An Improved Central Limit Theorem and Fast Convergence Rates for Entropic Transportation Costs

被引：17

作者：

del Barrio, Eustasio ^{[1
]}

Sanz, Alberto Gonzalez ^{[2
]}

Loubes, Jean-Michel ^{[2
]}

Niles-Weed, Jonathan ^{[3
,4
]}

机构：

[1] Univ Valladolid, IMUVA, Valladolid, Spain

[2] Univ Toulouse, IMT, Toulouse, France

[3] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[4] NYU, Ctr Data Sci, New York, NY 10012 USA

来源：

SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE | 2023年 / 5卷 / 03期

基金：

美国国家科学基金会;

关键词：

optimal transport; entropic regularization; central limit theorem; Sinkhorn divergence; REGULARIZED OPTIMAL TRANSPORT; MATCHING ESTIMATORS; ASYMPTOTICS; INFERENCE; SPACES; RANKS; TESTS;

D O I：

10.1137/22M149260X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal transport between measures which are not necessarily discrete. In the compactly supported case, we complement these results with new, faster, convergence rates for the expected entropic transportation cost between empirical measures. Our proof is based on strengthening convergence results for dual solutions to the entropic optimal transport problem.

引用

页码：639 / 669

页数：31

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