High dimensional matrix estimation with unknown variance of the noise - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2011

High dimensional matrix estimation with unknown variance of the noise

Abstract

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.
Fichier principal
Vignette du fichier
variance.pdf (268.35 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00649437 , version 1 (07-12-2011)
hal-00649437 , version 2 (13-12-2011)
hal-00649437 , version 3 (08-02-2012)
hal-00649437 , version 4 (30-01-2015)

Identifiers

  • HAL Id : hal-00649437 , version 1

Cite

Olga Klopp. High dimensional matrix estimation with unknown variance of the noise. 2011. ⟨hal-00649437v1⟩
442 View
430 Download

Share

Gmail Facebook X LinkedIn More