人工智能_贝叶斯网络.ppt

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1、1ArtificialIntelligence:BayesianNetworks2GraphicalModelsIfnoassumptionofindependenceismade,thenanexponentialnumberofparametersmustbeestimatedforsoundprobabilisticinference.Norealisticamountoftrainingdataissufficienttoestimatesomanyparameters.Ifablanketass

2、umptionofconditionalindependenceismade,efficienttrainingandinferenceispossible,butsuchastrongassumptionisrarelywarranted.Graphicalmodelsusedirectedorundirectedgraphsoverasetofrandomvariablestoexplicitlyspecifyvariabledependenciesandallowforlessrestrictivei

3、ndependenceassumptionswhilelimitingthenumberofparametersthatmustbeestimated.BayesianNetworks:Directedacyclicgraphsthatindicatecausalstructure.MarkovNetworks:Undirectedgraphsthatcapturegeneraldependencies.3BayesianNetworksDirectedAcyclicGraph(DAG)Nodesarera

4、ndomvariablesEdgesindicatecausalinfluencesBurglaryEarthquakeAlarmJohnCallsMaryCalls4ConditionalProbabilityTablesEachnodehasaconditionalprobabilitytable(CPT)thatgivestheprobabilityofeachofitsvaluesgiveneverypossiblecombinationofvaluesforitsparents(condition

5、ingcase).Roots(sources)oftheDAGthathavenoparentsaregivenpriorprobabilities.BurglaryEarthquakeAlarmJohnCallsMaryCallsP(B).001P(E).002BEP(A)TT.95TF.94FT.29FF.001AP(M)T.70F.01AP(J)T.90F.055CPTCommentsProbabilityoffalsenotgivensincerowsmustaddto1.Examplerequir

6、es10parametersratherthan25–1=31forspecifyingthefulljointdistribution.NumberofparametersintheCPTforanodeisexponentialinthenumberofparents(fan-in).6JointDistributionsforBayesNetsABayesianNetworkimplicitlydefinesajointdistribution.ExampleThereforeaninefficien

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

8、Y)forNaïveBayesprovideCPTsforthe

9、network.8IndependenciesinBayesNetsIfremovingasubsetofnodesSfromthenetworkrendersnodesXiandXjdisconnected,thenXiandXjareindependentgivenS,i.e.P(Xi

10、Xj,S)=P(Xi

11、S)However,thisistoostrictacriteriaforconditionalind