%0 Report
%9 Technical Report
%A Laurain, Vincent
%A Tóth, Roland
%A Piga, Dario
%C The Netherlands
%D 2013
%F eprints:2429
%I University of Technology, Eindhoven
%N 001
%T An instrumental Least Squares Support Vector Machine for nonlinear system identification: enforcing zero-centering constraints
%U http://eprints.imtlucca.it/2429/
%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 ℓ2 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.
%Z TUE-CS-2013-001