Sparse Reduced Rank Regression With Nonconvex Regularization

TL;DR

This paper introduces a nonconvex regularization approach for sparse reduced rank regression, improving estimation accuracy and computational efficiency over existing convex methods in signal processing and econometrics.

Contribution

It proposes a novel nonconvex sparsity-inducing function and an efficient alternating minimization algorithm for SRRR, outperforming benchmark methods.

Findings

The nonconvex regularization yields better sparsity and accuracy.

The proposed algorithm is significantly faster than benchmarks.

Numerical results confirm improved estimation performance.

Abstract

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The problem is formulated to minimize the least squares loss with a sparsity-inducing penalty considering an orthogonality constraint. Convex sparsity-inducing functions have been used for SRRR in literature. In this work, a nonconvex function is proposed for better sparsity inducing. An efficient algorithm is developed based on the alternating minimization (or projection) method to solve the nonconvex optimization problem. Numerical simulations show that the proposed algorithm is much more efficient compared to the benchmark methods and the nonconvex function can result in a better estimation accuracy.