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arXiv · 1506.04153

Existence and Consistency of Wasserstein Barycenters

Thibaut Le Gouic·Jean-Michel Loubes
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Abstract

In this paper, based on the Fr{\'e}chet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random distributions defined on a geodesic space (E, d). We also prove the consistency of this barycenter in a general setting, that includes taking barycenters of empirical versions of the distributions or of a growing set of distributions.

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Thibaut Le Gouic, Jean-Michel Loubes. 2015-06-12. Existence and Consistency of Wasserstein Barycenters. https://arxiv.org/abs/1506.04153

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