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Group lasso estimation of high-dimensional covariance matrices

Bigot, Jérémie and Biscay, Rolando and Loubes, Jean-Michel and Muñiz-Alvarez, Lilian Group lasso estimation of high-dimensional covariance matrices. (2011) Journal of Machine Learning Research, 12. 3187-3225. ISSN 1532-4435

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Official URL: http://jmlr.csail.mit.edu/papers/v12/

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.

Item Type:Article
Additional Information:Thanks to Massachusetts Institute of Technology Press editor. The definitive version is available at http://jmlr.csail.mit.edu/papers/v12/bigot11a.html
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Universidad de La Habana - UH (CUBA)
Other partners > Universidad de Chile - UCHILE (CHILE)
Other partners > Universidad de Valparaiso - UV (CHILE)
Laboratory name:
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Deposited By: Jérémie Bigot
Deposited On:15 Mar 2013 14:15

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