Rank penalized estimators for high-dimensional matrices
Klopp, Olga (2011), Rank penalized estimators for high-dimensional matrices, Electronic Journal of Statistics, 5, p. 1161-1183. http://dx.doi.org/10.1214/11-EJS637
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Article accepté pour publication ou publiéLien vers un document non conservé dans cette base
http://hal.archives-ouvertes.fr/hal-00583884/fr/Date
2011Nom de la revue
Electronic Journal of StatisticsVolume
5Éditeur
Institute of Mathematical Statistics
Pages
1161-1183
Identifiant publication
Métadonnées
Afficher la notice complèteAuteur(s)
Klopp, OlgaRésumé (EN)
In 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.Mots-clés
low rank matrix estimation; matrix completion; recovery of the rank; statistical learningPublications associées
Affichage des éléments liés par titre et auteur.
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Klopp, Olga (2011) Document de travail / Working paper
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