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Activity Number:
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390
- Functional and High-Dimensional Data
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Type:
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Contributed
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Date/Time:
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Wednesday, August 10, 2022 : 8:30 AM to 10:20 AM
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Sponsor:
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IMS
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Abstract #323542
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Title:
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Limit Distributions and Fast Rates for Sliced Wasserstein Distances
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Author(s):
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Ritwik Sadhu* and Ziv Goldfeld and Kengo Kato
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Companies:
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Department of Statistics and Data Science, Cornell University and Department of Electrical and Computer Engineering, Cornell University and Department of Statistics and Data Science, Cornell University
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Keywords:
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Wasserstein distance;
Optimal Transport;
Sliced distance;
log concavity;
U Process bootstrap;
Independence Testing
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Abstract:
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Sliced variants of the Wasserstein distance between probability measures (obtained by averaging or maximizing the classical distances over lower-dimensional marginals) have seen increasing popularity in statistics and machine learning. The case of unidimensional projections is of particular interest since the resulting sliced distance is computationally tractable and corresponding empirical convergence is parametric. This paper explores conditions under which the sliced Wasserstein distance between empirical and true measures, appropriately scaled, converges to a limiting distribution. We study the effect of the ambient data dimension d on the constant in empirical convergence rate bounds. For the case of log-concave distributions, we characterize sharper dependence on d than previously known in the literature, by virtue of new bounds on their Cheeger constants. We extend our results to the two-sample setup and prove consistency and efficiency results on tests of independence based on sliced Wasserstein distances. Results on the computation of the sliced Wasserstein distances and their estimates under log-concave distributions are also presented.
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Authors who are presenting talks have a * after their name.
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