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  Measuring Statistical Dependence with Hilbert-Schmidt Norms

Gretton, A., Bousquet, O., Smola, A., & Schölkopf, B. (2005). Measuring Statistical Dependence with Hilbert-Schmidt Norms. In S. Jain, H. Simon, & E. Tomita (Eds.), Algorithmic Learning Theory: 16th International Conference, ALT 2005, Singapore, October 8-11, 2005 (pp. 63-78). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-D3E5-E Version Permalink: https://hdl.handle.net/21.11116/0000-0005-0DAC-C
Genre: Conference Paper

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https://link.springer.com/content/pdf/10.1007%2F11564089_7.pdf (Publisher version)
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 Creators:
Gretton, A1, 2, Author           
Bousquet, O, Author           
Smola, A, 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: We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on methodname do not suffer from slow learning rates.
Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

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 Dates: 2005-10
 Publication Status: Issued
 Pages: -
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 Rev. Type: -
 Identifiers: BibTex Citekey: 3774
DOI: 10.1007/11564089_7
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Title: 16th International Conference on Algorithmic Learning Theory (ALT 2005)
Place of Event: Singapore
Start-/End Date: 2005-10-08 - 2005-10-11

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Title: Algorithmic Learning Theory: 16th International Conference, ALT 2005, Singapore, October 8-11, 2005
Source Genre: Proceedings
 Creator(s):
Jain, S, Editor
Simon, HU, Editor
Tomita, E, Editor
Affiliations:
-
Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 63 - 78 Identifier: ISBN: 978-3-540-29242-5

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Pages: - Volume / Issue: 3734 Sequence Number: - Start / End Page: - Identifier: -