• Mathematics
  • Published 2019

Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space

@inproceedings{Gouic2019FastCO,
  title={Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space},
  author={Thibaut Le Gouic and Quentin Paris and Philippe Rigollet and Austin Stromme},
  year={2019}
}
This work establishes fast rates of convergence for empirical barycenters over a large class of geodesic spaces with curvature bounds in the sense of Alexandrov. More specifically, we show that parametric rates of convergence are achievable under natural conditions that characterize the bi-extendibility of geodesics emanating from a barycenter. These results largely advance the state-of-the-art on the subject both in terms of rates of convergence and the variety of spaces covered. In particular… CONTINUE READING

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