arXiv Machine Learning
Generalized infinite dimensional Alpha-Procrustes based geometries
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arXiv Machine Learning
Jul 28
Distance-Matrix Wasserstein Statistics for Scalable Gromov--Wasserstein Learning
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 Statistics ML
Sep 4
Discrete Gromov-Wasserstein Duality: Algorithms and Isomorphism Testing
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 Machine Learning
Aug 31
Beyond Procrustes distances: a multilinear Gromov-Wasserstein distance capturing chirality
arXiv:2608. 27774v1 Announce Type: cross Abstract: Efficiently and robustly analyzing shape data is critical across many scientific disciplines.
arXiv Machine Learning
Aug 18
The Observable Wasserstein Distance
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 Machine Learning
Sep 16
Optimization over covariance matrices with a parameterized metric
arXiv:2609. 17089v1 Announce Type: cross Abstract: The choice of Riemannian metric can strongly influence the convergence of gradient-based optimization over covariance matrices.
arXiv Machine Learning
Jun 2
Convex Distance Operator Transport: A Convex and Geometry-Preserving Formulation
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.