A0987
Title: Best subset selection in reduced rank regression
Authors: Canhong Wen - University of Science and Technology of China (China) [presenting]
Abstract: Sparse reduced-rank regression is one of the most fundamental statistical approaches for investigating the association between large numbers of predictors and responses. While the advance in theory and algorithm is rapid, there still exists a gap between the algorithmic solution and theoretical guarantee, and no literature studies the computation complexity for achieving the statistical convergence rate. We propose a new method by constructing the algorithmic solution to estimate the sparse reduced-rank regression, which is motivated by the primal-dual formulation. Owing to the primal-dual mechanism, the main update of the algorithm is restricted to a small subset of predictors and thus its computation is efficient, especially in high dimensions. Under some mild conditions, we show that the algorithmic solution enjoys nice sampling properties including the consistency of estimation and support set recovery. Therefore, the new method fills up the gap between the theory and algorithm. Moreover, we propose a generalized-type information criterion for tuning the rank and sparsity level. Extensive numerical studies on synthetic and real data show that the proposal enjoys a nice performance on estimation, variable selection, and computation efficiency.