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1、MonteCarloHiddenMarkovModels:LearningNon-ParametricModelsofPartiallyObservableStochasticProcessesSebastianThrunJohnC.LangfordDieterFoxRobotLearningLaboratory,SchoolofComputerScienceCarnegieMellonUniversity5000ForbesAve.,Pittsburgh,PA15213fthrun,jcl,dfoxg@cs.cmu.eduAbstractlearnnon-parametr
2、ichiddenMarkovmodelswithcontin-uousstateandobservationspaces.Sincecontinuousstatespacesaresufficientlyrichtooverfitanydataset,ourap-Wepresentalearningalgorithmfornon-parametricproachusesshrinkageasamechanismforregularization.hiddenMarkovmodelswithcontinuousstateandTheshrinkagefactor,whichdet
3、erminestheeffectivecapac-observationspaces.Allnecessaryprobabilityden-ityoftheHMM,isannealeddownovermultipleiterationssitiesareapproximatedusingsamples,alongwithofEM,andearlystoppingisappliedformodelselection.densitytreesgeneratedfromsuchsamples.AMonteCarloversionofBaum-Welch(EM)isem-MCHMM
4、spossessthefollowingfourcharacteristics,ployedtolearnmodelsfromdata.RegularizationwhichdistinguishesthemfromthetraditionalHMMap-duringlearningisachievedusinganexponentialproach[27]:shrinkingtechnique.Theshrinkagefactor,whichdeterminestheeffectivecapacityofthelearningal-1.Real-valuedspaces.
5、Boththestatespaceandtheob-gorithm,isannealeddownovermultipleiterationsservationspaceofMCHMMsarecontinuous.ThisisofBaum-Welch,andearlystoppingisappliedtoimportantindomainswherethetruestateandobser-selecttherightmodel.Oncetrained,MonteCarlovationspaceoftheenvironmentiscontinuous.TheHMMscanbe
6、runinanany-timefashion.Weproveimportanceofcontinuous-valuedspaceshasbeenrec-thatundermildassumptions,MonteCarloHiddenognizedbyseveralauthors,whichhaveproposedreal-MarkovModelsconvergetoalocalmaximuminvaluedextensionsusingparametricmodelssuchaslikelihoodspace,justlikeconventionalHMMs.InGaus
7、siansandneuralnetworks[2,8,9,13,17].addition,weprovideempiricalresultsobtainedina2.Non-parametric.MostexistingHMMmodelsrelyongesturerecognitiondomain.parametricdensities,definedbyasmallsetofparam-eters(discretedistributionsincluded).Thisisclearlyappropriatewhen