Distribution's template estimate with Wasserstein metrics

@inproceedings{Boissard2011DistributionsTE,
  title={Distribution's template estimate with Wasserstein metrics},
  author={Emmanuel Boissard and Thibaut Le Gouic and Jean-Michel Loubes},
  year={2011}
}
In this paper we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an estimation of the mean distribution. Moreover, when the distributions are a common measure warped by a centered random operator, then the barycenter enables to recover this distribution template. 

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