Beyond GAP screening for Lasso by exploiting new dual cutting half-spaces with supplementary material

TL;DR

This paper introduces a new safe screening method for Lasso that uses a dome-shaped region based on dual cutting half-spaces, outperforming existing GAP-based methods in efficiency and acceleration.

Contribution

The paper presents a novel safe screening test for Lasso leveraging dual cutting half-spaces and a dome geometry, improving upon existing GAP screening methods.

Findings

The new safe region is always included in the GAP Sphere and Dome regions.

Numerical experiments show the new method provides more powerful screening.

The approach leads to significant acceleration in solving Lasso problems.

Abstract

In this paper, we propose a novel safe screening test for Lasso. Our procedure is based on a safe region with a dome geometry and exploits a canonical representation of the set of half-spaces (referred to as "dual cutting half-spaces" in this paper) containing the dual feasible set. The proposed safe region is shown to be always included in the state-of-the-art "GAP Sphere" and "GAP Dome" proposed by Fercoq et al. (and strictly so under very mild conditions) while involving the same computational burden. Numerical experiments confirm that our new dome enables to devise more powerful screening tests than GAP regions and lead to significant acceleration to solve Lasso.