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  Kernels, Regularization and Differential Equations

Steinke, F., & Schölkopf, B. (2008). Kernels, Regularization and Differential Equations. Pattern Recognition, 41(11), 3271-3286. doi:10.1016/j.patcog.2008.06.011.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-C657-4 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-2C70-E
Genre: Journal Article

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 Creators:
Steinke, F1, 2, Author              
Schölkopf, B1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: Many common machine learning methods such as Support Vector Machines or Gaussian process inference make use of positive definite kernels, reproducing kernel Hilbert spaces, Gaussian processes, and regularization operators. In this work these objects are presented in a general, unifying framework, and interrelations are highlighted. With this in mind we then show how linear stochastic differential equation models can be incorporated naturally into the kernel framework. And vice versa, many kernel machines can be interpreted in terms of differential equations. We focus especially on ordinary differential equations, also known as dynamical systems, and it is shown that standard kernel inference algorithms are equivalent to Kalman filter methods based on such models. In order not to cloud qualitative insights with heavy mathematical machinery, we restrict ourselves to finite domains, implying that differential equations are treated via their corresponding finite difference equations.

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 Dates: 2008-11
 Publication Status: Published in print
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 Table of Contents: -
 Rev. Method: -
 Identifiers: DOI: 10.1016/j.patcog.2008.06.011
BibTex Citekey: 5251
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Title: Pattern Recognition
  Other : Pattern Recognit.
Source Genre: Journal
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Publ. Info: Oxford : Pergamon
Pages: - Volume / Issue: 41 (11) Sequence Number: - Start / End Page: 3271 - 3286 Identifier: ISSN: 0031-3203
CoNE: https://pure.mpg.de/cone/journals/resource/954925431363