Group Lasso estimation of high-dimensional covariance matrices
Abstract
In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the process has a sparse representation in a large dictionary of basis functions. Using a matrix regression model, we propose a new methodology for high-dimensional covariance matrix estimation based on empirical contrast regularization by a group Lasso penalty. Using such a penalty, the method selects a sparse set of basis functions in the dictionary used to approximate the process, leading to an approximation of the covariance matrix into a low dimensional space. Consistency of the estimator is studied in Frobenius and operator norms and an application to sparse PCA is proposed.
Cite
@article{arxiv.1010.1601,
title = {Group Lasso estimation of high-dimensional covariance matrices},
author = {Jérémie Bigot and Rolando Biscay and Jean-Michel Loubes and Lilian Muniz Alvarez},
journal= {arXiv preprint arXiv:1010.1601},
year = {2011}
}