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arXiv: 1205.1481

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The Degrees of Freedom of the Group Lasso

Samuel Vaiter (  Corresponding author ) 1, Charles Deledalle 1, Gabriel Peyré 1, Jalal Fadili 2, Charles Dossal 3

(2012-05-07)

This paper studies the sensitivity to the observations of the block/group Lasso solution to an overdetermined linear regression model. Such a regularization is known to promote sparsity patterns structured as nonoverlapping groups of coefficients. Our main contribution provides a local parameterization of the solution with respect to the observations. As a byproduct, we give an unbiased estimate of the degrees of freedom of the group Lasso. Among other applications of such results, one can choose in a principled and objective way the regularization parameter of the Lasso through model selection criteria.

1:	CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
	CNRS : UMR7534 – Université Paris IX - Paris Dauphine
2:	Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen (GREYC)
	CNRS : UMR6072 – Université de Caen Basse-Normandie – Ecole Nationale Supérieure d'Ingénieurs de Caen
3:	Institut de Mathématiques de Bordeaux (IMB)
	CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II

Research team: image

Subject

:

Mathematics/Statistics Mathematics/Information Theory Computer Science/Signal and Image Processing Engineering Sciences/Signal and Image processing Statistics/Statistics Theory Computer Science/Information Theory and Coding

Keyword(s): sparsity – group lasso – block regularization – local variation – degrees of freedom – unbiased risk estimation

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From: Samuel Vaiter <>

Submitted on: Monday, 7 May 2012 17:06:35

Updated on: Monday, 7 May 2012 20:54:30