mlsanityData to 14 Oct 2026

Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm

arXiv 1905.13194 ↗First posted 30 May 2019stat.ML cs.LG math.STcited by 27

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Abstract (arXiv)

We present a novel algorithm to estimate the barycenter of arbitrary probability distributions with respect to the Sinkhorn divergence. Based on a Frank-Wolfe optimization strategy, our approach proceeds by populating the support of the barycenter incrementally, without requiring any pre-allocation. We consider discrete as well as continuous distributions, proving convergence rates of the proposed algorithm in both settings. Key elements of our analysis are a new result showing that the Sinkhorn divergence on compact domains has Lipschitz continuous gradient with respect to the Total Variation and a characterization of the sample complexity of Sinkhorn potentials. Experiments validate the effectiveness of our method in practice.

Key facts. Cited by 27 papers in the map (data through 14 Oct 2026). First posted on arXiv 30 May 2019.

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Citing papers per year: 2021: 12; 2022: 8; 2023: 3; 2024: 3; 2025: 1.

27 papers.

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  1. 2021Score-based Generative Neural Networks for Large-Scale Optimal Transportcited by 60
  2. 2021Automatic Text Evaluation through the Lens of Wasserstein Barycenterscited by 38
  3. 2022Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EMcited by 34
  4. 2021Wasserstein barycenters are NP-hard to computecited by 28
  5. 2022A Unified Framework for Implicit Sinkhorn Differentiationcited by 28
  6. 2023Energy-guided Entropic Neural Optimal Transportcited by 26
  7. 2022Heterogeneous manifolds for curvature-aware graph embeddingcited by 23
  8. 2022Faster Unbalanced Optimal Transport: Translation invariant Sinkhorn and 1-D Frank-Wolfecited by 22
  9. 2021Complexity of Linear Minimization and Projection on Some Setscited by 20
  10. 2022An improved central limit theorem and fast convergence rates for entropic transportation costscited by 18
  11. 2021Dimensionality Reduction for Wasserstein Barycentercited by 13
  12. 2021Quantitative Uniform Stability of the Iterative Proportional Fitting Procedurecited by 11
15 more
  1. 2023Minimum intrinsic dimension scaling for entropic optimal transportcited by 11
  2. 2023Doubly Regularized Entropic Wasserstein Barycenterscited by 10
  3. 2024Neural Sinkhorn Gradient Flowcited by 9
  4. 2021Heavy Ball Momentum for Conditional Gradientcited by 7
  5. 2024Operator World Models for Reinforcement Learningcited by 7
  6. 2021Sliced Multi-Marginal Optimal Transportcited by 5
  7. 2021Sampling From the Wasserstein Barycentercited by 5
  8. 2021Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transportcited by 5
  9. 2021Optimal transport with f-divergence regularization and generalized Sinkhorn algorithmcited by 4
  10. 2022Wasserstein Distributionally Robust Optimization with Wasserstein Barycenterscited by 3
  11. 2025Schr"odinger Bridge Matching for Tree-Structured Costs and Entropic Wasserstein Barycentrescited by 2
  12. 2022Conditional Gradients for the Approximate Vanishing Idealcited by 1
  13. 2021Approximate Frank-Wolfe Algorithms over Graph-structured Support Setscited by 0
  14. 2022Approximative Algorithms for Multi-Marginal Optimal Transport and Free-Support Wasserstein Barycenterscited by 0
  15. 2024Fused Gromov-Wasserstein Variance Decomposition with Linear Optimal Transportcited by 0