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

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Date
2011
Link to item file
http://hal.archives-ouvertes.fr/hal-00625219/fr/
Dewey
Traitement du signal
Sujet
un-derdetermined linear regression model; lasso estimate
Conference name
SPARS 2011
Conference date
06-2011
Conference city
Edinburgh
Conference country
Royaume-Uni
Book title
Book of abstracts of Proceedings of the 4th workshop on SPARS
Year
2011
Pages number
131
URI
https://basepub.dauphine.fr/handle/123456789/7011
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Author
Peyré, Gabriel
Dossal, Charles
Chesneau, Christophe
Fadili, Jalal
Kachour, Maher
Type
Communication / Conférence
Item number of pages
56
Abstract (EN)
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.