The Benefit of Group Sparsity

TL;DR

This paper develops a theoretical framework for group Lasso based on strong group sparsity, demonstrating its advantages over standard Lasso for signals with group structure, and identifying its limitations through simulations.

Contribution

It introduces the concept of strong group sparsity and provides a theoretical justification for the effectiveness of group Lasso in such settings.

Findings

Group Lasso outperforms standard Lasso for strongly group-sparse signals.

Theoretical predictions about limitations of group Lasso are confirmed by simulations.

The paper establishes a connection between data structure and regularization effectiveness.

Abstract

This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the theory predicts some limitations of the group Lasso formulation that are confirmed by simulation studies.