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  The Kernel Mutual Information

Gretton, A., Herbrich, R., & Smola, A.(2003). The Kernel Mutual Information. Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-DCBB-2 Version Permalink: http://hdl.handle.net/21.11116/0000-0005-736A-3
Genre: Report

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 Creators:
Gretton, A1, 2, Author              
Herbrich, R, Author
Smola, AJ, 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: We introduce two new functions, the kernel covariance (KC) and the kernel mutual information (KMI), to measure the degree of independence of several continuous random variables. The former is guaranteed to be zero if and only if the random variables are pairwise independent; the latter shares this property, and is in addition an approximate upper bound on the mutual information, as measured near independence, and is based on a kernel density estimate. We show that Bach and Jordan‘s kernel generalised variance (KGV) is also an upper bound on the same kernel density estimate, but is looser. Finally, we suggest that the addition of a regularising term in the KGV causes it to approach the KMI, which motivates the introduction of this regularisation. The performance of the KC and KMI is verified in the context of instantaneous independent component analysis (ICA), by recovering both artificial and real (musical) signals following linear mixing.

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 Dates: 2003-04
 Publication Status: Published in print
 Pages: 91
 Publishing info: Tübingen, Germany : Max Planck Institute for Biological Cybernetics
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 Identifiers: BibTex Citekey: 2212
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Title: Technical Report of the Max Planck Institute for Biological Cybernetics
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