Multiresolution Gaussian Processes多分辨率高斯过程

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1、MultiresolutionGaussianProcessesEmilyB.FoxDavidB.DunsonDepartmentofStatisticsDepartmentofStatisticalScienceUniversityofWashingtonDukeUniversitySeattle,WA98195Durham,NC27708ebfox@uw.edudunson@stat.duke.eduJanuary11,2018AbstractWeproposeamultiresolutionGaussi

2、anprocesstocapturelong-range,non-Markoviandependencieswhileallowingforabruptchanges.ThemultiresolutionGPhierarchicallycouplesacollectionofsmoothGPs,eachdefinedoveranelementofarandomnestedpartition.Long-rangedependenciesarecapturedbythetop-levelGPwhilethepart

3、itionpointsdefinetheabruptchanges.DuetotheinherentconjugacyoftheGPs,onecananalyticallymarginalizetheGPsandcomputetheconditionallikelihoodoftheobservationsgiventhepartitiontree.Thispropertyallowsforefficientinferenceofthepartitionitself,forwhichweemploygraph-th

4、eoretictechniques.WeapplythemultiresolutionGPtotheanalysisofMagnetoencephalography(MEG)recordingsofbrainactivity.1IntroductionAkeychallengeinmanytimeseriesapplicationsiscapturinglong-rangedependenciesforwhichMarkov-basedmodelsareinsufficient.Onemethodofaddres

5、singthischallengeisthroughem-ployingaGaussianprocess(GP)withanappropriate(non-band-limited)covariancefunction.However,GPstypicallyassumesmoothnesspropertiesoftheunderlyingfunctionbeingmodeledthatcanblurkeyelementsofthesignalifabruptchangesoccur.TheMat´ernke

6、rnelenableslesssmoothfunctions,butassumesastationaryprocessthatdoesnotadapttovaryinglevelsarXiv:1209.0833v1[stat.ME]5Sep2012ofsmoothness.Likewise,achangepoint[23]orpartition[9]modelbetweensmoothfunctionsfailstocapturelongrangedependenciesspanningchangepoint

7、s.Anotherlong-memoryprocessisthefractionalARIMAprocess[5],withextensionstoinfi-nitevarianceinnovationsin[15];however,theappropriatenessandrobustnessofsuchmodelsforrealdataanalysishasbeenquestioned[8].Waveletmethodshavealsobeenproposed,includingrecentlyforsmo

8、othfunctionswithdiscontinuities[2].Suchmethodsinheritthepropertiesandlimitationsofwaveletanalysis,forexample,lackofshiftinvariance.WetakeafundamentallydifferentapproachbasedonGPsthatallows(i)directinter