comp538 introduction to bayesian networks lecture 9 optimal structure learning

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1、COMP538:IntroductiontoBayesianNetworksLecture9:OptimalStructureLearningNevinL.Zhanglzhang@cse.ust.hkDepartmentofComputerScienceandEngineeringHongKongUniversityofScienceandTechnologySpring2007NevinL.Zhang(HKUST)BayesianNetworksSpring20071/47IntroductionAgoodstructurallearnin

2、galgorithmshould,amongothers,DiscoverthetruthprovidedthereissufficientdataFormulationofthisintuition:SupposesufficientdatasampledfromatrueBNmodel.Agoodlearningalgorithmshouldbeabletoreconstructthetruemodelfromdata.Objective:Assumes(complete)datageneratedbyaBN.Discusseswhenandho

3、wthegeneratingmodelcanbereconstructedfromdata.NevinL.Zhang(HKUST)BayesianNetworksSpring20072/47ReferencesChickering,D.M.(1995).AtransformationalcharacterizationofequivalentBayesiannetworkstructures.InProc.11thConf.onUncertaintyinArtificialIntelligence,87-98.Chickering,D.M.(2

4、002).LearningEquivalenceClassesofBayesian-NetworkStructures.JournalofMachineLearningResearch,2:445-498.Chickering,D.M.(2002b).OptimalStructureIdentificationwithGreedySearch.JournalofMachineLearningResearch3:507-554.Kocka,T.andCastelo,R.(2001).ImprovedLearningofBayesianNetwor

5、ks.InProc.17thConf.onUncertaintyinArtificialIntelligence,269-276.Meek,C.(1997).Graphicalmodels:Selectingcausalandstatisticalmodels.PhDthesis,CarnegieMellonUniversity.NevinL.Zhang(HKUST)BayesianNetworksSpring20073/47ModelEquivalenceOutline1ModelEquivalenceConditionsforModelEq

6、uivalenceRepresentingEquivalenceClassofModelsModelEquivalenceandScoringFunctions2ModelInclusionModelinclusionandScoringFunctions3OptimalityConditions4GreedyEquivalenceSearch(GES)NevinL.Zhang(HKUST)BayesianNetworksSpring20074/47ModelEquivalenceModelequivalenceBNsrepresentjoi

7、ntprobabilities.TwodifferentBNsareequivalentiftheyrepresentthesamejointprobability.EquivlenceofBNstructuresLetSandS0betwoBNmodels(DAGstructures)overvariablesV.WesaySandS0areequivalentifforanyparameterizationθofS,thereexistsaparameterizationθ0ofS0suchthatP(V

8、S,θ)=P(V

9、S0,θ0),a

10、ndviceversaInwords,ScanrepresentanyjointdistributionthatS0can,andviceversa.NevinL.