Learning Linear Dynamical Systems with Sparsity Structure

Abstract

We study the problem of system identification for discrete-time linear dynamical systems when the unknown parameter matrix exhibits a row-wise sparsity pattern. Such a structural constraint should reduce sample complexity of the estimation procedure. We give error bounds for the constrained LASSO algorithm in the independent inputs setting. We also work towards extending recent results on single trajectory estimation via constrained LASSO under the row-wise sparsity assumption. We discuss future directions to improve upon existing proof techniques for the estimation of structured parameter matrices in the single trajectory setting.