Linear parametric noise models for Least Squares Support Vector Machines

In the identification of nonlinear dynamical models it happens that not only the system dynamics have to be modeled but also the noise has a dynamic character. We show how to adapt Least Squares Support Vector Machines (LS-SVMs) to take advantage of a known or unknown noise model. We furthermore investigate a convex approximation based on over-parametrization to estimate a linear autoregressive noise model jointly with a model for the nonlinear system. Considering a noise model can improve generalization performance. We discuss several properties of the proposed scheme on synthetic data sets and finally demonstrate its applicability on real world data.