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Wasserstein Identity Testing by Deng, Shichuan; Li, Wenzheng; Wu, Xuan is a scholarly article available to read on EtoBox.

What is Wasserstein Identity Testing about?

Uniformity testing and the more general identity testing are well studied problems in distributional property testing. Most previous work focuses on testing under $L_1$-distance. However, when the support is very large or even continuous, testing under $L_1$-distance may require a huge (even infinite) number of samples. Motivated by such issues, we consider the identity testing in Wasserstein distance (a.k.a. transportation distance and earthmover distance) on a metric space (discrete or continuous). In this paper, we propose the Wasserstein identity testing problem (Identity Testing in Wasserstein distance). We obtain nearly optimal worst-case sample complexity for the problem. Moreover, for a large class of probability distributions satisfying the so-called "Doubling Condition", we provide nearly instance-optimal sample complexity.

Author

Deng, Shichuan; Li, Wenzheng; Wu, Xuan

Published

2017

Language

EN