The GenCol algorithm for high-dimensional optimal transport: general formulation and application to barycenters and Wasserstein splines

TL;DR

This paper extends the GenCol algorithm to general high-dimensional optimal transport problems, enabling accurate computation of Wasserstein barycenters and splines without mesh constraints.

Contribution

It generalizes the GenCol algorithm for broader high-dimensional optimal transport applications, including barycenters and splines.

Findings

Successfully computes mesh-free Wasserstein barycenters.

Accurately constructs cubic Wasserstein splines.

Extends algorithm applicability to non-symmetric problems.

Abstract

We extend the recently introduced genetic column generation algorithm for high-dimensional multi-marginal optimal transport from symmetric to general problems. We use the algorithm to calculate accurate mesh-free Wasserstein barycenters and cubic Wasserstein splines.