TY  - UNPB
A1  - Laurain, Vincent
A1  - Tóth, Roland
A1  - Piga, Dario
Y1  - 2013/04//
CY  - The Netherlands
PB  - University of Technology, Eindhoven
EP  - 4
N2  - 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.
N1  - TUE-CS-2013-001
UR  - http://eprints.imtlucca.it/2429/
ID  - eprints2429
TI  - An instrumental Least Squares Support Vector Machine for nonlinear system identification: enforcing zero-centering constraints
AV  - public
M1  - technical_report
ER  -