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# Learning Heteroscedastic Models by Convex Programming under Group Sparsity

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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https://hal-enpc.archives-ouvertes.fr/hal-00813908
Contributeur : Arnak Dalalyan Connectez-vous pour contacter le contributeur
Soumis le : mardi 16 avril 2013 - 11:44:14
Dernière modification le : mardi 18 janvier 2022 - 15:23:28
Archivage à long terme le : : mercredi 17 juillet 2013 - 04:03:49

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• HAL Id : hal-00813908, version 1
• ARXIV : 1304.4549

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Arnak S. Dalalyan, Mohamed Hebiri, Katia Meziani, Joseph Salmon. Learning Heteroscedastic Models by Convex Programming under Group Sparsity. Proceedings of the 30 th International Conference on Machine Learning, 2013, http://icml.cc/2013/?page_id=43. ⟨hal-00813908⟩

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