arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.
By Ao Xu, Tieru Wu
arXiv:2605. 09916v2 Announce Type: replace-cross Abstract: We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal transport in large-scale, non-Euclidean datasets.
By Edivaldo Lopes dos Santos, Leandro Vicente Mauri, Washington Mio, Tom Needham
arXiv:2608.27500v3 Announce Type: replace-cross
Abstract: Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport...
By James Hyun, Fran\c{c}ois G. Meyer
The paper introduces a geometric framework for measuring how far empirical datasets deviate from the Gaussian family using optimal transport theory. It defines two new quantities—the relative Wasserstein angle and the orthogonal projection distance—based on the cone structure of the relative translation invariant quadratic Wasserstein space, and shows that the usual moment‑matching Gaussian is not generally the $W_2$‑nearest Gaussian. Closed‑form expressions are derived for one‑dimensional and several location–scale families, while a numerical approximation is proposed for higher dimensions, with experiments demonstrating convergence, stability, and the angle’s robustness as a non‑Gaussianity indicator.
By Binshuai Wang, Peng Wei
arXiv:2606. 27767v1 Announce Type: new Abstract: Optimizing functionals over the space of probability measures is now ubiquitous in machine learning.
By Cl\'ement Bonet, Pierre-Cyril Aubin-Frankowski, Youssef Mroueh
arXiv:2606. 04695v1 Announce Type: new Abstract: High-dimensional optimal transport is seldom available in closed form.
By Lei Luo, Hongliang Zhang, Jian Yang