Abstract:Wasserstein barycentres represent average distributions between multiple probability measures for the Wasserstein distance. The numerical computation of Wasserstein barycentres is notoriously challenging. A common approach is to use Sinkhorn iterations, where an entropic regularisation term is introduced to make the problem more manageable. Another approach involves using fixed-point methods, akin to those employed for computing Fréchet means on manifolds. The convergence of such methods for 2-Wasserstein barycentres, specifically with a quadratic cost function and absolutely continuous measures, was studied by Alvarez-Esteban et al. (2016). In this paper, we delve into the main ideas behind this fixed-point method and explore how it can be generalised to accommodate more diverse transport costs and generic probability measures, thereby extending its applicability to a broader range of problems. We show convergence results for this approach and illustrate its numerical behaviour on several barycentre problems.
From: Eloi Tanguy [view email]
[v1]
Fri, 20 Dec 2024 22:16:36 UTC (1,805 KB)
[v2]
Fri, 20 Jun 2025 13:41:05 UTC (4,828 KB)
[v3]
Fri, 27 Mar 2026 17:08:00 UTC (4,067 KB)
[v4]
Thu, 16 Jul 2026 13:44:20 UTC (4,068 KB)
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