February 2024 Quantitative uniform stability of the iterative proportional fitting procedure
George Deligiannidis, Valentin de Bortoli, Arnaud Doucet
Author Affiliations +
Ann. Appl. Probab. 34(1A): 501-516 (February 2024). DOI: 10.1214/23-AAP1970

Abstract

We establish that the iterates of the iterative proportional fitting procedure, also known as Sinkhorn’s algorithm and commonly used to solve entropy-regularised optimal transport problems, are stable w.r.t. perturbations of the marginals, uniformly in time. 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.

Citation

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George Deligiannidis. Valentin de Bortoli. Arnaud Doucet. "Quantitative uniform stability of the iterative proportional fitting procedure." Ann. Appl. Probab. 34 (1A) 501 - 516, February 2024. https://doi.org/10.1214/23-AAP1970

Information

Received: 1 October 2021; Revised: 1 January 2023; Published: February 2024
First available in Project Euclid: 28 January 2024

MathSciNet: MR4696283
zbMATH: 07829148
Digital Object Identifier: 10.1214/23-AAP1970

Subjects:
Primary: 49Q22
Secondary: 60-08

Keywords: Entropy regularized optimal transport , iterative proportional fitting procedure , particle filtering , Schrödinger bridge , Sinkhorn algorithm

Rights: Copyright © 2024 Institute of Mathematical Statistics

Vol.34 • No. 1A • February 2024
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