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  Behaviour and Convergence of the Constrained Covariance

Gretton, A., Smola, A., Bousquet, O., Herbrich, R., Schölkopf, B., & Logothetis, N.(2004). Behaviour and Convergence of the Constrained Covariance (130). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-F353-1 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-8B27-6
Genre: Report

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MPIK-TR-130.pdf (Publisher version), 348KB
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Gretton, A1, 2, Author              
Smola, A, Author              
Bousquet, O1, 2, Author              
Herbrich, R, Author
Schölkopf, B1, 2, Author              
Logothetis, NK2, 3, 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              
3Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497798              

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 Abstract: We discuss reproducing kernel Hilbert space (RKHS)-based measures of statistical dependence, with emphasis on constrained covariance (COCO), a novel criterion to test dependence of random variables. We show that COCO is a test for independence if and only if the associated RKHSs are universal. That said, no independence test exists that can distinguish dependent and independent random variables in all circumstances. Dependent random variables can result in a COCO which is arbitrarily close to zero when the source densities are highly non-smooth, which can make dependence hard to detect empirically. All current kernel-based independence tests share this behaviour. Finally, we demonstrate exponential convergence between the population and empirical COCO, which implies that COCO does not suffer from slow learning rates when used as a dependence test.

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 Dates: 2004-10
 Publication Status: Published in print
 Pages: 18
 Publishing info: Tübingen, Germany : Max Planck Institute for Biological Cybernetics
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 Identifiers: Report Nr.: 130
BibTex Citekey: 2936
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Title: Technical Report of the Max Planck Institute for Biological Cybernetics
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Pages: - Volume / Issue: 130 Sequence Number: - Start / End Page: - Identifier: -