期刊
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
卷 80, 期 1, 页码 5-31出版社
WILEY
DOI: 10.1111/rssb.12235
关键词
Causal inference; Independence test; Kernel methods; V-statistics
资金
- Max Planck ETH Center for Learning Systems
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.
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