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
TypeCommunication / Conférence
External document linkhttp://hal.archives-ouvertes.fr/hal-00625219/fr/
Conference titleSPARS 2011
Book titleBook of abstracts of Proceedings of the 4th workshop on SPARS
Number of pages131
MetadataShow full item record
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 / Keywordsun-derdetermined linear regression model; lasso estimate
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