Efficient Sparse Reduced-Rank Regression With Covariance Estimation

Multivariate linear regression is a fundamental model widely used in many fields of signal processing and machine learning. To enhance its interpretability and predicting performance, many approaches have been developed. Among them, the sparse reduced-rank regression with covariance estimation (SRRRCE) method has been shown to be promising. SRRRCE is powerful, which jointly considers the dimension reduction and variable selection of the regression coefficient, as well as a covariance selection target. In this paper, we will propose a new optimization formulation for SRRRCE by modifying the variable coupling constraint in the existing formulation. For efficient problem solving, a convergent single-loop algorithm based on the block majorization-minimization algorithmic framework is developed. Numerical experiments demonstrate the proposed estimation method possesses better prediction performance and faster convergence speed compared to the existing one.