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Implicit estimation of Wiener series

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Franz,  MO
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Franz, M., & Schölkopf, B. (2004). Implicit estimation of Wiener series. In A. Barros, J. Principe, J. Larsen, T. Adali, & S. Douglas (Eds.), 14th IEEE Signal Processing Society Workshop Machine Learning for Signal Processing 2004 (pp. 735-744). Piscataway, NJ, USA: IEEE Operations Center.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-F397-9
Abstract
The Wiener series is one of the standard methods to systematically characterize the nonlinearity of a 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 an implicit estimation method based on regression in a reproducing kernel Hilbert space that alleviates these problems. Experiments show performance advantages in terms of convergence, interpretability, and system sizes that can be handled.