Kernel-based tests for joint independence

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...

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Vydáno v:Journal of the Royal Statistical Society. Series B, Statistical methodology Ročník 80; číslo 1; s. 5 - 31
Hlavní autoři: Pfister, Niklas, Bühlmann, Peter, Schölkopf, Bernhard, Peters, Jonas
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford John Wiley & Sons Ltd 01.01.2018
Oxford University Press
Témata:
Causal inference
Criteria
data collection
Discovery
equations
Hilbert space
Independence
Independence test
Independent variables
Kernel methods
Permutations
Random variables
Regression analysis
Statistical methods
Statistics
Variables
V‐statistics
ISSN:1369-7412, 1467-9868
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Shrnutí: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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ISSN:1369-7412
1467-9868
DOI:10.1111/rssb.12235