Sampling From the Wasserstein Barycenter

• URL: http://arxiv.org/abs/2105.01706v1
• Date: Tue, 4 May 2021 18:57:41 GMT
• Title: Sampling From the Wasserstein Barycenter
• Authors: Chiheb Daaloul (1), Thibaut Le Gouic (2), Jacques Liandrat (1), Magali Tournus (1) ((1) Aix-Marseille Univ., CNRS, I2M, UMR7373, Centrale Marseille, Marseille, France, (2) Massachusetts Institute of Technology, Department of Mathematics, USA)
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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