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.

Author(s): Franz, MO. and Schölkopf, B.
Number (issue): 114
Year: 2003
Month: June
Day: 0
Bibtex Type: Technical Report (techreport)
Electronic Archiving: grant_archive
Institution: Max Planck Institute for Biological Cybernetics
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik
Links:

BibTex

@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}
}