Sparse Reduced-Rank Regression With Adaptive Selection of Groups of Predictors

Sparse reduced-rank regression (SRRR) model has been widely used for dimension reduction and variable selection with wide applications in machine learning, signal processing, econometrics, etc. In this paper, the SRRR estimation problem is investigated which aims at adaptively selecting the whole group of predictors. The problem is formulated to minimize the least squares loss with a sparsity-inducing penalty. For effective variable selection, a novel sparse estimation scheme, called Sorted L-One Penalized Estimation (SLOPE), is considered, where a group-SLOPE type penalty is adopted. An algorithm leveraging the block majorization-minimization framework is developed for efficient problem resolution. Simulations on synthetic data illustrate the effectiveness of the proposed algorithm. The competitive performance of the proposed model in prediction accuracy is numerically demonstrated on real data with comparison to the state-of-the-art methods.