Wasserstein Identity Testing

نویسندگان

  • Shichuan Deng
  • Wenzheng Li
  • Xuan Wu
چکیده

Uniformity testing and the more general identity testing are well studied problems in distributional property testing. Most previous work focuses on testing under L1-distance. However, when the support is very large or even continuous, testing under L1-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.

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عنوان ژورنال:
  • CoRR

دوره abs/1710.10457  شماره 

صفحات  -

تاریخ انتشار 2017