Estimating Barycenters of Distributions with Neural Optimal Transport
Alexander Kolesov Petr Mokrov Igor Udovichenko Milena Gazdieva Gudmund Pammer Evgeny Burnaev Alexander Korotin
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 on illustrative scenarios and image data
setups.