mlsanityData to 14 Oct 2026

Linearized Wasserstein Barycenters: Synthesis, Analysis, Representational Capacity, and Applications

arXiv 2410.23602 ↗First posted 31 Oct 2024stat.ML cs.LGcited by 1

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Abstract (arXiv)

We propose the linear barycentric coding model (LBCM) which utilizes the linear optimal transport (LOT) metric for analysis and synthesis of probability measures. We provide a closed-form solution to the variational problem characterizing the probability measures in the LBCM and establish equivalence of the LBCM to the set of 2-Wasserstein barycenters in the special case of compatible measures. Computational methods for synthesizing and analyzing measures in the LBCM are developed with finite sample guarantees. One of our main theoretical contributions is to identify an LBCM, expressed in terms of a simple family, which is sufficient to express all probability measures on the closed unit interval. We show that a natural analogous construction of an LBCM in 2 dimensions fails, and we leave it as an open problem to identify the proper extension in more than 1 dimension. We conclude by demonstrating the utility of LBCM for covariance estimation and data imputation.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 20 of its 63 references that are in the map. First posted on arXiv 31 Oct 2024.

Builds on

20 of 63 references.

References · 20

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  2. 2018Computational Optimal Transportcited by 780
  3. 2021Entropic estimation of optimal transport mapscited by 90
  4. 2019Statistical bounds for entropic optimal transport: sample complexity and the central limit theoremcited by 85
  5. 2021Plugin Estimation of Smooth Optimal Transport Mapscited by 68
  6. 2021Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projectionscited by 53
  7. 2024Statistical optimal transportcited by 47
  8. 2020Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbationscited by 37
  9. 2017Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learningcited by 35
  10. 2020Debiased Sinkhorn barycenterscited by 34
  11. 2019Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein spacecited by 25
  12. 2023Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein spacecited by 20
8 more
  1. 2018Distilled Wasserstein Learning for Word Embedding and Topic Modelingcited by 18
  2. 2021Dynamical Wasserstein Barycenters for Time-series Modelingcited by 10
  3. 2023Doubly Regularized Entropic Wasserstein Barycenterscited by 10
  4. 2022Measure Estimation in the Barycentric Coding Modelcited by 9
  5. 2022Tangential Wasserstein Projectionscited by 4
  6. 2022Nonparametric and Regularized Dynamical Wasserstein Barycenters for Sequential Observationscited by 4
  7. 2023On Rank Energy Statistics via Optimal Transport: Continuity, Convergence, and Change Point Detectioncited by 3
  8. 2023Estimation of entropy-regularized optimal transport maps between non-compactly supported measurescited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Static and Dynamic Approaches to Computing Barycenters of Probability Measures on Graphscited by 1