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  Kernel Constrained Covariance for Dependence Measurement

Gretton, A., Smola, A., Bousquet, O., Herbrich, R., Belitski, A., Augath, M., et al. (2005). Kernel Constrained Covariance for Dependence Measurement. In R. Cowell, & Z. Ghahramani (Eds.), AISTATS 2005: Tenth International Workshop onArtificial Intelligence and Statistics (pp. 112-119). The Society for Artificial Intelligence and Statistics.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-D693-A Version Permalink: http://hdl.handle.net/21.11116/0000-0005-3A83-6
Genre: Conference Paper

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 Creators:
Gretton, A1, 2, Author              
Smola, AJ, Author              
Bousquet, O1, 2, Author              
Herbrich, R, Author
Belitski, A2, 3, Author              
Augath, M2, 3, Author              
Murayama, Y2, 3, Author              
Pauls, J2, 3, 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. All current kernel-based independence tests share this behaviour. We demonstrate exponential convergence between the population and empirical COCO. Finally, we use COCO as a measure of joint neural activity between voxels in MRI recordings of the macaque monkey, and compare the results to the mutual information and the correlation. We also show the effect of removing breathing artefacts from the MRI recording.

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 Dates: 2005-01
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 3174
 Degree: -

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Title: Tenth International Workshop on Artificial Intelligence and Statistics (AI Statistics 2005)
Place of Event: Barbados
Start-/End Date: 2005-01-06 - 2005-01-08

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Title: AISTATS 2005: Tenth International Workshop onArtificial Intelligence and Statistics
Source Genre: Proceedings
 Creator(s):
Cowell, R, Editor
Ghahramani, Z, Editor
Affiliations:
-
Publ. Info: The Society for Artificial Intelligence and Statistics
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 112 - 119 Identifier: ISBN: 0-9727358-1-X