Thumbnail - No thumbnail

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

Peyré, Gabriel; Dossal, Charles; Chesneau, Christophe; Fadili, Jalal; Kachour, Maher (2011), The degrees of freedom of the Lasso in underdetermined linear regression models, Book of abstracts of Proceedings of the 4th workshop on SPARS, p. 56

Type
Communication / Conférence
External document link
http://hal.archives-ouvertes.fr/hal-00625219/fr/
Date
2011
Conference title
SPARS 2011
Conference date
2011-06
Conference city
Edinburgh
Conference country
Royaume-Uni
Book title
Book of abstracts of Proceedings of the 4th workshop on SPARS
Number of pages
131
Pages
56
Metadata
Show full item record
Author(s)
Peyré, Gabriel
Dossal, Charles
Chesneau, Christophe
Fadili, Jalal
Kachour, Maher
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.
Subjects / Keywords
un-derdetermined linear regression model; lasso estimate