arXiv:2601. 17171v2 Announce Type: replace-cross Abstract: We study Kantorovich duality for multimarginal optimal transport (MOT) with bounded continuous cost functions.
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arXiv:2606. 04695v1 Announce Type: new Abstract: High-dimensional optimal transport is seldom available in closed form.
arXiv:2609.23163v1 Announce Type: cross Abstract: Comparing probability measures in machine learning trades transport geometry against computational cost: Wasserstein distances encode the geometry of...
arXiv:2310. 09149v3 Announce Type: replace-cross Abstract: We study the approximation of probability measures in the Wasserstein-$p$ distance by structured classes of approximators, motivated by applications in imaging, machine learning, and physical measurement under sensor constraints.
arXiv:2608. 08414v1 Announce Type: new Abstract: We study constrained statistical learning over infinite-dimensional hypothesis classes in the fully nonconvex setting, and establish universal PACC learnability of the solutions of dual algorithms: Probably Approximately Correct on Constraints, guaranteeing optimality and constraint satisfaction at once.
The paper introduces a weak Gromov-Wasserstein (wGW) framework that compares source relations with relations between target conditional laws, focusing on inner-product relations and preserving conditional means. It defines the barycentric weak inner-product GW (wIGW) distance, proves existence of minimizers under finite second moments, and presents a ridge-regularized dual formulation leading to an iterative algorithm for finitely supported measures. Experiments on point clouds, graphs, and a PBMC multiome study demonstrate that mean-preserving target refinements can incur zero cost and improve atlas-based cell type transfer.
arXiv:2609. 26647v1 Announce Type: cross Abstract: We study statistical rates in entropic optimal transport in the semi-discrete regime where one measure has finite support and the other is subGaussian.