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Annual Review of Statistics and Its ApplicationStatistical Aspects of Wasserstein Distances

机译：统计年度审查及其默认统计方面的距离

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摘要

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in order to recover the other distribution. They are ubiquitous in mathematics, with a long history that has seen them catalyze core developments in analysis, optimization, and probability. Beyond their intrinsic mathematical richness, they possess attractive features that make them a versatile tool for the statistician: They can be used to derive weak convergence and convergence of moments, and can be easily bounded; they are well-adapted to quantify a natural notion of perturbation of a probability distribution; and they seamlessly incorporate the geometry of the domain of the distributions in question, thus being useful for contrasting complex objects. Consequently, they frequently appear in the development of statistical theory and inferential methodology, and they have recently become an objectofinference inthemselves. Inthis review, we provide a snapshotofthe mainconcepts involved inWassersteindistances and optimaltransportation, and a succinct overview of some of their many statistical aspects.
机译：Wassersein距离是概率分布的指标，受到最佳批量运输问题的启发。粗略地说，他们测量重新配置一个分配概率质量所需的最小努力，以便恢复其他分布。它们在数学中普遍存在，历史悠久，这些历史已经看到它们在分析，优化和概率中催化了核心发展。除了其内在的数学丰富度之外，它们具有吸引力的功能，使它们为统计学家成为一个多功能的工具：它们可用于导出弱趋势和瞬间的收敛性，并且可以很容易地界限;它们很适应，以量化概率分布的扰动的自然概念;并且它们无缝地纳入所讨论的分布域的几何形状，因此对于对比复杂对象有用。因此，它们经常出现在统计理论和推理方法的发展中，它们最近成为独立的Inthem。综述，我们提供了一个快照的MainConcepts涉及InwasserSteIndistances和OptimalTransportation，以及一些许多统计方面的简洁概述。

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