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  Kernel Methods for Measuring Independence

Gretton, A., Herbrich, R., Smola, A., Bousquet, O., & Schölkopf, B. (2005). Kernel Methods for Measuring Independence. The Journal of Machine Learning Research, 6, 2075-2129.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-D367-8 Version Permalink: http://hdl.handle.net/21.11116/0000-0004-D75B-4
Genre: Journal Article

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 Creators:
Gretton, A1, 2, Author              
Herbrich, R, Author
Smola, AJ, Author              
Bousquet, O, 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, ou_1497794              

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 Abstract: We introduce two new functionals, the constrained covariance and the kernel mutual information, to measure the degree of independence of random variables. These quantities are both based on the covariance between functions of the random variables in reproducing kernel Hilbert spaces (RKHSs). We prove that when the RKHSs are universal, both functionals are zero if and only if the random variables are pairwise independent. We also show that the kernel mutual information is an upper bound near independence on the Parzen window estimate of the mutual information. Analogous results apply for two correlation-based dependence functionals introduced earlier: we show the kernel canonical correlation and the kernel generalised variance to be independence measures for universal kernels, and prove the latter to be an upper bound on the mutual information near independence. The performance of the kernel dependence functionals in measuring independence is verified in the context of independent component analysis.

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 Dates: 2005-12
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: -
 Identifiers: BibTex Citekey: 3779
 Degree: -

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Title: The Journal of Machine Learning Research
Source Genre: Journal
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Publ. Info: Cambridge, MA : MIT Press
Pages: - Volume / Issue: 6 Sequence Number: - Start / End Page: 2075 - 2129 Identifier: ISSN: 1532-4435
CoNE: https://pure.mpg.de/cone/journals/resource/111002212682020_1