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Kernel-based tests for joint independence
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DOI：10.1111/rssb.12235.png)
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Abstract
En 中文
We investigate the problem of testing whether d possibly multivariate random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two-variable Hilbert-Schmidt independence criterion but allows for an arbitrary number of variables. We embed the joint distribution and the product of the marginals in a reproducing kernel Hilbert space and define the d-variable Hilbert-Schmidt independence criterion dHSIC as the squared distance between the embeddings. In the population case, the value of dHSIC is 0 if and only if the d variables are jointly independent, as long as the kernel is characteristic. On the basis of an empirical estimate of dHSIC, we investigate three non-parametric hypothesis tests: a permutation test, a bootstrap analogue and a procedure based on a gamma approximation. We apply non-parametric independence testing to a problem in causal discovery and illustrate the new methods on simulated and real data sets.
Keywords:
Causal inference
Independence test
Kernel methods
V-statistics
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