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Research questionHow can Gromov–Wasserstein distance reliably compare finitely supported metric-measure spaces from samples?Comparing metric-measure spaces through intrinsic structure requires more than a distance definition: finite samples need statistical guarantees, while computational procedures need justified convergence. These gaps complicate isomorphism testing for distributions on graphs.
Machine Learning
Research Paper
Statistical Machine Learning
Latest papersRecent research connected to this question, newest first.Discrete Gromov-Wasserstein Duality: Algorithms and Isomorphism TestingThe work addresses finitely supported metric-measure spaces, with duality results for Gromov–Wasserstein distances with and without entropic regularization. It provides sample-complexity and limit-distribution results for empirical distances, convergence-guaranteed algorithms for the regularized problem, and an application to testing isomorphism between sampled distributions of graphs with a fixed number of nodes.research paper · Sep 2, 2026
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