Year: 2017
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Deng, Shichuan, Li, Wenzheng, Wu, Xuan
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2765520501