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Learning Heteroscedastic Models by Convex Programming under Group Sparsity

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dalalyan13.pdf (447.4Kb)
Date
2013
Collection Id
28
Dewey
Probabilités et mathématiques appliquées
Sujet
Machine Learning
Conference name
30th International Conference on Machine Learning
Conference date
06-2013
Conference city
Atlanta
Conference country
États-Unis
Book title
Proceedings of The 30th International Conference on Machine Learning
Author
Dasgupta, Sanjoy; McAllester, David
Year
2013
URI
https://basepub.dauphine.fr/handle/123456789/14943
Collections
  • CEREMADE : Publications
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Author
Dalalyan, Arnak S.
Hebiri, Mohamed
Meziani, Katia
Salmon, Joseph
Type
Communication / Conférence
Item number of pages
379-387
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.

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