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1、ProbabilisticMatrixFactorizationRuslanSalakhutdinovandAndriyMnihDepartmentofComputerScience,UniversityofToronto6King'sCollegeRd,M5S3G4,Canada{rsalakhu,amnih}@cs.toronto.eduAbstractManyexistingapproachestocollaborativefilteringcanneitherhandleverylargedatas
2、etsnoreasilydealwithuserswhohaveveryfewratings.InthispaperwepresenttheProbabilisticMatrixFactorization(PMF)modelwhichscaleslinearlywiththenumberofobservationsand,moreimportantly,performswellonthelarge,sparse,andveryimbalancedNetflixdataset.Wefurtherextendt
3、hePMFmodeltoincludeanadaptiveprioronthemodelparametersandshowhowthemodelcapacitycanbecontrolledautomatically.Finally,weintroduceacon-strainedversionofthePMFmodelthatisbasedontheassumptionthatuserswhohaveratedsimilarsetsofmoviesarelikelytohavesimilarprefer
4、ences.Theresult-ingmodelisabletogeneralizeconsiderablybetterforuserswithveryfewratings.WhenthepredictionsofmultiplePMFmodelsarelinearlycombinedwiththepredictionsofRestrictedBoltzmannMachinesmodels,weachieveanerrorrateof0.8861,thatisnearly7%betterthanthesc
5、oreofNetflix'sownsystem.1IntroductionOneofthemostpopularapproachestocollaborativefilteringisbasedonlow-dimensionalfactormodels.Theideabehindsuchmodelsisthatattitudesorpreferencesofauseraredeterminedbyasmallnumberofunobservedfactors.Inalinearfactormodel,ause
6、r'spreferencesaremodeledbylinearlycombiningitemfactorvectorsusinguser-specificcoefficients.Forexample,forNusersandMmovies,theN×MpreferencematrixRisgivenbytheproductofanN×DusercoefficientmatrixUTandaD×MfactormatrixV[7].Trainingsuchamodelamountstofindingthebest
7、rank-DapproximationtotheobservedN×MtargetmatrixRunderthegivenlossfunction.Avarietyofprobabilisticfactor-basedmodelshasbeenproposedrecently[2,3,4].Allthesemodelscanbeviewedasgraphicalmodelsinwhichhiddenfactorvariableshavedirectedconnectionstovariablesthatr
8、epresentuserratings.Themajordrawbackofsuchmodelsisthatexactinferenceisintractable[12],whichmeansthatpotentiallysloworinaccurateapproximationsarerequiredforcomputingtheposteriordistributionoverhiddenfactorsinsuchmode
