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2021 Wasserstein gradients for the temporal evolution of probability distributions
Yaqing Chen, Hans-Georg Müller
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Electron. J. Statist. 15(2): 4061-4084 (2021). DOI: 10.1214/21-EJS1883


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.

Funding Statement

Research supported in part by NSF Grants DMS-1712864 and DMS-2014626.


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Yaqing Chen. Hans-Georg Müller. "Wasserstein gradients for the temporal evolution of probability distributions." Electron. J. Statist. 15 (2) 4061 - 4084, 2021.


Received: 1 January 2021; Published: 2021
First available in Project Euclid: 31 August 2021

Digital Object Identifier: 10.1214/21-EJS1883

Primary: 62G05
Secondary: 62G20

Keywords: dynamics of income distributions , evolution of human mortality , Time-varying density functions , Wasserstein metric


Vol.15 • No. 2 • 2021
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