Randomised Wasserstein Barycenter Computation: Resampling with Statistical Guarantees

We propose a hybrid resampling method to approximate finitely supported Wasserstein barycenters on large-scale datasets, which can be combined with any exact solver. Nonasymptotic bounds on the expected error of the objective value as well as the barycenters themselves allow to calibrate computation...

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Bibliographic Details
Main Authors Heinemann, Florian, Munk, Axel, Zemel, Yoav
Format Journal Article
LanguageEnglish
Published 11.12.2020
Subjects
Statistics - Computation
Statistics - Methodology
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Summary:We propose a hybrid resampling method to approximate finitely supported Wasserstein barycenters on large-scale datasets, which can be combined with any exact solver. Nonasymptotic bounds on the expected error of the objective value as well as the barycenters themselves allow to calibrate computational cost and statistical accuracy. The rate of these upper bounds is shown to be optimal and independent of the underlying dimension, which appears only in the constants. Using a simple modification of the subgradient descent algorithm of Cuturi and Doucet, we showcase the applicability of our method on a myriad of simulated datasets, as well as a real-data example from cell microscopy which are out of reach for state of the art algorithms for computing Wasserstein barycenters.
DOI:10.48550/arxiv.2012.06397