A Novel Recursive Solution to LS-SVR for Robust Identification of Dynamical Systems

Abstract

Least Squares Support Vector Regression (LS-SVR) is a powerful kernel-based learning tool for regression problems. However, since it is based on the ordinary least squares (OLS) approach for parameter estimation, the standard LS-SVR model is very sensitive to outliers. Robust variants of the LS-SVR model, such as the WLS-SVR and IRLS-SVR models, have been developed aiming at adding robustness to the parameter estimation process, but they still rely on OLS solutions. In this paper we propose a totally different approach to robustify the LS-SVR. Unlike previous models, we maintain the original LS-SVR loss function, while the solution of the resulting linear system for parameter estimation is obtained by means of the Recursive Least M-estimate (RLM) algorithm. We evaluate the proposed approach in nonlinear system identification tasks, using artificial and real-world datasets contaminated with outliers. The obtained results for infinite-steps-ahead prediction shows that proposed model consistently outperforms the WLS-SVR and IRLS-SVR models for all studied scenarios.