Generalized bootstrap in the Bures-Wasserstein space

TL;DR

This paper introduces a generalized bootstrap method for inference on the Bures-Wasserstein barycenters, providing non-asymptotic guarantees and comparing its performance with existing asymptotic approaches through experiments.

Contribution

It develops a novel bootstrap procedure tailored for the Bures-Wasserstein space, offering finite-sample inference with theoretical guarantees and practical validation.

Findings

Bootstrap confidence sets outperform asymptotic sets in finite samples.

The proposed method has favorable computational complexity.

Experimental results confirm the effectiveness of the bootstrap approach.

Abstract

This study focuses on finite-sample inference on the non-linear Bures-Wasserstein manifold and introduces a generalized bootstrap procedure for estimating Bures-Wasserstein barycenters. We provide non-asymptotic statistical guarantees for the resulting bootstrap confidence sets. The proposed approach incorporates classical resampling methods, including the multiplier bootstrap highlighted as a specific example. Additionally, the paper compares bootstrap-based confidence sets with asymptotic sets obtained in the work arXiv:1901.00226v2, evaluating their statistical performance and computational complexities. The methodology is validated through experiments on synthetic datasets and real-world applications.