Nuclear norm regularization for overparametrized Hammerstein systems

In this paper we study the overparametrization scheme for Hammerstein systems in the presence of regularization. The quality of the convex approximation is analysed, that is obtained by relaxing the implicit rank one constraint. To obtain an improved convex relaxation we propose the use of nuclear norms, instead of using ridge regression. On several simple examples we illustrate that this yields a solution close to the best possible convex approximation. Furthermore the experiments suggest that ridge regression in combination with a projection step yield a generalization performance close to the one obtained by nuclear norms.