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Existence and consistency of Wasserstein barycenters


Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random probabilities defined on a geodesic space (Ed). We also prove the consistency of this barycenter in a general setting, that includes taking barycenters of empirical versions of the probability measures or of a growing set of probability measures.

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Correspondence to Thibaut Le Gouic.

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Le Gouic, T., Loubes, J. Existence and consistency of Wasserstein barycenters. Probab. Theory Relat. Fields 168, 901–917 (2017).

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  • Fréchet mean
  • Wasserstein distance
  • Barycenter
  • Existence
  • Consistency

Mathematics Subject Classification

  • 60D05
  • 62H10
  • 62G20