mlsanityData to 7 Oct 2026

Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure

arXiv 2108.08129 ↗First posted 18 Aug 2021stat.ML cs.LG math.OCcited by 11

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Abstract (arXiv)

We establish the uniform in time stability, w.r.t. the marginals, of the Iterative Proportional Fitting Procedure, also known as Sinkhorn algorithm, used to solve entropy-regularised Optimal Transport problems. Our result is quantitative and stated in terms of the 1-Wasserstein metric. As a corollary we establish a quantitative stability result for Schr"odinger bridges.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 13 of its 40 references that are in the map. First posted on arXiv 18 Aug 2021.

Builds on

13 of 40 references.

References · 13

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  2. 2018Computational Optimal Transportcited by 765
  3. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  4. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 286
  5. 2017Near-linear time approximation algorithms for optimal transport via Sinkhorn iterationcited by 219
  6. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  7. 2021Differentiable Particle Filtering via Entropy-Regularized Optimal Transportcited by 59
  8. 2015Entropic and displacement interpolation: a computational approach using the Hilbert metriccited by 34
  9. 2020Continuous Regularized Wasserstein Barycenterscited by 32
  10. 2019Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithmcited by 27
  11. 2019Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein spacecited by 25
  12. 2021Stability of Entropic Optimal Transport and Schr"odinger Bridgescited by 25
1 more
  1. 2021Entropic Optimal Transport: Geometry and Large Deviationscited by 20

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 4; 2025: 1; 2026: 2.

11 papers.

  1. 2022Rethinking Initialization of the Sinkhorn Algorithmcited by 14
  2. 2024Reflected Schr"odinger Bridge for Constrained Generative Modelingcited by 12
  3. 2023Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithmcited by 10
  4. 2023Hilbert's projective metric for functions of bounded growth and exponential convergence of Sinkhorn's algorithmcited by 8
  5. 2024Soft-constrained Schrodinger Bridge: a Stochastic Control Approachcited by 8
  6. 2023Non-asymptotic convergence bounds for Sinkhorn iterates and their gradients: a coupling approachcited by 7
  7. 2024Optimal Transport on the Lie Group of Roto-translationscited by 4
  8. 2024A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn's algorithmcited by 4
  9. 2026Robust Sublinear Convergence Rates for Iterative Bregman Projectionscited by 1
  10. 2025Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavitycited by 0
  11. 2026Low-Budget Active Learning through Entropic Optimal Transportcited by 0