%T An instrumental Least Squares Support Vector Machine for nonlinear system identification: enforcing zero-centering constraints
%C The Netherlands
%O TUE-CS-2013-001
%N 001
%L eprints2429
%I University of Technology, Eindhoven
%X Least-Squares Support Vector Machines (LS-SVM's), originating from Stochastic Learning
theory, represent a promising approach to identify nonlinear systems via nonparametric es-
timation of nonlinearities in a computationally and stochastically attractive way. However,
application of LS-SVM's in the identification context is formulated as a linear regression aim-
ing at the minimization of the ?2 loss in terms of the prediction error. This formulation
corresponds to a prejudice of an auto-regressive noise structure, which, especially in the non-
linear context, is often found to be too restrictive in practical applications. In [1], a novel
Instrumental Variable (IV) based estimation is integrated into the LS-SVM approach provid-
ing, under minor conditions, a consistent identification of nonlinear systems in case of a noise
modeling error. It is shown how the cost function of the LS-SVM is modified to achieve an IV-based solution.
In this technical report, a detailed derivation of the results presented in Section 5.2 of [1]
is given as a supplement material for interested readers.
%A Vincent Laurain
%A Roland T?th
%A Dario Piga
%D 2013