A geometric proximal gradient method for sparse least squares regression with probabilistic simplex constraint

TL;DR

This paper introduces a geometric proximal gradient method to solve sparse least squares regression with probabilistic simplex constraints, reformulating the problem to enable efficient optimization without L1 regularization.

Contribution

It proposes a novel geometric proximal gradient algorithm tailored for nonconvex, nonsmooth sparse regression under probabilistic constraints, with proven convergence.

Findings

Algorithm effectively finds sparse solutions

Global convergence is established under mild assumptions

Numerical results demonstrate the method's efficiency

Abstract

In this paper, we consider the sparse least squares regression problem with probabilistic simplex constraint. Due to the probabilistic simplex constraint, one could not apply the L1 regularization to the considered regression model. To find a sparse solution, we reformulate the least squares regression problem as a nonconvex and nonsmooth L1 regularized minimization problem over the unit sphere. Then we propose a geometric proximal gradient method for solving the regularized problem, where the explicit expression of the global solution to every involved subproblem is obtained. The global convergence of the proposed method is established under some mild assumptions. Some numerical results are reported to illustrate the effectiveness of the proposed algorithm.