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Sampling From the Wasserstein Barycenter

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arxiv 2105.01706 v1 pith:UTM64OBL submitted 2021-05-04 cs.LG stat.ML

Chiheb Daaloul (1) , Thibaut Le Gouic (2) , Jacques Liandrat (1) , Magali Tournus (1) ((1) Aix-Marseille Univ. , CNRS , I2M , UMR7373 , Centrale Marseille
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Marseille France (2) Massachusetts Institute of Technology Department of Mathematics USA)
This is my paper · ORCID
classification cs.LGstat.ML
keywords barycenterwassersteinalgorithmformulationmultimarginalabsolutelyaccountachieved
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This work presents an algorithm to sample from the Wasserstein barycenter of absolutely continuous measures. Our method is based on the gradient flow of the multimarginal formulation of the Wasserstein barycenter, with an additive penalization to account for the marginal constraints. We prove that the minimum of this penalized multimarginal formulation is achieved for a coupling that is close to the Wasserstein barycenter. The performances of the algorithm are showcased in several settings.

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