SWAGGER: Sparsity Within and Across Groups for General Estimation and Recovery

TL;DR

This paper introduces a nonconvex structured sparsity penalty that enforces one-sparsity within overlapping groups, enabling mutual exclusivity in solutions, with applications demonstrated and an efficient algorithm proposed.

Contribution

It presents a novel nonconvex regularizer promoting intra-group sparsity and mutual exclusivity, along with an algorithm for efficient optimization.

Findings

Effective enforcement of mutual exclusivity in solutions.

Demonstrated synergy with other regularizers.

Applicable to various problems including total variation variants.

Abstract

Penalty functions or regularization terms that promote structured solutions to optimization problems are of great interest in many fields. Proposed in this work is a nonconvex structured sparsity penalty that promotes one-sparsity within arbitrary overlapping groups in a vector. This allows one to enforce mutual exclusivity between components within solutions to optimization problems. We show multiple example use cases (including a total variation variant), demonstrate synergy between it and other regularizers, and propose an algorithm to efficiently solve problems regularized or constrained by the proposed penalty.