Sparse Reduced-Rank Regression for Simultaneous Rank and Variable Selection via Manifold Optimization

TL;DR

This paper introduces a novel manifold optimization approach for sparse reduced-rank regression that simultaneously performs rank and variable selection, improving estimation accuracy in high-rank scenarios.

Contribution

It develops a new estimation algorithm combining sparse regularization and manifold optimization for better rank and variable selection in reduced-rank regression.

Findings

Effective in high-rank settings

Accurate estimation of coefficient parameters

Successful application to real data

Abstract

We consider the problem of constructing a reduced-rank regression model whose coefficient parameter is represented as a singular value decomposition with sparse singular vectors. The traditional estimation procedure for the coefficient parameter often fails when the true rank of the parameter is high. To overcome this issue, we develop an estimation algorithm with rank and variable selection via sparse regularization and manifold optimization, which enables us to obtain an accurate estimation of the coefficient parameter even if the true rank of the coefficient parameter is high. Using sparse regularization, we can also select an optimal value of the rank. We conduct Monte Carlo experiments and real data analysis to illustrate the effectiveness of our proposed method.