Introducing instrumental variables in the LS-SVM based identification framework

Least-Squares Support Vector Machines (LS-SVM) represent a promising approach to identify nonlinear systems via nonparametric estimation of the nonlinearities in a computationally and stochastically attractive way. All the methods dedicated to the solution of this problem rely on the minimization of a squared-error criterion. In the identification literature, an instrumental variable based optimization criterion was introduced in order to cope with estimation bias in case of a noise modeling error. This principle has never been used in the LS-SVM context so far. Consequently, an instrumental variable scheme is introduced into the LS-SVM regression structure, which not only preserves the computationally attractive feature of the original approach, but also provides unbiased estimates under general noise model structures. The effectiveness of the proposed scheme is demonstrated by a representative example.