The Degrees of Freedom of the Group Lasso

TL;DR

This paper analyzes the sensitivity of the group Lasso solution to data changes, providing a local parameterization and an unbiased degrees of freedom estimate to improve model selection.

Contribution

It introduces a local parameterization of the group Lasso solution and derives an unbiased degrees of freedom estimate, aiding principled regularization parameter selection.

Findings

Unbiased degrees of freedom estimate for the group Lasso

Local parameterization of the solution with respect to observations

Facilitates objective regularization parameter tuning

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.