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Consistent estimation of a population barycenter in the Wasserstein space

Abstract : We define a notion of barycenter for random probability measures in the Wasserstein space. We give a characterization of the population barycenter in terms of existence and uniqueness for compactly supported measures. Then, the problem of estimating this barycenter from n independent and identically distributed random probability measures is considered. We study the convergence of the empirical barycenter proposed in Agueh and Carlier (2011) to its population counterpart as the number of measures n tends to infinity. To illustrate the benefits of this approach for data analysis and statistics, we finally discuss the usefulness of barycenters in the Wasserstein space for curve and image warping.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00763668
Contributor : Jérémie Bigot <>
Submitted on : Tuesday, December 11, 2012 - 11:38:42 AM
Last modification on : Wednesday, June 9, 2021 - 10:00:09 AM
Long-term archiving on: : Tuesday, March 12, 2013 - 4:20:10 AM

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  • HAL Id : hal-00763668, version 1
  • ARXIV : 1212.2562

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Jérémie Bigot, Thierry Klein. Consistent estimation of a population barycenter in the Wasserstein space. 2012. ⟨hal-00763668v1⟩

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