A low variance consistent test of relative dependency

Abstract : We describe a novel non parametric statistical hypothesis test of relative dependence between a source variable and two candidate target variables. Such a test enables one to answer whether one source variable is significantly more dependent on the first target variable or the second. Dependence is measured via the Hilbert-Schmidt Independence Criterion (HSIC), resulting in a pair of empirical dependence measures (source-target 1, source-target 2). Modeling the covariance between these HSIC statistics leads to a provably more powerful test than the construction of independent HSIC statistics by sub sampling. The resulting test is consistent and unbiased, and (being based on U-statistics) has favorable convergence properties. The test can be computed in quadratic time, matching the computational complexity of standard empirical HSIC estimators. We demonstrate the effectiveness of the test on a real-world linguistics problem of identifying language groups from a multilingual corpus.
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https://hal.inria.fr/hal-01005828
Contributor : Matthew Blaschko <>
Submitted on : Friday, July 11, 2014 - 2:37:35 PM
Last modification on : Tuesday, February 5, 2019 - 1:52:14 PM
Long-term archiving on: Saturday, October 11, 2014 - 12:45:38 PM

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  • HAL Id : hal-01005828, version 3
  • ARXIV : 1406.3852

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Wacha Bounliphone, Arthur Gretton, Matthew Blaschko. A low variance consistent test of relative dependency. 2014. ⟨hal-01005828v3⟩

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