马尔科夫逻辑网简介课件.ppt

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1、MarkovLogicNetworksPedroDomingosDept.ComputerScience&Eng.UniversityofWashington(JointworkwithMattRichardson)OverviewRepresentationInferenceLearningApplicationsMarkovLogicNetworksAlogicalKBisasetofhardconstraintsonthesetofpossibleworldsLet’smakethemsoftconstrain

2、ts:Whenaworldviolatesaformula,Itbecomeslessprobable,notimpossibleGiveeachformulaaweight(HigherweightStrongerconstraint)DefinitionAMarkovLogicNetwork(MLN)isasetofpairs(F,w)whereFisaformulainfirst-orderlogicwisarealnumberTogetherwithafinitesetofconstants,itde

3、finesaMarkovnetworkwithOnenodeforeachgroundingofeachpredicateintheMLNOnefeatureforeachgroundingofeachformulaFintheMLN,withthecorrespondingweightwExampleofanMLNCancer(A)Smokes(A)Smokes(B)Cancer(B)Supposewehavetwoconstants:Anna(A)andBob(B)ExampleofanMLNCancer(A)S

4、mokes(A)Friends(A,A)Friends(B,A)Smokes(B)Friends(A,B)Cancer(B)Friends(B,B)Supposewehavetwoconstants:Anna(A)andBob(B)ExampleofanMLNCancer(A)Smokes(A)Friends(A,A)Friends(B,A)Smokes(B)Friends(A,B)Cancer(B)Friends(B,B)Supposewehavetwoconstants:Anna(A)andBob(B)Examp

5、leofanMLNCancer(A)Smokes(A)Friends(A,A)Friends(B,A)Smokes(B)Friends(A,B)Cancer(B)Friends(B,B)Supposewehavetwoconstants:Anna(A)andBob(B)MoreonMLNsGraphstructure:ArcbetweentwonodesiffpredicatesappeartogetherinsomeformulaMLNistemplateforgroundMarkovnetsTypedvariab

6、lesandconstantsgreatlyreducesizeofgroundMarkovnetFunctions,existentialquantifiers,etc.MLNwithoutvariables=Markovnetwork(subsumesgraphicalmodels)MLNsandFirst-OrderLogicInfiniteweightsFirst-orderlogicSatisfiableKB,positiveweightsSatisfyingassignments=Modesofdi

7、stributionMLNsallowcontradictionsbetweenformulasHowtobreakKBintoformulas?AddingprobabilityincreasesdegreesoffreedomKnowledgeengineeringdecisionDefault:ConverttoclausalformOverviewRepresentationInferenceLearningApplicationsConditionalInferenceP(Formula

8、MLN,C)=?M

9、CMC:Sampleworlds,checkformulaholdsP(Formula1

10、Formula2,MLN,C)=?IfFormula2=ConjunctionofgroundatomsFirstconstructminsubsetofnetworknecessarytoanswerquery(generalizationofKBMC)