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Implicit Wiener Series
The Wiener series is one of the standard methods to systematically characterize the nonlinearity of a neural system. The classical estimation method of the expansion coefficients via cross-correlation suffers from severe problems that prevent its application to high-dimensional and strongly nonlinear systems. We propose a new estimation method based on regression in a reproducing kernel Hilbert space that overcomes these problems. Numerical experiments show performance advantages in terms of convergence, interpretability and system size that can be handled.
@techreport{2291, title = {Implicit Wiener Series}, abstract = {The Wiener series is one of the standard methods to systematically characterize the nonlinearity of a neural system. The classical estimation method of the expansion coefficients via cross-correlation suffers from severe problems that prevent its application to high-dimensional and strongly nonlinear systems. We propose a new estimation method based on regression in a reproducing kernel Hilbert space that overcomes these problems. Numerical experiments show performance advantages in terms of convergence, interpretability and system size that can be handled.}, number = {114}, organization = {Max-Planck-Gesellschaft}, institution = {Max Planck Institute for Biological Cybernetics}, school = {Biologische Kybernetik}, month = jun, year = {2003}, slug = {2291}, author = {Franz, MO. and Sch{\"o}lkopf, B.}, month_numeric = {6} }