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1、ATutorialonLearningWithBayesianNetworksDavidHeckermanheckerma@microsoft.comMarch1995(RevisedNovember1996)TechnicalReportMSR-TR-95-06MicrosoftResearchAdvancedTechnologyDivisionMicrosoftCorporationOneMicrosoftWayRedmond,WA98052Acompanionsetoflectureslidesisavailableatftp://ftp.resea
2、rch.microsoft.com/pub/dtg/david/tutorial.ps.AbstractABayesiannetworkisagraphicalmodelthatencodesprobabilisticrelationshipsamongvariablesofinterest.Whenusedinconjunctionwithstatisticaltechniques,thegraph-icalmodelhasseveraladvantagesfordataanalysis.One,becausethemodelencodesdepende
3、nciesamongallvariables,itreadilyhandlessituationswheresomedataentriesaremissing.Two,aBayesiannetworkcanbeusedtolearncausalrelationships,andhencecanbeusedtogainunderstandingaboutaproblemdomainandtopredicttheconsequencesofintervention.Three,becausethemodelhasbothacausalandprob-abili
4、sticsemantics,itisanidealrepresentationforcombiningpriorknowledge(whichoftencomesincausalform)anddata.Four,Bayesianstatisticalmethodsinconjunc-tionwithBayesiannetworkso eranecientandprincipledapproachforavoidingtheover ttingofdata.Inthispaper,wediscussmethodsforconstructingBayesi
5、annet-worksfrompriorknowledgeandsummarizeBayesianstatisticalmethodsforusingdatatoimprovethesemodels.Withregardtothelattertask,wedescribemethodsforlearningboththeparametersandstructureofaBayesiannetwork,includingtechniquesforlearningwithincompletedata.Inaddition,werelateBayesian-ne
6、tworkmethodsforlearningtotechniquesforsupervisedandunsupervisedlearning.Weillustratethegraphical-modelingapproachusingareal-worldcasestudy.1IntroductionABayesiannetworkisagraphicalmodelforprobabilisticrelationshipsamongasetofvariables.Overthelastdecade,theBayesiannetworkhasbecomea
7、popularrepresentationforencodinguncertainexpertknowledgeinexpertsystems(Heckermanetal.,1995a).Morerecently,researchershavedevelopedmethodsforlearningBayesiannetworksfromdata.Thetechniquesthathavebeendevelopedarenewandstillevolving,buttheyhavebeenshowntoberemarkablye ectiveforsomed
8、ata-analysisproblems.Inthispaper,
