Group Lasso with Overlaps: the Latent Group Lasso approach

TL;DR

This paper introduces the latent group Lasso, a structured sparsity norm that promotes predictors with supports as unions of overlapping groups, with theoretical analysis and applications to gene expression data.

Contribution

It presents a detailed analysis of the latent group Lasso norm, including conditions for correct group identification and guidance on weight selection, with practical demonstrations.

Findings

Conditions for correct group support recovery

Effective weight selection strategies

Successful application to gene expression data

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.