On kernel structures for regularized system identification (I): a machine learning perspective

Abstract

A center issue for system identification is how to get a model estimate that achieves a good balance between the data fit and the model complexity. For the recently introduced kernel-based regularization method for linear system identification, the problem becomes first how to design a suitable kernel structure and second how to determine a right kernel among the kernel structure. In this paper and its companion one, we will focus on the issue of kernel structure design. Depending on the type of the prior knowledge, we provide two different ways: from a machine learning perspective or from a system theory perspective. We will focus on the first perspective here. In particular, we show that both the stable spline kernel and the diagonal correlated kernel belong to the class of the so-called exponentially convex locally stationary (ECLS) kernels. This finding motivates to construct ECLS or LS kernels for this regularization method in different ways, e.g., based on carefully designed state space models.