The statistical rate for support matrix machines under low rankness and row (column) sparsity

This paper proposes a novel estimator for support vector machines with matrix-valued covariates in a high-dimensional setting. We assume that the underlying parameter matrix lies in a low-dimensional subspace that is simultaneously low-rank and row (column) sparse. We formulate the problem as a regularized hinge loss minimization problem using the nuclear and group lasso norms as penalties to exploit the low-dimensional structure. Our primary focus is deriving the statistical convergence rate of the regularized estimator for the unknown parameter matrix. To validate our theoretical findings, we conducted numerical experiments on both simulated and real-world datasets, demonstrating the efficacy of the regularized support matrix machines framework.