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2015

A simpler condition for consistency of a kernel independence test

Gretton, Arthur

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A statistical test of independence may be constructed using the Hilbert-Schmidt Independence Criterion (HSIC) as a test statistic.

The HSIC is defined as the distance between the embedding of the joint distribution, and the embedding of the product of the marginals, in a Reproducing Kernel Hilbert Space (RKHS).
It has previously been shown that when the kernel used in defining the joint embedding is characteristic (that is, the embedding of the joint distribution to the feature space is injective), then the HSIC-based test is consistent.
In particular, it is sufficient for the product of kernels on the individual domains to be characteristic on the joint domain.

A simpler condition for consistency of a kernel independence test · Around

Built on

Measuring statistical dependence with Hilbert-Schmidt norms
A. Gretton, O. Bousquet, A. J. Smola, and B. Schölkopf · 2005
Earlier work this paper cites.
A Hilbert space embedding for distributions
A. J. Smola, A. Gretton, L. Song, and B. Schölkopf · 2007
Earlier work this paper cites.
Measuring and testing dependence by correlation of distances
G. Székely, M. Rizzo, and N. Bakirov · 2007
Earlier work this paper cites.
Kernel measures of conditional dependence
K. Fukumizu, A. Gretton, X. Sun, and B. Schölkopf · 2008
Earlier work this paper cites.

Similar

A kernel statistical test of independence
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Consistent nonparametric tests of independence
A. Gretton and L. Gyorfi · 2010
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B. Sriperumbudur, A. Gretton, K. Fukumizu, G. Lanckriet, and B. Schölkopf · 2010
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Then

Universality, characteristic kernels and RKHS embedding of measures
B. Sriperumbudur, K. Fukumizu, and G. Lanckriet · 2011
Later among the works it cites.
A kernel two-sample test
A. Gretton, K. Borgwardt, M. Rasch, B. Schoelkopf, and A. Smola · 2012
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Distance covariance in metric spaces
R. Lyons · 2013
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Equivalence of distance-based and rkhs-based statistics in hypothesis testing
D. Sejdinovic, B. Sriperumbudur, A. Gretton, and K. Fukumizu · 2013
Later among the works it cites.

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