Minimax rates of distribution estimation in wasserstein distance

作     者：Singh, Shashank Poczos, Barnabas 

作者机构：Machine Learning Department and Department of Statistics and Data Science Carnegie Mellon University Machine Learning Department Carnegie Mellon University 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2018年

核心收录：

主　　题：Probability distributions 

摘      要：The Wasserstein metric is an important measure of distance between probability distributions, with many applications in machine learning, statistics, probability theory, and data analysis. This paper provides new upper and lower bounds on statistical minimax rates for the problem of estimating a probability distribution under Wasserstein loss. Specifically, we provide matching rates in a very general setting, using only metric properties, such as covering and packing numbers of balls in the sample space, and moment bounds on the probability distribution. Copyright © 2018, The Authors. All rights reserved.