Rank-1 kernels for regularized system identification

Abstract

A kernel-based regularization method to linear system identification was introduced and studied recently. Its novelty is that it finds a reliable way to tackle the bias-variance tradeoff via well-tuned regularization. Kernel design is a key issue for this method and several single kernels have been proposed. Very recently, we introduced and studied the multiple kernel, a conic combination of some suitably chosen fixed kernels. In particular, we investigated the possibility of constructing multiple kernels based on a special class of rank-1 kernels, called output error (OE) kernels. In this contribution, we study OE kernels in more details. The peculiarity of OE kernels lies in that their structure depends on the data. Special cares are thus needed for the use of OE kernels. Two topics are considered: how to select the best OE kernel among a number of candidate OE kernels and how to construct multiple OE kernels in a good way. Numerical experiments show that the proposed OE kernel based regularization method behaves well.