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ID:39756860
大小:4.64 MB
页数:94页
时间:2019-07-10
《Multivariate Latent Variable》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、TowardsSmoothParticleFiltersforLikelihoodEstimationwithMultivariateLatentVariablesbyAnthonyLeeB.Sc.,TheUniversityofBritishColumbia,2006ATHESISSUBMITTEDINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEinTheFacultyofGraduateStudies(ComputerScience)THEUNIVERSITYOFBRITISHCOLU
2、MBIA(Vancouver)August,2008cAnthonyLee2008AbstractInparametrizedcontinuousstate-spacemodels,onecanobtainestimatesofthelikelihoodofthedataforfixedparametersviatheSequentialMonteCarlomethodology.Unfortunately,evenifthelikelihoodiscontinuousintheparameters,theestimatesproducedbypracticalpartic
3、lefiltersarenot,evenwhencommonrandomnumbersareusedforeachfilter.Thisisbecausethesameresamplingstepwhichdrasticallyreducesthevarianceoftheestimatesalsointroducesdiscontinuitiesintheparticlesthatareselectedacrossfilterswhentheparameterschange.Whenthestatevariablesareunivariate,themethodologyof
4、[23]givesanestimatorofthelog-likelihoodthatiscontinuousintheparameters.Wepresentanon-trivialgeneralizationofthismethodusingtree-basedo(N2)(andaslowasO(NlogN))resamplingschemesthatinducesignifi-cantcorrelationamongsttheselectedparticlesacrossfilters.Inturn,thisreducesthevarianceofthedifferenc
5、ebetweenthelikelihoodevaluatedfordifferentvaluesoftheparametersandtheresultingestimatorisconsiderablysmootherthannaivelyrunningthefilterswithcommonrandomnumbers.Importantly,inpracticeourmethodsrequireonlyachangetotheresampleoperationintheSMCframeworkwithouttheadditionofanyextraparametersand
6、canthereforebeusedforanyapplica-tioninwhichparticlefiltersarealreadyused.Inaddition,exceptingtheoptionaluseofinterpolationintheschemes,therearenoregularityconditionsfortheirusealthoughcertainconditionsmakethemmoreadvantageous.Inthisthesis,wefirstintroducetherelevantaspectsoftheSMCmethodolog
7、ytothetaskoflikelihoodestimationincontinuousstate-spacemodelsandpresentanoverviewofworkrelatedtothetaskofsmoothlikelihoodestimation.Followingthis,weintroducetheoreticallycorrectresamplingschemesthatcannotbeimplementedandthepracticaltree-basedresamplingschemesthatwer
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