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
TypeCommunication / Conférence
External document linkhttp://proceedings.mlr.press/v28/dalalyan13.html
Conference titleInternational Conference on Machine Learning
Conference countryUnited States
Book titleVolume 28: International Conference on Machine Learning, 17-19 June 2013, Atlanta, Georgia, USA
Number of pages1497
MetadataShow full item record
Author(s)Dalalyan, Arnak S.
Centre de Recherche en Économie et Statistique [CREST]
Laboratoire d'Analyse et de Mathématiques Appliquées [LAMA]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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 / Keywordsheteroscedastic regression; group sparsity; time series prediction
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