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A Unifying View of Wiener and Volterra Theory and Polynomial Kernel Regression

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons83919

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

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

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

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Citation

Franz, M., & Schölkopf, B. (2006). A Unifying View of Wiener and Volterra Theory and Polynomial Kernel Regression. Neural Computation, 18(12), 3097-3118. doi:10.1162/neco.2006.18.12.3097.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CF3F-3
Abstract
Volterra and Wiener series are perhaps the best understood nonlinear system representations in signal processing. Although both approaches have enjoyed a certain popularity in the past, their application has been limited to rather low-dimensional and weakly nonlinear systems due to the exponential growth of the number of terms that have to be estimated. We show that Volterra and Wiener series can be represented implicitly as elements of a reproducing kernel Hilbert space by utilizing polynomial kernels. The estimation complexity of the implicit representation is linear in the input dimensionality and independent of the degree of nonlinearity. Experiments show performance advantages in terms of convergence, interpretability, and system sizes that can be handled.