Fast algorithm for sparse least trimmed squares via trimmed-regularized reformulation

TL;DR

This paper introduces a fast, theoretically convergent algorithm for sparse least trimmed squares regression, improving computational efficiency when incorporating sparsity-inducing penalties like the l1 norm.

Contribution

It proposes a novel proximal gradient-based reformulation for sparse LTS, enhancing speed and convergence over existing methods.

Findings

Efficiently achieves small objective values in numerical experiments.

Outperforms existing methods in computational speed.

Provides theoretical convergence guarantees.

Abstract

The least trimmed squares (LTS) is a reasonable formulation of robust regression whereas it suffers from high computational cost due to the nonconvexity and nonsmoothness of its objective function. The most frequently used FAST-LTS algorithm is particularly slow when a sparsity-inducing penalty such as the $\ell_1$ norm is added. This paper proposes a computationally inexpensive algorithm for the sparse LTS, which is based on the proximal gradient method with a reformulation technique. Proposed method is equipped with theoretical convergence preferred over existing methods. Numerical experiments show that our method efficiently yields small objective value.