Estimating Barycenters of Distributions with Neural Optimal Transport
This work provides a more efficient solution for practitioners needing to average distributions, though it is incremental by building on existing neural OT solvers.
The authors tackled the problem of computing Wasserstein barycenters for aggregating probability distributions by proposing a scalable neural optimal transport method that works for general cost functions, achieving theoretical error bounds and demonstrating effectiveness on image data.
Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions. A theoretically appealing notion of such an average is the Wasserstein barycenter, which is the primal focus of our work. By building upon the dual formulation of Optimal Transport (OT), we propose a new scalable approach for solving the Wasserstein barycenter problem. Our methodology is based on the recent Neural OT solver: it has bi-level adversarial learning objective and works for general cost functions. These are key advantages of our method since the typical adversarial algorithms leveraging barycenter tasks utilize tri-level optimization and focus mostly on quadratic cost. We also establish theoretical error bounds for our proposed approach and showcase its applicability and effectiveness in illustrative scenarios and image data setups. Our source code is available at https://github.com/justkolesov/NOTBarycenters.