Estimation of functions from sparse and noisy data is a central theme in machine learning. In the last few years, many algorithms have been developed that exploit Tikhonov regularization theory and reproducing kernel Hilbert spaces. These are the so-called kernel-based methods, which include powerful approaches like regularization networks, support vector machines, and Gaussian regression. Recently, these techniques have also gained popularity in the system identification community. In both linear and nonlinear settings, kernels that incorporate information on dynamic systems, such as the smoothness and stability of the input–output map, can challenge consolidated approaches based on parametric model structures. In the classical parametric setting, the complexity of the model (the model order) needs to be chosen, typically from a finite family of alternatives, by trading bias and variance. This (discrete) model order selection step may be critical, especially when the true model does not belong to the model class. In regularization-based approaches, model complexity is controlled by tuning (continuous) regularization parameters, making the model selection step more robust. In this article, we review these new kernel-based system identification approaches and discuss extensions based on nuclear and [Formula: see text] norms.
Kernel methods in system identification, machine learning and function estimation: A survey