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Conference Paper

A Kernel Statistical Test of Independence

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Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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https://papers.nips.cc/paper/3201-a-kernel-statistical-test-of-independence.pdf
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Citation

Gretton, A., Fukumizu, K., Teo, C., Song, L., Schölkopf, B., & Smola, A. (2008). A Kernel Statistical Test of Independence. In J. Platt, D. Koller, Y. Singer, & S. Roweis (Eds.), Advances in Neural Information Processing Systems 20: 21st Annual Conference on Neural Information Processing Systems 2007 (pp. 585-592). Red Hook, NY, USA: Curran.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-C725-8
Abstract
Whereas kernel measures of independence have been widely applied in machine learning (notably in kernel ICA), there is as yet no method to determine whether they have detected statistically significant dependence. We provide a novel test of the independence hypothesis for one particular kernel independence measure, the Hilbert-Schmidt independence criterion (HSIC). The resulting test costs O(m^2), where m is the sample size. We demonstrate that this test outperforms established contingency table-based tests. Finally, we show the HSIC test also applies to text (and to structured data more generally), for which no other independence test presently exists.