Group Lasso with Overlaps: the Latent Group Lasso approach

Guillaume Obozinski 1, 2, * Laurent Jacob 3, * Jean-Philippe Vert 4, 5
* Corresponding author
2 SIERRA - Statistical Machine Learning and Parsimony
Inria Paris-Rocquencourt, DI-ENS - Département d'informatique de l'École normale supérieure, ENS Paris - École normale supérieure - Paris, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : We study a norm for structured sparsity which leads to sparse linear predictors whose supports are unions of prede ned overlapping groups of variables. We call the obtained formulation latent group Lasso, since it is based on applying the usual group Lasso penalty on a set of latent variables. A detailed analysis of the norm and its properties is presented and we characterize conditions under which the set of groups associated with latent variables are correctly identi ed. We motivate and discuss the delicate choice of weights associated to each group, and illustrate this approach on simulated data and on the problem of breast cancer prognosis from gene expression data.
Document type :
[Research Report] 2011, pp.60
Contributor : Guillaume Obozinski <>
Submitted on : Monday, October 3, 2011 - 2:49:33 PM
Last modification on : Wednesday, September 28, 2016 - 4:16:37 PM
Document(s) archivé(s) le : Tuesday, November 13, 2012 - 3:01:34 PM


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  • HAL Id : inria-00628498, version 1
  • ARXIV : 1110.0413



Guillaume Obozinski, Laurent Jacob, Jean-Philippe Vert. Group Lasso with Overlaps: the Latent Group Lasso approach. [Research Report] 2011, pp.60. <inria-00628498>




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