人工智能_贝叶斯网络

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1、1ArtificialIntelligence:BayesianNetworks2GraphicalModelsIfnoassumptionofindependenceismade,thenanexponentialnumberofparametersmustbeestimatedforsoundprobabilisticinference.Norealisticamountoftrainingdataissufficienttoestimatesomanyparameters.Ifablanketassumptionofconditionalindependenceismade,effi

2、cienttrainingandinferenceispossible,butsuchastrongassumptionisrarelywarranted.Graphicalmodelsusedirectedorundirectedgraphsoverasetofrandomvariablestoexplicitlyspecifyvariabledependenciesandallowforlessrestrictiveindependenceassumptionswhilelimitingthenumberofparametersthatmustbeestimated.BayesianNe

3、tworks:Directedacyclicgraphsthatindicatecausalstructure.MarkovNetworks:Undirectedgraphsthatcapturegeneraldependencies.3BayesianNetworksDirectedAcyclicGraph(DAG)NodesarerandomvariablesEdgesindicatecausalinfluencesBurglaryEarthquakeAlarmJohnCallsMaryCalls4ConditionalProbabilityTablesEachnodehasacondi

4、tionalprobabilitytable(CPT)thatgivestheprobabilityofeachofitsvaluesgiveneverypossiblecombinationofvaluesforitsparents(conditioningcase).Roots(sources)oftheDAGthathavenoparentsaregivenpriorprobabilities.BurglaryEarthquakeAlarmJohnCallsMaryCallsP(B).001P(E).002BEP(A)TT.95TF.94FT.29FF.001AP(M)T.70F.01

5、AP(J)T.90F.055CPTCommentsProbabilityoffalsenotgivensincerowsmustaddto1.Examplerequires10parametersratherthan25–1=31forspecifyingthefulljointdistribution.NumberofparametersintheCPTforanodeisexponentialinthenumberofparents(fan-in).6JointDistributionsforBayesNetsABayesianNetworkimplicitlydefinesajoint

6、distribution.ExampleThereforeaninefficientapproachtoinferenceis:1)Computethejointdistributionusingthisequation.2)Computeanydesiredconditionalprobabilityusingthejointdistribution.7NaïveBayesasaBayesNetNaïveBayesisasimpleBayesNetYX1X2…XnPriorsP(Y)andconditionalsP(Xi

7、Y)forNaïveBayesprovideCPTsforthene

8、twork.8IndependenciesinBayesNetsIfremovingasubsetofnodesSfromthenetworkrendersnodesXiandXjdisconnected,thenXiandXjareindependentgivenS,i.e.P(Xi

9、Xj,S)=P(Xi

10、S)However,thisistoostrictacriteriaforconditionalind