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Activity Number:
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32
- Nonparametric Methods with High-Dimensional Data
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Type:
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Contributed
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Date/Time:
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Sunday, August 7, 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 #323641
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Title:
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Plugin Estimation of Smooth Optimal Transport Maps and Wasserstein Distances
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Author(s):
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Tudor Manole* and Sivaraman Balakrishnan and Jonathan Niles-Weed and Larry Wasserman
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Companies:
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Carnegie Mellon University and Carnegie Mellon University and New York University and Carnegie Mellon University
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Keywords:
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Optimal Transport;
Wasserstein Distance;
Transport Map;
Minimax Estimation;
Asymptotic Efficiency;
Density Estimation
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Abstract:
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Motivated by the growing popularity of optimal transport as a methodological tool in statistics and machine learning, we study the question of efficiently estimating the optimal transport map between two unknown multivariate distributions. The minimax rate for this problem was recently derived by Huetter and Rigollet (2021), but was only shown to be achievable by a computationally intractable estimator. We prove that various plugin estimators--which are defined as the optimal transport map between nonparametric estimators of the two distributions--are also minimax optimal. Such estimators are simple to compute using standard numerical solvers. Our proofs rely on new stability arguments for the quadratic optimal transport problem. As a byproduct of these results, we also derive new convergence rates and central limit theorems for plugin estimators of the quadratic Wasserstein distance, showing that they are asymptotically efficient.
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Authors who are presenting talks have a * after their name.
