High dimensional matrix estimation with unknown variance of the noise

Klopp, Olga

Klopp, Olga (2011), High dimensional matrix estimation with unknown variance of the noise. https://basepub.dauphine.fr/handle/123456789/7822

Type

Document de travail / Working paper

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http://hal.archives-ouvertes.fr/hal-00649437/fr/

Date

2011

Éditeur

Université Paris-Dauphine

Ville d’édition

Paris

Métadonnées

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Auteur(s)

Klopp, Olga

Résumé (EN)

We propose a new pivotal method for estimating high-dimensional matrices. 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 method for estimating $A_0$ which does not rely on the knowledge or an estimation of the standard deviation of the noise $\sigma$. Our estimator achieves, up to a logarithmic factor, optimal rates of convergence under the Frobenius risk and, thus, has the same prediction performance as previously proposed estimators which rely on the knowledge of $\sigma$. Our method is based on the solution of a convex optimization problem which makes it computationally attractive.

Mots-clés

recovery of the rank; low rank matrix estimation; matrix regression; Matrix completion