Central limit theorems and bootstrap for sparse regularized multimarginal optimal transport and barycenters
Abstract
Wasserstein barycenters are a fundamental tool for the analysis of distribution-valued data, but their computation and statistical analysis become challenging in high-dimensional and multi-sample settings. The unregularized barycenter problem is computationally demanding and suffers severely from the curse of dimensionality, making regularization essential in many applications. While regularized optimal transport methods are widely used, approaches based on entropic penalization tend to overspread mass and may blur the geometric structure of the solution. Motivated by barycenter estimation, we propose a more general methodology based on sparse regularized multimarginal optimal transport (RMOT). Our formulation creates sparse transport plans and is designed to avoid this overspreading effect. We establish consistency, central limit theorems, and bootstrap validity for the optimal potentials and couplings for the empirical RMOT problem. Specializing to sparse regularized barycenters, our results yield a uniform weak limit and bootstrap consistency. Numerical simulations show that sparsity plays a fundamental role in preserving the structure of the solution and avoiding the overspreading behavior typical of entropic regularization.
Related
- Continuous Dual Maximizers for Fixed-Reference Entropy-Regularized Wasserstein Barycenters
- Faster Algorithms for Multimarginal Optimal Transport
- Gaussian-Restricted Barycenters for KL-Unbalanced Optimal Transport: Variational Theory and Fixed-Point Convergence
- Quantum Optimal Transport Barycenters: Existence, Duality, and Gaussian Rigidity
- Sparsity of Quadratically Regularized Optimal Transport: Scalar Case
BibTeX
@misc{li2026central,
title = {{Central limit theorems and bootstrap for sparse regularized multimarginal optimal transport and barycenters}},
author = {Pengtao Li and Alberto González-Sanz and Xiaohui Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09538},
eprint = {2609.09538},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09538},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Central limit theorems and bootstrap for sparse regularized multimarginal optimal transport and barycenters
AU - Pengtao Li
AU - Alberto González-Sanz
AU - Xiaohui Chen
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09538
UR - https://arxiv.org/abs/2609.09538
AB - Wasserstein barycenters are a fundamental tool for the analysis of distribution-valued data, but their computation and statistical analysis become challenging in high-dimensional and multi-sample settings. The unregularized barycenter problem is computationally demanding and suffers severely from the curse of dimensionality, making regularization essential in many applications. While regularized optimal transport methods are widely used, approaches based on entropic penalization tend to overspread mass and may blur the geometric structure of the solution. Motivated by barycenter estimation, we propose a more general methodology based on sparse regularized multimarginal optimal transport (RMOT). Our formulation creates sparse transport plans and is designed to avoid this overspreading effect. We establish consistency, central limit theorems, and bootstrap validity for the optimal potentials and couplings for the empirical RMOT problem. Specializing to sparse regularized barycenters, our results yield a uniform weak limit and bootstrap consistency. Numerical simulations show that sparsity plays a fundamental role in preserving the structure of the solution and avoiding the overspreading behavior typical of entropic regularization.
ER -