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Activity Number:
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203
- Advances in Nonparametric Testing
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Type:
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Contributed
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Date/Time:
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Monday, August 8, 2022 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #322558
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Title:
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Independence Testing with Entropy Regularized Optimal Transport
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Author(s):
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Lang Liu* and Soumik Pal and Zaid Harchaoui
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Companies:
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University of Washington and University of Washington and University of Washington
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Keywords:
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independence testing;
optimal transport;
entropy regularization;
non-asymptotic bound;
U-process
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Abstract:
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Optimal transport (OT) has recently gained a lot of attention in statistical inference such as independence testing and density estimation. While OT has been used to develop independence tests, its empirical estimator is known to suffer from the curse of dimensionality. We introduce in this paper an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples, with a convergence rate that is independent of the dimension. We establish non-asymptotic bounds for our test statistic and study its statistical behavior under both the null and alternative hypotheses. Our theoretical results rely on tools from U-process theory and optimal transport theory. We illustrate the interest of the proposed test by comparing it with other independence tests on existing benchmarks.
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Authors who are presenting talks have a * after their name.
