Sparse Linear Regression via Generalized Orthogonal Least-Squares

TL;DR

This paper introduces a generalized Orthogonal Least-Squares algorithm for sparse linear regression, improving feature selection efficiency and accuracy over existing greedy methods.

Contribution

It proposes a novel recursive relation-based generalization of OLS that selects multiple features per step, enhancing performance in sparse solutions.

Findings

Generalized OLS outperforms existing greedy algorithms in accuracy.

The new method is computationally efficient.

Simulation results confirm superior performance.

Abstract

Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm sequentially selects the features (i.e., columns of the coefficient matrix) to greedily find an approximate sparse solution. In this paper, a generalization of Orthogonal Least-Squares which relies on a recursive relation between the components of the optimal solution to select L features at each step and solve the resulting overdetermined system of equations is proposed. Simulation results demonstrate that the generalized OLS algorithm is computationally efficient and achieves performance superior to that of existing greedy algorithms broadly used in the literature.