arXiv:2606. 02047v1 Announce Type: cross Abstract: We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure.
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.
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.
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...
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.
arXiv:2606. 27767v1 Announce Type: new Abstract: Optimizing functionals over the space of probability measures is now ubiquitous in machine learning.
arXiv:2606. 04695v1 Announce Type: new Abstract: High-dimensional optimal transport is seldom available in closed form.
The paper reviews the use of optimal transport for comparing undirected, unweighted graphs, focusing on three main distances: Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein. It discusses closed-form solutions for the Wasserstein distance in one dimension, how transport plans identify influential nodes after perturbations, and derives spectral bounds for the Bures-Wasserstein distance to avoid full decompositions. The authors evaluate these distances on synthetic clustering data and a real-world time‑series network for anomaly detection.
The paper presents a new duality formulation for the Gromov‑Wasserstein distance that applies to all finitely supported metric‑measure spaces, with and without entropic regularization. Using this duality, the authors derive sample‑complexity bounds and limit distributions for empirical GW distances, and introduce algorithms with formal convergence guarantees. These results enable a principled, efficient method for testing isomorphism between distributions on graphs with a fixed number of nodes based on samples.
arXiv:2412. 20556v2 Announce Type: replace-cross Abstract: We study distributionally robust optimization (DRO) for robust inference when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization problem.
The paper introduces EGGroW, efficient algorithms for computing geodesic Gromov-Wasserstein distances using entropic Sinkhorn-like methods, GenusSink techniques, and random features. It addresses the cubic time complexity of traditional GWD calculations on dense intra-space distance matrices, enabling scalable comparisons of probabilistic distributions on general geodesic manifolds and graph shortest‑path distances. The authors demonstrate EGGroW’s effectiveness in downstream tasks such as 3D pose estimation and partial 3D template recovery, showing accurate results where Euclidean‑based methods fail while maintaining a light computational footprint.
arXiv:2203. 04711v2 Announce Type: replace Abstract: We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem.
arXiv:2603.07014v2 Announce Type: replace-cross Abstract: Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univ...