文章基本信息

标题：Wasserstein gradients for the temporal evolution of probability distributions
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作者：Yaqing Chen ; Hans-Georg Müller
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2021
卷号：15
期号：2
页码：4061-4084
DOI：10.1214/21-EJS1883
语种：English
出版社：Institute of Mathematical Statistics
摘要：Many studies have been conducted on flows of probability measures, often in terms of gradient flows. We utilize a generalized notion of derivatives with respect to time to model the instantaneous evolution of empirically observed one-dimensional distributions that vary over time and develop consistent estimates for these derivatives. Employing local Fréchet regression and working in local tangent spaces with regard to the Wasserstein metric, we derive the rate of convergence of the proposed estimators. The resulting time dynamics are illustrated with time-varying distribution data that include yearly income distributions and the evolution of mortality over calendar years.
关键词：62G05; 62G20; dynamics of income distributions; evolution of human mortality; Time-varying density functions; Wasserstein metric