HIGH-DIMENSIONAL LEAST SQUARE MATRIX REGRESSION VIA ELASTIC NET PENALTY

Matrix regression model was recently developed by Zhou and Li [Journal of the Royal Statistical Society, Series B, 2014, 76: 463-483] and Negahban and Wainwright [Annals of Statistics, 2011, 39(2): 10691097] and Obozinski, Wainwright and Jordan [Annals of Statistics, 2011, 39(1): 1-47]. In this paper, we focus on high-dimensional least square matrix regression via elastic net penalty, which can deal with group variables. We show that elastic net-penalized matrix regression has grouping effect property. Moreover, we give a upper bound of deviation between two correlated prediction vectors. Finally we propose the VNS-EN method to compute the estimator of elastic net-penalized matrix regression. We give its convergence results and iteration-complexity. The numerical experiments are reported.