Matrix covariates regression with simultaneously low rank and row(column) sparse parameter

In this paper, we consider the estimation of the parameters in the regression model with matrix covariates, where the matrix parameter is simultaneously low rank and row(column) sparse. A commonly used way is to reformulate the parameter as the sum of rank one matrix. This approach usually involves nonconvex optimization and the global solution is not guaranteed. In this paper, we propose a new method formulating a convex optimization problem. An alternative direction method of multipliers (ADMM) algorithm is proposed to solve this convex optimization problem. Simulation shows the effectiveness of our algorithm.