Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transport

Published: 22 Jan 2025, Last Modified: 28 Mar 2025ICLR 2025 PosterEveryoneRevisionsBibTeXCC BY 4.0
Keywords: unbalanced optimal transport, barycenter, generative modeling
Abstract:

Aggregating data from multiple sources can be formalized as an Optimal Transport (OT) barycenter problem, which seeks to compute the average of probability distributions with respect to OT discrepancies. However, in real-world scenarios, the presence of outliers and noise in the data measures can significantly hinder the performance of traditional statistical methods for estimating OT barycenters. To address this issue, we propose a novel scalable approach for estimating the robust continuous barycenter, leveraging the dual formulation of the (semi-)unbalanced OT problem. To the best of our knowledge, this paper is the first attempt to develop an algorithm for robust barycenters under the continuous distribution setup. Our method is framed as a $\min$-$\max$ optimization problem and is adaptable to general cost functions. We rigorously establish the theoretical underpinnings of the proposed method and demonstrate its robustness to outliers and class imbalance through a number of illustrative experiments. Our source code is publicly available at https://github.com/milenagazdieva/U-NOTBarycenters.

Supplementary Material: zip
Primary Area: generative models
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 11104
Loading

OpenReview is a long-term project to advance science through improved peer review with legal nonprofit status. We gratefully acknowledge the support of the OpenReview Sponsors. © 2025 OpenReview