Learning Bayesian Networks with Local Structure

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1、LearningBayesianNetworkswithLocalStructureNirFriedmanMoisesGoldszmidtStanfordUniversitySRIInternationalDept.ofComputerScience333RavenswoodWay,EK329GatesBuilding1AMenloPark,CA94025Stanford,CA94305-9010moises@erg.sri.comnir@cs.stanford.eduAbstractInthispaperw

2、eexamineanoveladditiontothe knownmethodsforlearningBayesiannetworksPrfromdatathatimprovesthequalityofthelearned1110.95networks.Ourapproachexplicitlyrepresentsand1100.95learnsthelocalstructureintheconditionalproba-1010.201000.05bilityt

3、ables(CPTs),thatquantifythesenetworks.0110.000100.00Thisincreasesthespaceofpossiblemodels,en-0010.00ablingtherepresentationofCPTswithavariable0000.00numberofparametersthatdependsonthelearnedlocalstructures.TheresultinglearningprocedureFigure1:Asimplenetworkstr

4、uctureandtheassociatediscapableofinducingmodelsthatbetteremulateCPTfornode.therealcomplexityoftheinteractionspresentinthedata.Wedescribethetheoreticalfoundationsandpracticalaspectsoflearninglocalstructures,ABayesiannetworkrepresentsaprobabilitydistributionaswe

5、llasanempiricalevaluationoftheproposedwhoseparametersarespeci®edbyasetofCPTs.Eachmethod.ThisevaluationindicatesthatlearningnodeinthenetworkhasanassociatedCPTthatdescribescurvescharacterizingtheprocedurethatexploitstheconditionalprobabilitydistributionofthatnode

6、giventhelocalstructureconvergefasterthantheseofthedifferentvaluesforitsparents.Initsmostnaiveform,thestandardprocedure.OurresultsalsoshowaCPTisencodedusingatabularrepresentationwhichisthatnetworkslearnedwithlocalstructuretendtolocallyexponentialonthenumberofpar

7、entsofanode:bemorecomplex(intermsofarcs),yetrequireeachassignmentofvaluestotheparentsofanoderequireslessparameters.thespeci®cationofaconditionaldistributionoverthatnode.Thus,forexample,considerthesimplenetworkinFigure1,1Introductionwherethenodes,,andcorresp

8、ondtotheeventsªalarmarmed,ºªburglary,ºªearthquakeºandªloudalarmInrecentyearstherehasbeenagrowingnumberofinterest-sound,ºrespectively.Assumingthatallvariablesarebinary,ingres