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Statistics > Machine Learning

arXiv:2108.08129 (stat)
[Submitted on 18 Aug 2021 (v1), last revised 22 Oct 2021 (this version, v2)]

Title:Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure

Authors:George Deligiannidis, Valentin De Bortoli, Arnaud Doucet
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Abstract: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 Schrödinger bridges.
Comments: 14 pages
Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG); Optimization and Control (math.OC); Probability (math.PR)
Cite as: arXiv:2108.08129 [stat.ML]
  (or arXiv:2108.08129v2 [stat.ML] for this version)
  https://doi.org/10.48550/arXiv.2108.08129

Submission history

From: George Deligiannidis [view email]
[v1] Wed, 18 Aug 2021 13:02:31 UTC (26 KB)
[v2] Fri, 22 Oct 2021 12:40:30 UTC (30 KB)
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