The Degrees of Freedom of the Group Lasso

Abstract : 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.
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Soumis le : lundi 7 mai 2012 - 17:06:35
Dernière modification le : mercredi 28 septembre 2016 - 16:08:36
Document(s) archivé(s) le : mercredi 8 août 2012 - 02:36:31

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  • HAL Id : hal-00695292, version 1
  • ARXIV : 1205.1481

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Samuel Vaiter, Charles Deledalle, Gabriel Peyré, Jalal M. Fadili, Charles Dossal. The Degrees of Freedom of the Group Lasso. International Conference on Machine Learning Workshop (ICML), 2012, Edinburgh, United Kingdom. <hal-00695292>

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