The University of Tokyo, Meguro, Tokyo 153-0041, Japan.
RIKEN Center for Advanced Intelligence Project, Chuo, Tokyo, 103-0027, Japan
Neural Comput. 2022 May 19;34(6):1448-1487. doi: 10.1162/neco_a_01501.
We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its excellent properties. However, hypothesis tests and a confidence analysis for it have not been established in a general multivariate setting. This is because the limit distribution of the empirical distribution with the Wasserstein distance is unavailable without strong restriction. To address this problem, in this study, we develop a novel nonasymptotic gaussian approximation for the empirical 1-Wasserstein distance. Using the approximation method, we develop a hypothesis test and confidence analysis for the empirical 1-Wasserstein distance. We also provide a theoretical guarantee and an efficient algorithm for the proposed approximation. Our experiments validate its performance numerically.
我们开发了一个使用 1-Wasserstein 距离进行统计推断的通用框架。最近，Wasserstein 距离因其优异的性质而引起了相当多的关注，并已广泛应用于各种机器学习任务。然而，其在一般多元环境下的假设检验和置信度分析尚未建立。这是因为在没有强限制的情况下，Wasserstein 距离的经验分布的极限分布是不可用的。为了解决这个问题，在本研究中，我们为经验 1-Wasserstein 距离开发了一种新颖的非渐近高斯逼近。使用逼近方法，我们为经验 1-Wasserstein 距离开发了假设检验和置信度分析。我们还为所提出的逼近方法提供了理论保证和有效的算法。我们的实验在数值上验证了它的性能。
