Accéder directement au contenu Accéder directement à la navigation
Article dans une revue

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.
Type de document :
Article dans une revue
Liste complète des métadonnées

Littérature citée [10 références]  Voir  Masquer  Télécharger

https://hal-enpc.archives-ouvertes.fr/hal-00813908
Contributeur : Arnak Dalalyan <>
Soumis le : mardi 16 avril 2013 - 11:44:14
Dernière modification le : lundi 19 octobre 2020 - 09:36:07
Archivage à long terme le : : mercredi 17 juillet 2013 - 04:03:49

Fichiers

Var_adap_ICML2013.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

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

Citation

Arnak S. Dalalyan, Mohamed Hebiri, Katia Méziani, 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⟩

Partager

Métriques

Consultations de la notice

551

Téléchargements de fichiers

495