The degrees of freedom of the Group Lasso for a General Design

Vaiter, Samuel; Peyré, Gabriel; Fadili, Jalal; Deledalle, Charles-Alban; Dossal, Charles

Vaiter, Samuel; Peyré, Gabriel; Fadili, Jalal; Deledalle, Charles-Alban; Dossal, Charles (2013), The degrees of freedom of the Group Lasso for a General Design, SPARS'13, 2013-07, Lausanne, SWITZERLAND

Type

Communication / Conférence

External document link

https://hal.archives-ouvertes.fr/hal-00926929

Date

2013

Conference title

SPARS'13

Conference date

2013-07

Conference city

Lausanne

Conference country

SWITZERLAND

Published in

Paris

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Author(s)

Vaiter, Samuel

Peyré, Gabriel
Fadili, Jalal
Deledalle, Charles-Alban
Dossal, Charles

Abstract (EN)

In this paper, we are concerned with regression problems where covariates can be grouped in nonoverlapping blocks, from which a few are active. In such a situation, the group Lasso is an attractive method for variable selection since it promotes sparsity of the groups. We study the sensitivity of any group Lasso solution to the observations and provide its precise local parameterization. When the noise is Gaussian, this allows us to derive an unbiased estimator of the degrees of freedom of the group Lasso. This result holds true for any fixed design, no matter whether it is under- or overdetermined. Our results specialize to those of [1], [2] for blocks of size one, i.e. l1 norm. These results allow objective choice of the regularisation parameter through e.g. the SURE.

Subjects / Keywords

Group Lasso; Sparsity; Model selection criteria; Degrees of freedom