Joint Screening Tests for LASSO

TL;DR

This paper introduces a novel 'joint' screening test for LASSO that efficiently screens multiple atoms simultaneously using sphere and dome region approximations, enhancing low-complexity algorithm performance.

Contribution

It proposes a new joint screening method for LASSO that reduces computational complexity by screening multiple atoms at once, with specific techniques for sphere and dome regions.

Findings

The joint screening test effectively reduces the number of atoms to consider.

The method is applicable to sphere and dome region atom sets.

Practical implementation details are discussed.

Abstract

This paper focusses on "safe" screening techniques for the LASSO problem. Motivated by the need for low-complexity algorithms, we propose a new approach, dubbed "joint" screening test, allowing to screen a set of atoms by carrying out one single test. The approach is particularized to two different sets of atoms, respectively expressed as sphere and dome regions. After presenting the mathematical derivations of the tests, we elaborate on their relative effectiveness and discuss the practical use of such procedures.