The degrees of freedom of the Lasso in underdetermined linear regression models

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Date
2011
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http://hal.archives-ouvertes.fr/hal-00625219/fr/
Indexation documentaire
Traitement du signal
Subject
un-derdetermined linear regression model; lasso estimate
Titre du colloque
SPARS 2011
Date du colloque
06-2011
Ville du colloque
Edinburgh
Pays du colloque
Royaume-Uni
Titre de l'ouvrage
Book of abstracts of Proceedings of the 4th workshop on SPARS
Année
2011
Nombre total de pages
131
URI
https://basepub.dauphine.fr/handle/123456789/7011
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Auteur
Peyré, Gabriel
Dossal, Charles
Chesneau, Christophe
Fadili, Jalal
Kachour, Maher
Type
Communication / Conférence
Nombre de pages du document
56
Résumé en anglais
In this paper, we investigate the degrees of freedom (df) of penalized `1 minimization (also known as the Lasso) for an un- derdetermined linear regression model. We show that under a suitable condition on the design matrix, the number of nonzero coefficients of the Lasso solution is an unbiased estimate for the degrees of freedom. An effective estimator of the number of degrees of freedom may have several applications including an objectively guided choice of the regularization parameter in the Lasso through the SURE framework. Index Terms—Lasso, degrees of freedom, SURE.