QUANTITATIVE UNIFORM STABILITY OF THE ITERATIVE PROPORTIONAL FITTING PROCEDURE

被引：2
|
作者：
Deligiannidis, George [1 ]
de Bortoli, Valentin [1 ]
Doucet, Arnaud [1 ]
机构：
[1] Univ Oxford, Dept Stat, Oxford, England
来源：
ANNALS OF APPLIED PROBABILITY | 2024年 / 34卷 / 1A期
关键词：
Entropy regularized optimal transport; Schrodinger bridge; iterative proportional fitting procedure; Sinkhorn algorithm; particle filtering; OPTIMAL TRANSPORT; CONVERGENCE; GEOMETRY;
D O I：
10.1214/23-AAP1970
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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 Schrodinger bridges.
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页码：501 / 516
页数：16
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