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Rank penalized estimators for high-dimensional matrices

dc.contributor.authorKlopp, Olga
dc.date.accessioned2011-04-18T09:38:44Z
dc.date.available2011-04-18T09:38:44Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/5982
dc.language.isoenen
dc.subjectlow rank matrix estimationen
dc.subjectmatrix completionen
dc.subjectrecovery of the ranken
dc.subjectstatistical learningen
dc.subject.ddc519en
dc.titleRank penalized estimators for high-dimensional matricesen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherCentre de Recherche en Économie et Statistique (CREST) http://www.crest.fr/ INSEE – École Nationale de la Statistique et de l'Administration Économique;France
dc.description.abstractenIn this paper we consider the trace regression model. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A_0$ corrupted by noise. We propose a new rank penalized estimator of $A_0$. For this estimator we establish general oracle inequality for the prediction error both in probability and in expectation. We also prove upper bounds for the rank of our estimator. Then we apply our general results to the problem of matrix completion when our estimator has a particularly simple form: it is obtained by hard thresholding of the singular values of a matrix constructed from the observations.en
dc.relation.isversionofjnlnameElectronic Journal of Statistics
dc.relation.isversionofjnlvol5
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages1161-1183
dc.relation.isversionofdoihttp://dx.doi.org/10.1214/11-EJS637
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00583884/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statistics
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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