dc.contributor.author | Chesneau, Christophe | |
dc.contributor.author | Peyré, Gabriel | |
dc.contributor.author | Fadili, Jalal | |
dc.contributor.author | Kachour, Maher | |
dc.contributor.author | Dossal, Charles | |
dc.date.accessioned | 2011-11-09T14:44:10Z | |
dc.date.available | 2011-11-09T14:44:10Z | |
dc.date.issued | 2011 | |
dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/7429 | |
dc.language.iso | en | en |
dc.subject | SURE | en |
dc.subject | degrees of freedom | en |
dc.subject | model selection criteria | en |
dc.subject | Lasso | en |
dc.subject.ddc | 519 | en |
dc.title | The degrees of freedom of penalized l1 minimization | en |
dc.type | Document de travail / Working paper | |
dc.contributor.editoruniversityother | Laboratoire de Mathématiques Nicolas Oresme (LMNO) http://www.math.unicaen.fr/lmno/ CNRS : UMR6139 – Université de Caen;France | |
dc.contributor.editoruniversityother | Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen (GREYC) http://www.greyc.unicaen.fr/ CNRS : UMR6072 – Université de Caen – Ecole Nationale Supérieure d'Ingénieurs de Caen;France | |
dc.contributor.editoruniversityother | Institut de Mathématiques de Bordeaux (IMB) http://www.math.u-bordeaux.fr/IMB/ CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II;France | |
dc.description.abstracten | In this paper, we investigate the degrees of freedom (df) of penalized l1 minimization (also known as the Lasso) for linear regression models. We give a closed-form expression of the degrees of freedom of the Lasso response. Namely, we show that for any given Lasso regularization parameter$ \lambda$ and any observed data y belongs to a set of full measure, the cardinal of the support of a particular solution of the Lasso problem is an unbiased estimator of the degrees of freedom of the Lasso response. This work is achieved without any assumption on the uniqueness of the Lasso solution. Thus, our result remains true for both the underdetermined and the overdetermined case studied originally in Zou et al.. We also prove that a key result in Zou et al. is not true by providing a simple counterexample. 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. | en |
dc.publisher.name | Université Paris-Dauphine | en |
dc.publisher.city | Paris | en |
dc.identifier.citationpages | 15 | en |
dc.identifier.urlsite | http://hal.archives-ouvertes.fr/hal-00638417/fr/ | en |
dc.description.sponsorshipprivate | oui | en |
dc.subject.ddclabel | Probabilités et mathématiques appliquées | en |