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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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Contributor : Matthew Blaschko <>
Submitted on : Friday, June 13, 2014 - 1:50:24 PM
Last modification on : Thursday, July 9, 2020 - 4:06:04 PM
Document(s) archivé(s) le : Saturday, September 13, 2014 - 11:06:58 AM


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  • HAL Id : hal-01005828, version 1


Wacha Bounliphone, Arthur Gretton, Matthew Blaschko. A low variance consistent test of relative dependency. 2014. ⟨hal-01005828v1⟩



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