mlsanityData to 7 Oct 2026

Stochastic Wasserstein Barycenters

arXiv 1802.05757 ↗First posted 15 Feb 2018cs.LG math.OC stat.MLcited by 25

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Abstract (arXiv)

We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and allows the support of the barycenter to be adjusted in each iteration. We tackle the problem without regularization, allowing us to recover a sharp output whose support is contained within the support of the true barycenter. We give examples where our algorithm recovers a more meaningful barycenter than previous work. Our method is versatile and can be extended to applications such as generating super samples from a given distribution and recovering blue noise approximations.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Feb 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 5; 2023: 5; 2024: 5; 2025: 4; 2026: 1.

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  1. 2021Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projectionscited by 52
  2. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  3. 2022Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformercited by 22
  4. 2023Tree-Based Diffusion Schr"odinger Bridge with Applications to Wasserstein Barycenterscited by 16
  5. 2022An Optimal Transport Approach to Personalized Federated Learningcited by 12
  6. 2021Fixed Support Tree-Sliced Wasserstein Barycentercited by 10
  7. 2023Doubly Regularized Entropic Wasserstein Barycenterscited by 10
  8. 2022Measure Estimation in the Barycentric Coding Modelcited by 9
  9. 2021Projection Robust Wasserstein Barycenterscited by 8
  10. 2021Variational Wasserstein Barycenters with c-Cyclical Monotonicitycited by 7
  11. 2023Nonparametric Teaching for Multiple Learnerscited by 7
  12. 2024A New Robust Partial p-Wasserstein-Based Metric for Comparing Distributionscited by 7
13 more
  1. 2021Learning to Generate Wasserstein Barycenterscited by 6
  2. 2022An Accelerated Stochastic Variance-Reduced Algorithm for Entropic Wasserstein Barycenterscited by 6
  3. 2024Approximate Algorithms For k-Sparse Wasserstein Barycenter With Outlierscited by 3
  4. 2025Schr"odinger Bridge Matching for Tree-Structured Costs and Entropic Wasserstein Barycentrescited by 2
  5. 2025A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systemscited by 2
  6. 2025Differentially Private Wasserstein Barycenterscited by 2
  7. 2022Fixed-point iterations for several dissimilarity measure barycenters in the Gaussian casecited by 1
  8. 2024ScoreFusion: Fusing Score-based Generative Models via Kullback-Leibler Barycenterscited by 1
  9. 2024Low dimensional representation of multi-patient flow cytometry datasets using optimal transport for minimal residual disease detection in leukemiacited by 1
  10. 2024Relax and Merge: A Simple Yet Effective Framework for Solving Fair k-Means and k-sparse Wasserstein Barycenter Problemscited by 1
  11. 2025Multivariate Uncertainty Quantification with Tomographic Quantile Forestscited by 1
  12. 2023An Asynchronous Decentralized Algorithm for Wasserstein Barycenter Problemcited by 0
  13. 2026A Sub-4 Approximation for Fair k-Meanscited by 0