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1、ProbabilisticInferenceUsingMarkovChainMonteCarloMethodsRadfordM.NealTechnicalReportCRG-TR-93-1DepartmentofComputerScienceUniversityofTorontoE-mail:radford@cs.toronto.edu25September1993cCopyright1993byRadfordM.NealAbstractProbabilisticinferenceisanattractiveapproachtouncertainreasoningandem-pirica
2、llearninginarti cialintelligence.Computationaldicultiesarise,however,becauseprobabilisticmodelswiththenecessaryrealismand
exibilityleadtocom-plexdistributionsoverhigh-dimensionalspaces.Relatedproblemsinother eldshavebeentackledusingMonteCarlomethodsbasedonsamplingusingMarkovchains,providingarich
3、arrayoftechniquesthatcanbeappliedtoproblemsinarti cialintelligence.TheMetropolisalgorithm"hasbeenusedtosolvedicultproblemsinstatisticalphysicsforoverfortyyears,and,inthelastfewyears,therelatedmethodofGibbssampling"hasbeenappliedtoproblemsofstatisticalinference.Concurrently,analternativemethodf
4、orsolvingproblemsinstatisticalphysicsbymeansofdynamicalsimulationhasbeendevelopedaswell,andhasrecentlybeenuni edwiththeMetropolisalgorithmtoproducethehybridMonteCarlo"method.Incomputerscience,Markovchainsamplingisthebasisoftheheuristicoptimizationtechniqueofsimulatedannealing",andhasrecentlybee
5、nusedinrandomizedalgorithmsforapproximatecountingoflargesets.Inthisreview,Ioutlinetheroleofprobabilisticinferenceinarti cialintelligence,presentthetheoryofMarkovchains,anddescribevariousMarkovchainMonteCarloalgorithms,alongwithanumberofsupportingtechniques.Itrytopresentacomprehensivepictureofther
6、angeofmethodsthathavebeendeveloped,includingtechniquesfromthevariedliteraturethathavenotyetseenwideapplicationinarti cialintelligence,butwhichappearrelevant.Asillustrativeexamples,Iusetheproblemsofprobabilisticinferenceinexpertsystems,discoveryoflatentclassesfromdata,andBayesianlearningforneuraln
7、etworks.AcknowledgementsIthankDavidMacKay,RichardMann,ChrisWilliams,andthemembersofmyPh.Dcommittee,Geo reyHinton,RudiMathon,DemetriTerzopoulos,andRobTibshirani,fortheirhelpfulcommentsonthisreview.Thisworkwassupportedby
