mlsanityData to 7 Oct 2026

Sampling From the Wasserstein Barycenter

arXiv 2105.01706 ↗First posted 4 May 2021cs.LG stat.MLcited by 5

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Abstract (arXiv)

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.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 12 of its 40 references that are in the map. First posted on arXiv 4 May 2021.

Builds on

12 of 40 references.

References · 12

  1. 2018Computational Optimal Transportcited by 765
  2. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  3. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  4. 2013Fast Computation of Wasserstein Barycenterscited by 216
  5. 2020SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergencecited by 64
  6. 2015Scalable Bayes via Barycenter in Wasserstein Spacecited by 44
  7. 2020Exponential ergodicity of mirror-Langevin diffusionscited by 37
  8. 2021Wasserstein barycenters are NP-hard to computecited by 28
  9. 2019Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithmcited by 27
  10. 2015Fast Optimal Transport Averaging of Neuroimaging Datacited by 26
  11. 2020Sinkhorn Barycenter via Functional Gradient Descentcited by 9
  12. 2020Averaging Atmospheric Gas Concentration Data using Wasserstein Barycenterscited by 1

Built on by

Cited by year

Citing papers per year: 2021: 1; 2022: 2; 2023: 2.

5 papers.

  1. 2022Wasserstein Iterative Networks for Barycenter Estimationcited by 23
  2. 2023Doubly Regularized Entropic Wasserstein Barycenterscited by 10
  3. 2021Variational Wasserstein Barycenters with c-Cyclical Monotonicitycited by 7
  4. 2022Wasserstein Distributionally Robust Optimization with Wasserstein Barycenterscited by 3
  5. 2023Computational Guarantees for Doubly Entropic Wasserstein Barycenters via Damped Sinkhorn Iterationscited by 0