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dc.contributor.authorRousseau, Judith
dc.contributor.authorChopin, Nicolas
dc.contributor.authorCottet, Vincent
dc.contributor.authorAlquier, Pierre
dc.subjectBayesian matrix completionen
dc.titleBayesian matrix completion: prior specification and consistencyen
dc.typeDocument de travail / Working paper
dc.contributor.editoruniversityotherUCD School of Mathematical Sciences;Irlande
dc.contributor.editoruniversityotherCREST-LS ENSAE;France
dc.description.abstractenLow-rank matrix estimation from incomplete measurements recently received increased attention due to the emergence of several challenging applications, such as recommender systems; see in particular the famous Netflix challenge. While the behaviour of algorithms based on nuclear norm minimization is now well understood [SRJ05, SS05, CP09, CT09, CR09, Gro11, RT11, Klo11, KLT11], an as yet unexplored avenue of re- search is the behaviour of Bayesian algorithms in this context. In this paper, we briefly review the priors used in the Bayesian literature for ma- trix completion. A standard approach is to assign an inverse gamma prior to the singular values of a certain singular value decomposition of the ma- trix of interest; this prior is conjugate. However, we show that two other types of priors (again for the singular values) may be conjugate for this model: a gamma prior, and a discrete prior. Conjugacy is very convenient, as it makes it possible to implement either Gibbs sampling or Variational Bayes. Interestingly enough, the maximum a posteriori for these different priors is related to the nuclear norm minimization problems. Our main contribution is to prove the consistency of the posterior expectation when the discrete prior is used. We also compare all these priors on simulated datasets, and on the classical MovieLens and Netflix datasets.en
dc.publisher.nameUniversité Paris-Dauphineen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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