Performance Evaluation of Least Squares SVR in Robust Dynamical System Identification

Least Squares Support Vector Regression (LS-SVR) is a powerful kernel-based learning tool for regression problems. Nonlinear system identification is one of such problems where we aim at capturing the behavior in time of a dynamical system by building a black-box model from the measured input-output time series. Besides the difficulties involved in the specification a suitable model itself, most real-world systems are subject to the presence of outliers in the observations. Hence, robust methods that can handle outliers suitably are desirable. In this regard, despite the existence of a few previous works on robustifying the LS-SVR for regression applications with outliers, its use for dynamical system identification has not been fully evaluated yet. Bearing this in mind, in this paper we assess the performances of two existing robust LS-SVR variants, namely WLS-SVR and RLS-SVR, in nonlinear system identification tasks containing outliers. These robust approaches are compared with standard LS-SVR in experiments with three artificial datasets, whose outputs are contaminated with different amounts of outliers, and a real-world benchmarking dataset. The obtained results for infinite step ahead prediction confirm that the robust LS-SVR variants consistently outperforms the standard LS-SVR algorithm.