Learning Heteroscedastic Models by Convex Programming under Group Sparsity

Arnak S. Dalalyan; Mohamed Hebiri; Katia Méziani; Joseph Salmon

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arXiv · 1304.4549

Learning Heteroscedastic Models by Convex Programming under Group Sparsity

Arnak S. Dalalyan·Mohamed Hebiri·Katia Méziani·Joseph Salmon

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Abstract

Popular sparse estimation methods based on $\ell_1$-relaxation, such as the Lasso and the Dantzig selector, require the knowledge of the variance of the noise in order to properly tune the regularization parameter. This constitutes a major obstacle in applying these methods in several frameworks---such as time series, random fields, inverse problems---for which the noise is rarely homoscedastic and its level is hard to know in advance. In this paper, we propose a new approach to the joint estimation of the conditional mean and the conditional variance in a high-dimensional (auto-) regression setting. An attractive feature of the proposed estimator is that it is efficiently computable even for very large scale problems by solving a second-order cone program (SOCP). We present theoretical analysis and numerical results assessing the performance of the proposed procedure.

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Arnak S. Dalalyan, Mohamed Hebiri, Katia Méziani, Joseph Salmon. 2013-04-16. Learning Heteroscedastic Models by Convex Programming under Group Sparsity. https://arxiv.org/abs/1304.4549

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