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1、OnthePartitionFunctionandRandomMaximumA-PosterioriPerturbationsTamirHazantamir@ttic.eduTommiJaakkolatommi@csail.mit.eduAbstractcoveryofthe3Djointpositionsfrom2Dimagesisof-teninherentlyambiguous.Similarly,inparsingthereInthispaperwerelatethepartitionfunctio
2、nmightbeequallylikelyparsetreesforthesamesen-tothemax-statisticsofrandomvariables.tence.Inafullyprobabilistictreatment,allpossibleInparticular,weprovideanovelframeworkalternativeassignmentsareconsidered.Thisrequiresforapproximatingandboundingtheparti-summi
3、ngovertheassignmentswiththeirrespectivetionfunctionusingMAPinferenceonran-weights{evaluatingthepartitionfunction{whichisdomlyperturbedmodels.Asaresult,wecanconsiderablyharder.Infact,anyalgorithmforcom-useecientMAPsolverssuchasgraph-cutsputingthepartitionf
4、unctionwouldbeabletoapprox-toevaluatethecorrespondingpartitionfunc-imatetheMAPvaluearbitrarilywellviaatempera-tion.Weshowthatourmethodexcelsinthetureargument(Landau&Lifshitz,1980).Incontrast,typicalhighsignal-highcoupling"regimeMAPinference(maximization)c
5、anbetractableeventhatresultsinraggedenergylandscapesdif-whentheproblemofevaluatingthepartitionfunction cultforalternativeapproaches.(weightedcounting)isnot.ThemainsurprisingresultofourworkisthatMAPin-1.Introductionferencecanbeusedtoapproximatethepartitionf
6、unc-tion.Inotherwords,givenanalgorithmforcomputingLearningandinferenceincomplexmodelsdrivesmuchtheMAPvalue,wecanapproximateorboundthepar-oftheresearchinmachinelearningapplications,fromtitionfunction.TheMAPvaluesinourcasearisefromcomputervision,naturallangu
7、ageprocessing,tocom-randomlyperturbedmodels.Whilemodelsbasedonputationalbiology.Examplesincludeobjectdetec-randomperturbationshavebeenconsideredrecentlytion(Felzenszwalbetal.,2009),stereovision(Szeliski(Papandreou&Yuille,2011;Keshetetal.,2011;Tar-etal.,200
8、7),parsing(Kooetal.,2010),orproteinlowetal.,2012),theirrelationtothepartitionfunctiondesign(Sontagetal.,2008).Theinferenceproblemhasnot.Speci cally,werelatethepartitionfunctioninsuchcasesinvolvesassessingthel
