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We introduce and study a novel model-selection strategy for Bayesian learning, based on optimal transport, along with its associated predictive posterior law: the Wasserstein population barycenter of the posterior law over models.
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The Fréchet distance between multivariate normal distributions
D. C. Dowson and B. V. Landau · 1982
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Clark R. Givens and Rae Michael Shortt · 1984
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Persi Diaconis and David Freedman · 1986
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Ran Wang, Xinyu Wang, and Liming Wu · 2010
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Steve Brooks, Andrew Gelman, Galin Jones, and Xiao-Li Meng · 2011
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Tarek A El Moselhy and Youssef M Marzouk · 2012
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The Bernstein-von-Mises theorem under misspecification
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Kevin P Murphy · 2012
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Subhashis Ghosal and Aad van der Vaart · 2017
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Wasserstein barycenters over Riemannian manifolds
Young-Heon Kim and Brendan Pass · 2017
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Existence and consistency of Wasserstein barycenters
Thibaut Le Gouic and Jean-Michel Loubes · 2017
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Wide consensus aggregation in the Wasserstein space. application to location-scatter families
Pedro C Álvarez-Esteban, Eustasio del Barrio, Juan A Cuesta-Albertos, and Carlos Matrán · 2018
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Jérémie Bigot and Thierry Klein · 2018
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