The degrees of freedom of the Group Lasso for a General Design
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 / ConférenceExternal document link
https://hal.archives-ouvertes.fr/hal-00926929Date
2013Conference title
SPARS'13Conference date
2013-07Conference city
LausanneConference country
SWITZERLANDPublished in
Paris
Metadata
Show full item recordAbstract (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 freedomRelated items
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