的;更好的方法:iftoothachethenproblemiscavitywith0.8probabilityorP(cavity|toothache)=0.8theprobabilityofcavityis0.8giventoothacheisobserved不确定性LetactionAt=离起飞时间提前t分钟动身去机场At会使我准时到达机场吗?Problems:1.partialobservability/部分可观察性(roadstate,otherdrivers‘plans)2.noisysensors(trafficreports)3.行动结果的不确定性(flattire,etc.)4.immensecomplexityofmodelingandpredictingtraffic因此一个纯粹的逻辑描述方法：1.risksfalsehood（错误风险）:“A25willgetmethereontime”,or2.leadstoconclusionsthataretooweakfordecisionmaking:“A25willgetmethereontimeifthere’snoaccidentonthebridgeanditdoesn‘trainandmytiresremainintactetcetc.”(A1440mightreasonablybesaidtogetmethereontimebutI’dhavetostayovernightintheairport…)世界与模型中的不确定性•Trueuncertainty:rulesareprobabilisticinnature掷骰子，抛硬币•惰性:把所有意外的规则都列举出来是很困难的花费太多时间来确定所有的相关因素这些规则过于繁杂而难以使用•理论的无知:某些领域中还没有完整的理论(e.g.,medicaldiagnosis)•实践的无知:掌握了所有规则但是并不是所有的相关信息都能被收集到处理不确定性的方法•概率理论作为一种正式的方法for：不确定知识的表示和推理命题中的模型信度(event,conclusion,diagnosis,etc.)给定可获得的证据,A25willgetmethereontimewithprobability0.04•概率是不确定性的语言现代AI的中心支柱Probability概率概率理论提供了一种方法以概括来自我们的惰性和无知的不确定性。ProbabilisticassertionssummarizeeffectsofLaziness（惰性）:failuretoenumerateexceptions（例外）,qualifications（条件）,etc.Ignorance（理论的无知）:lackofrelevantfacts,initialconditions,etc.Subjectiveprobability（主观概率）:Probabilitiesrelatepropositions（命题）toagent'sownstateofknowledgee.g.,P(A25|noreportedaccidents)=0.06Thesearenotassertions（断言）abouttheworld命题的概率随着新证据的发现而改变:e.g.,P(A25|noreportedaccidents,5a.m.)=0.15不确定条件下的决策假设下述概率是真的:P(A25getsmethereontime|…)=0.04P(A90getsmethereontime|…)=0.70P(A120getsmethereontime|…)=0.95P(A1440getsmethereontime|…)=0.9999Whichactiontochoose?Dependsonmypreferences（偏好）formissingflightvs.timespentwaiting,etc.Utilitytheory（效用理论）用来对偏好进行表示和推理Decisiontheory=probabilitytheory+utilitytheory决策理论=概率理论+效用理论Syntax语法基本元素:randomvariable（随机变量）Arandomvariableissomeaspectoftheworldaboutwhichwe(may)haveuncertainty通常大写e.g.,Cavity,Weather,Temperature类似于命题逻辑:未知世界被随机变量的赋值所定义Booleanrandomvariables（布尔随机变量）e.g.,Cavity（牙洞）(doIhaveacavity?)Discreterandomvariables（离散随机变量）e.g.,Weatherisoneofsunny,rainy,cloudy,snow定义域mustbeexhaustive（穷尽的）andmutuallyexclusive（互斥的）Continuousrandomvariables（连续随机变量）e.g.,Temp=21.6;alsoallow,e.g.,Temp22.0SyntaxElementaryproposition（命题）constructedbyassignmentofavaluetoarandomvariable:e.g.,Weather=sunny,Cavity=false(简写为¬cavity)Complexpropositionsformedfromelementarypropositionsandstandardlogicalconnectivese.g.,Weather=sunny∨Cavity=falseSyntaxAtomicevent:Acompletespecificationofthestateoftheworldaboutwhichtheagentisuncertain原子事件：对智能体无法确定的世界状态的一个完整的详细描述。E.g.,iftheworldconsistsofonlytwoBooleanvariablesCavityandToothache,thenthereare4distinctatomicevents:Cavity=false∧Toothache=falseCavity=false∧Toothache=trueCavity=true∧Toothache=falseCavity=true∧Toothache=trueAtomiceventsaremutuallyexclusiveandexhaustive穷尽和互斥概率公理对任意命题A,B0≤P(A)≤1P(true)=1andP(false)=0P(A∨B)=P(A)+P(B)-P(A∧B)Priorprobability（先验概率）Priororunconditionalprobabilities（无条件概率）ofpropositions在没有任何其它信息存在的情况下关于命题的信度e.g.,P(Cavity=true)=0.1andP(Weather=sunny)=0.72correspondtobeliefpriortoarrivalofany(new)evidenceProbabilitydistributiongivesvaluesforallpossibleassignments:概率分布给出一个随机变量所有可能取值的概率P(Weather)=0.72,0.1,0.08,0.1(normalized（归一化的）,i.e.,sumsto1)Jointprobabilitydistributionforasetofrandomvariablesgivestheprobabilityofeveryatomiceventonthoserandomvariables(i.e.,everysamplepoint)联合概率分布给出一个随机变量集的值的全部组合的概率P(Weather,Cavity)=a4×2matrixofvalues:Everyquestionaboutadomaincanbeansweredbythejointdistributionbecauseeveryeventisasumofsamplepoints连续变量的概率Expressdistributionasaparameterized（参数化的）functionofvalue:P(X=x)=U[18,26](x)=uniform（均匀分布）densitybetween18and26连续变量的概率MarginalDistributions（边缘概率分布）•Marginaldistributionsaresub-tableswhicheliminatevariables•Marginalization(summingout):CombinecollapsedrowsbyaddingConditionalprobability（条件概率）Conditionalorposteriorprobabilities（后验概率）P(a|b)证据累积过程的形式化和发现新证据后的概率更新当一个命题为真的条件下，指定命题的概率e.g.,P(cavity|toothache)=0.8i.e.,鉴于牙疼是已知证据(Notationforconditionaldistributions（条件概率分布）:P(cavity|toothache)=asinglenumberP(Cavity,Toothache)=2x2tablesummingto1P(Cavity|Toothache)=2-elementvectorof2-elementvectorsIfweknowmore,e.g.,cavityisalsogiven,thenwehaveP(cavity|toothache,cavity)=1新证据可能是不相关的，可以简化,e.g.,P(cavity|toothache,sunny)=P(cavity|toothache)=0.8条件概率定义条件概率为:P(a|b)=P(a∧b)/P(b)ifP(b)0Productrule（乘法规则）givesanalternativeformulation:P(a∧b)=P(a|b)P(b)=P(b|a)P(a)Ageneralversionholdsforwholedistributions,e.g.,P(Weather,Cavity)=P(Weather|Cavity)P(Cavity)(Viewasasetof4×2equations,notmatrixmultiplication)Chainrule（链式法则）isderivedbysuccessiveapplicationofproductrule:条件概率条件概率跟标准概率一样,forexample:0=P(a|e)=1conditionalprobabilitiesarebetween0and1in