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The Degrees of Freedom of the Group Lasso

Vaiter, Samuel; Deledalle, Charles-Alban; Peyré, Gabriel; Fadili, Jalal; Dossal, Charles (2012), The Degrees of Freedom of the Group Lasso, International Conference on Machine Learning Workshop (ICML), 2012, Edinburgh, UNITED KINGDOM

Type
Communication / Conférence
External document link
https://hal.archives-ouvertes.fr/hal-00695292
Date
2012
Conference title
International Conference on Machine Learning Workshop (ICML), 2012
Conference city
Edinburgh
Conference country
UNITED KINGDOM
Published in
Paris
Metadata
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Author(s)
Vaiter, Samuel cc
Deledalle, Charles-Alban
Peyré, Gabriel
Fadili, Jalal
Dossal, Charles
Abstract (EN)
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.
Subjects / Keywords
group lasso; unbiased risk estimation; block regularization; local variation; degrees of freedom; sparsity