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Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure

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arxiv 2108.08129 v2 pith:HIMUWMHJ submitted 2021-08-18 stat.ML cs.LGmath.OCmath.PR

Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure

George Deligiannidis , Valentin De Bortoli , Arnaud Doucet This is my paper
classification stat.ML cs.LGmath.OCmath.PR
keywords quantitativestabilityestablishfittingiterativeprocedureproportionalresult
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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.

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  1. Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithm

    math.PR 2023-07 unverdicted novelty 7.0

    Sinkhorn iterations converge to a Wasserstein mirror gradient flow (the Sinkhorn flow) as regularization epsilon goes to zero with iterations scaled as 1/epsilon.