Existence and consistency of Wasserstein barycenters

@article{Gouic2015ExistenceAC,
  title={Existence and consistency of Wasserstein barycenters},
  author={Thibaut Le Gouic and Jean-Michel Loubes},
  journal={Probability Theory and Related Fields},
  year={2015},
  volume={168},
  pages={901-917}
}
  • Thibaut Le Gouic, Jean-Michel Loubes
  • Published 2015
  • Mathematics
  • Probability Theory and Related Fields
  • 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 (E, d). 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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    • 10
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    • Highly Influenced
    • PDF
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    • 2
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    References

    SHOWING 1-10 OF 39 REFERENCES
    Barycenters in the Wasserstein Space
    • 414
    • Highly Influential
    • PDF
    Consistent estimation of a population barycenter in the Wasserstein space
    • 49
    • PDF
    Wasserstein Barycenters over Riemannian manifolds
    • 46
    • PDF
    Ricci curvature for metric-measure spaces via optimal transport
    • 890
    • PDF
    Gradient Flows: In Metric Spaces and in the Space of Probability Measures
    • 2,327
    • PDF