The degrees of freedom of the group Lasso for a general design

Abstract : 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.
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Communication dans un congrès
SPARS'13, Jul 2013, Lausanne, Switzerland. 1 page, 2013
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Samuel Vaiter, Gabriel Peyré, Jalal M. Fadili, Charles-Alban Deledalle, Charles Dossal. The degrees of freedom of the group Lasso for a general design. SPARS'13, Jul 2013, Lausanne, Switzerland. 1 page, 2013. <hal-00926929>

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