Minimax Distribution Estimation in Wasserstein Distance

02/24/2018

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by   Shashank Singh, et al.

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The Wasserstein metric is an important measure of distance between probability distributions, with several applications in machine learning, statistics, probability theory, and data analysis. In this paper, we upper and lower bound minimax rates for the problem of estimating a probability distribution under Wasserstein loss, in terms of metric properties, such as covering and packing numbers, of the underlying sample space.