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1、BayesianInferenceThepurposeofthisdocumentistoreviewbeliefnetworksandnaiveBayesclassifiers.DefinitionsfromProbability:Beliefnetworks:NaiveBayesClassifiers:AdvantagesandDisadvantagesofNaiveBayesClassifiers:Attheendoflesson9,CharlesintroducestheBayesoptimalclassifier.Althoughthisisthebestperfor
2、mingclassificationmodelforagivenhypothesisspace,datasetandaprioriknowledge,theBayesoptimalclassifieriscomputationallyverycostly.ThisisbecausetheposteriorprobabilityP(h
3、D)mustbecomputedforeachhypothesish∈HandcombinedwiththepredictionP(v
4、h)beforevMAPcanbecomputed.Inlesson10,MichaeldiscussesBay
5、esianinference.TheendgoalofthislessonistointroduceanalternativeclassificationmodeltotheoptimalBayesclassifier:thenaiveBayesclassifier.ThismodelismuchmorecomputationallyefficientthanoptimalBayesclassification,andundercertainconditionsithasperformance1comparabletoneuralnetworksanddecisiontrees
6、.NaiveBayesclassifiersrepresentaspecialcaseofclassifiersderivedfrombeliefnetworksgraphicalmodelswhichrepresentasetofrandom2variablesandtheirconditionaldependencies.InthesenoteswereviewbeliefnetworksandthespecialcaseofnaiveBayesclassifiers,alongwithsomedefinitionsfromprobability.Definitionsfr
7、omProbability:Inthissectionwerecallafewdefinitionsfromprobabilitythatwewillneedmovingforward.FeelfreetoskipthissectionifyouarefamiliarwithconditionalprobabilityandBayes’theorem.1Mitchell,TomM."Machinelearning.1997."BurrRidge,IL:McGrawHill45(1997).2"BayesiannetworkWikipedia,thefreeencyclopedi
8、a."2003.9May.2014Copyright?2014Udacity,Inc.AllRightsReserved.WesaythatXisconditionallyindependentofYgivenZifforallvalues(xi,yj,zk)wehaveP(X=xi
9、Y=yj,Z=zk)=P(X=xi
10、Z=zk).Writingoutalldefinitions,weseethatitisequivalenttosaythatforallvalues(xi,yj,zk
11、)wehaveP(X=xi,Y=yj
12、Z=zk)=P(X=xi
13、Z=zk)P(Y=yj
14、Z=zk).Wewillalsorecallthefollowinginferencingrules:Theproductrule(aka,thechainrule):P(X,Y)=P(X
15、Y)P(Y)=P(Y
16、X)P(X)Itishelpfultonotethatthisrulealsohasthemoregeneralform:P(X1,...,Xn)=P(X1
17、X2,...,Xn)P(X2
18、X3,.
