• Corpus ID: 234790295

Generalized Wasserstein barycenters between probability measures living on different subspaces

@inproceedings{Delon2021GeneralizedWB,
  title={Generalized Wasserstein barycenters between probability measures living on different subspaces},
  author={Julie Delon and Nathael Gozlan and Alexandre Saint‐Dizier},
  year={2021}
}
In this paper, we introduce a generalization of the Wasserstein barycenter, to a case where the initial probability measures live on different subspaces of R. We study the existence and uniqueness of this barycenter, we show how it is related to a larger multimarginal optimal transport problem, and we propose a dual formulation. Finally, we explain how to compute numerically this generalized barycenter on discrete distributions, and we propose an explicit solution for Gaussian distributions. 

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