The degrees of freedom of the Lasso in underdetermined linear regression modelsReportar como inadecuado




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1 GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen 2 Equipe Image - Laboratoire GREYC - UMR6072 GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen 3 LMNO - Laboratoire de Mathématiques Nicolas Oresme 4 IMB - Institut de Mathématiques de Bordeaux 5 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Abstract : In this paper, we investigate the degrees of freedom df of penalized l1 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 or GCV frameworks.

Keywords : SURE Lasso degrees of freedom SURE.





Autor: Maher Kachour - Jalal M. Fadili - Christophe Chesneau - Charles Dossal - Gabriel Peyré -

Fuente: https://hal.archives-ouvertes.fr/



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