Sparse Linear Regression via Generalized Orthogonal Least-Squares

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.