Robust Matrix Completion - Laboratoire Jean-Alexandre Dieudonné Accéder directement au contenu
Article Dans Une Revue Probability Theory and Related Fields Année : 2017

Robust Matrix Completion

Résumé

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank matrix, which we wish to recover, with a second matrix having a complementary sparse structure such as element-wise or column-wise sparsity. We analyze a class of estimators obtained by solving a constrained convex optimization problem that combines the nuclear norm and a convex relaxation for a sparse constraint. Our results are obtained for the simultaneous presence of random and deterministic patterns in the sampling scheme. We provide guarantees for recovery of low-rank and sparse components from partial and corrupted observations in the presence of noise and show that the obtained rates of convergence are minimax optimal.
Fichier principal
Vignette du fichier
Robust_HAL_V2.pdf (385.2 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01098492 , version 1 (25-12-2014)
hal-01098492 , version 2 (01-07-2016)

Identifiants

Citer

Olga Klopp, Karim Lounici, Alexandre B. Tsybakov. Robust Matrix Completion. Probability Theory and Related Fields, 2017, 169 (1 - 2), pp.523 - 564. ⟨hal-01098492v2⟩
184 Consultations
660 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More