Section: New Results

Group Lasso with Overlaps: the Latent Group Lasso approach

Participant : Guillaume Obozinski.

Collaboration with: Laurent Jacob (Department of Statistics, University of California at Berkeley) and Jean-Philippe Vert (INSERM U900, Mines ParisTech, Institut Curie).

We study in [25] a norm for structured sparsity which leads to sparse linear predictors whose supports are unions of predefined 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 identified. 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.