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A simpler condition for consistency of a kernel independence test

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arxiv 1501.06103 v1 pith:ULZ6FT6M submitted 2015-01-25 stat.ML

A simpler condition for consistency of a kernel independence test

classification stat.ML
keywords jointcharacteristicembeddingindependencetestkernelkernelsproduct
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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. In this note, it is established via a result of Lyons (2013) that HSIC-based independence tests are consistent when kernels on the marginals are characteristic on their respective domains, even when the product of kernels is not characteristic on the joint domain.

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Cited by 2 Pith papers

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    Calibrating aggregated test statistics on the permutation distribution itself is finite-sample valid and at least as powerful as Bonferroni-type worst-case calibration, with sequential and two-batch extensions.