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1、IEEETRANSACTIONSONPATTERNANALYSISANDMACHINEINTELLIGENCE,VOL.33,NO.10,OCTOBER20112093TheEffectofModelMisspecificationonSemi-SupervisedClassificationTingYangandCareyE.Priebe,SeniorMember,IEEEAbstract—Semi-supervisedclassification—trainingbothonlabeledandunlabeledobservations—can
2、yieldimprovedperformancecomparedtotheclassifierbasedononlythelabeledobservations.Unlabeledobservationsarealwaysbeneficialtoclassificationifthemodelweassumeiscorrect.However,theymaydegradetheclassifierperformancewhenthemodelismisspecified.Intheclassicalclassificationproblemsett
3、ing,manyfactorsaffectthesemi-supervisedperformance,includingtrainingdata,modelspecification,estimationmethod,andtheclassifieritself.Forconcreteness,weconsidermaximumlikelihoodestimationinfinitemixturemodelsandtheBayesplug-inclassifier,duetotheirubiquitousnessandtractability.In
4、thisspecificsetting,weexaminetheeffectofmodelmisspecificationonsemi-supervisedclassificationperformanceandshedsomelightonwhenandwhyperformancedegradationoccurs.IndexTerms—Semi-supervisedclassification,finitemixturemodel,Bayesplug-inclassifier.Ç1INTRODUCTION1.1ProbabilisticMode
5、lLetbethelimitofthesupervisedMLEof,andsupthelimitoftheunsupervisedMLEof.BothandETðX;YÞFXY.ThefeatureobservationXisanunsupsupLIRd-valuedrandomvariable.Thenatureoftheobserva-existundermildregularityconditions.unsuptioniscalledaclasslabel,denotedbyYandtakingvaluesForsi
6、mplicity,weconsidertwo-classclassificationinafinitesetf1;2;...;Kg.Forj¼1;...;K,denotetheclassproblemsthroughoutthispaper.ThejointdensityofconditionaldistributionsbyFj¼FXjY¼j,andassumeweareðX;YÞ,fðX;YÞðx;yÞ,canbewrittenasinthecontinuouscase,sotheclassconditionaldensitiesfjexist
7、.Letj¼PfY¼jgbeclasspriors,whichcanalsobe1fðxj1Þ11fy¼1gþð11Þfðxj2Þ11fy¼2g:referredtoascomponentcoefficients.WeassumethattheclasslabelYisnotobserved,andour1.2PreviousWorkgoalistoclassifythefeatureobservationXwithsmallThequestionsofvalueandriskofsemi-supervisedlearningclassif
8、icationerrorLðgÞ¼PfgðXÞ6¼Yg.Supposewearehasbeeninvestigatedby
