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1、VirtualVectorMachineforBayesianOnlineClassi cationThomasP.MinkaRongjingXiangYuan(Alan)QiMicrosoftResearchDepartmentofCSDepartmentsofCS&Statistics7JJThomsonAvenuePurdueUniversityPurdueUniversityCambridge,CB30FB,UKWestLafayette,IN47907WestLafayette,IN47907Abstractc
2、eptronalgorithmforbinary(two-class)classi cation.Foronlineregressionproblems,aclassicalalgorithmistheKalman lter.Forlinear-Gaussianregression,theInatypicalonlinelearningscenario,aKalman lterisanexactalgorithm,inthesensethatlearnerisrequiredtoprocessalargedataitre
3、tainsalloftheinformationinthedatanecessarystreamusingasmallmemorybu er.Suchtomakeoptimalpredictions.arequirementisusuallyincon
ictwithalearner'sprimarypursuitofpredictionac-Ingeneral,youcanconstructonlinelearningalgo-curacy.Toaddressthisdilemma,weintro-rithmsbyfo
4、llowingaBayesianparadigm(Opper&duceanovelBayesianonlineclassi cational-Winther,1999).Givenastatisticalmodelofthedata,gorithm,calledtheVirtualVectorMachine.youmaintainaposteriordistributiononthemodelThevirtualvectormachineallowsyoutoparameters.Aseachdatapointarriv
5、es,theposteriorsmoothlytrade-o predictionaccuracywithdistributionisupdated.Tomakepredictions,youav-memorysize.Thevirtualvectormachineerageaccordingtoyouruncertaintyintheparameters.summarizestheinformationcontainedintheTheKalman ltercanbeseenasaspecialcaseofthispr
6、ecedingdatastreambyaGaussiandistri-method.Tokeepthemethodwithinamemorybound,butionovertheclassi cationweightsplusayouwilltypicallyneedtoapproximatetheposteriorconstantnumberofvirtualdatapoints.Thedistribution.Anecientande ectiveapproachtovirtualdatapointsaredesi
7、gnedtoaddextrathisiscalledassumed-density ltering(ADF)(Oppernon-Gaussianinformationabouttheclassi-&Winther,1999;Minka,2001).ADFmaintainsan cationweights.Tomaintaintheconstantapproximateposteriordistributionwithinagivenfam-numberofvirtualpoints,thevirtualvectorily
8、F.Uponreceivinganewpoint,theposteriorisup-machineaddsthecurrentrealdatapointintodatedexactlyandthenprojectedbackontoFby nd-thevirtualpointset,mergestwomostsimi
