An adaptive shortest-solution guided decimation approach to sparse high-dimensional linear regression

TL;DR

This paper introduces ASSD, an adaptive heuristic algorithm for sparse high-dimensional linear regression that outperforms existing methods in accuracy and robustness, especially with correlated measurement matrices.

Contribution

The paper proposes a novel adaptive decimation algorithm, ASSD, for sparse high-dimensional linear regression, improving support recovery and robustness over existing methods.

Findings

ASSD outperforms LASSO and other greedy algorithms in accuracy.

ASSD is robust with highly correlated measurement matrices.

Numerical results validate the effectiveness of ASSD.

Abstract

High-dimensional linear regression model is the most popular statistical model for high-dimensional data, but it is quite a challenging task to achieve a sparse set of regression coefficients. In this paper, we propose a simple heuristic algorithm to construct sparse high-dimensional linear regression models, which is adapted from the shortest solution-guided decimation algorithm and is referred to as ASSD. This algorithm constructs the support of regression coefficients under the guidance of the least-squares solution of the recursively decimated linear equations, and it applies an early-stopping criterion and a second-stage thresholding procedure to refine this support. Our extensive numerical results demonstrate that ASSD outperforms LASSO, vector approximate message passing, and two other representative greedy algorithms in solution accuracy and robustness. ASSD is especially suitable for linear regression problems with highly correlated measurement matrices encountered in real-world applications.