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Barycenter in Wasserstein space existence and consistency

Abstract : We study barycenters in the Wasserstein space Pp(E) of a locally compact geodesic space (E, d). In this framework, we define the barycenter of a measure P on Pp(E) as its Fréchet mean. The paper establishes its existence and states consistency with respect to P. We thus extends previous results on R^d , with conditions on P or on the sequence converging to P for consistency.
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Submitted on : Monday, March 21, 2016 - 5:31:19 PM
Last modification on : Monday, April 4, 2022 - 3:24:12 PM
Long-term archiving on: : Sunday, November 13, 2016 - 9:00:02 PM

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Thibaut Le Gouic, Jean-Michel Loubes. Barycenter in Wasserstein space existence and consistency. GSI2015 2nd conference on Geometric Science of Information, Oct 2015, Palaiseau, France. pp.104-108, ⟨10.1007/978-3-319-25040-3_12⟩. ⟨hal-01291307⟩

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