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Learning Heteroscedastic Models by Convex Programming under Group Sparsity

Dalalyan, Arnak S.; Hebiri, Mohamed; Meziani, Katia; Salmon, Joseph (2013), Learning Heteroscedastic Models by Convex Programming under Group Sparsity, Volume 28: International Conference on Machine Learning, 17-19 June 2013, Atlanta, Georgia, USA, Proceedings of Machine Learning Research, p. 379–387

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Var_adap_ICML2013.pdf (434.1Kb)
Type
Communication / Conférence
External document link
http://proceedings.mlr.press/v28/dalalyan13.html
Date
2013
Conference title
International Conference on Machine Learning
Conference date
2013-06
Conference city
Atlanta
Conference country
United States
Book title
Volume 28: International Conference on Machine Learning, 17-19 June 2013, Atlanta, Georgia, USA
Publisher
Proceedings of Machine Learning Research
Number of pages
1497
Pages
379–387
Metadata
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Author(s)
Dalalyan, Arnak S.
Centre de Recherche en Économie et Statistique [CREST]
Hebiri, Mohamed
Laboratoire d'Analyse et de Mathématiques Appliquées [LAMA]
Meziani, Katia
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Salmon, Joseph cc
Laboratoire Traitement et Communication de l'Information [LTCI]
Abstract (EN)
Popular sparse estimation methods based on ℓ1-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.
Subjects / Keywords
heteroscedastic regression; group sparsity; time series prediction

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