Proves finite-sample bounds for the optimal coupling in unbalanced entropic OT via compactness and strong convexity of a translation-invariant dual.
A new optimal transport distance on the space of finite Radon measures
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We introduce a new optimal transport distance between nonnegative finite Radon measures with possibly different masses. The construction is based on non-conservative continuity equations and a corresponding modified Benamou-Brenier formula. We establish various topological and geometrical properties of the resulting metric space, derive some formal Riemannian structure, and develop differential calculus following F. Otto's approach. Finally, we apply these ideas to identify an ideal free distribution model of population dynamics as a gradient flow and obtain new long-time convergence results.
verdicts
UNVERDICTED 4representative citing papers
Constructive isometry of tangent spaces along lifted geodesics equates local HK Riemannian geometry with Wasserstein geometry on the cone, enabling approximation of HK parallel transport.
Derives MSIP algorithm from MMD gradient flows for weighted quantization, extending mean shift and relating to preconditioned gradient descent and Lloyd's clustering.
MUST-FM is a simulation-free multiscale supervised framework that scales unbalanced optimal transport flow matching for trajectory inference in single-cell data by exploiting hierarchical structure and transition priors.
citing papers explorer
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Sample complexity of unbalanced entropic OT
Proves finite-sample bounds for the optimal coupling in unbalanced entropic OT via compactness and strong convexity of a translation-invariant dual.
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On the Differential-Geometric Equivalence of Hellinger-Kantorovich and Cone-Wasserstein Spaces
Constructive isometry of tangent spaces along lifted geodesics equates local HK Riemannian geometry with Wasserstein geometry on the cone, enabling approximation of HK parallel transport.
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Weighted quantization using MMD: From mean field to mean shift via gradient flows
Derives MSIP algorithm from MMD gradient flows for weighted quantization, extending mean shift and relating to preconditioned gradient descent and Lloyd's clustering.
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Multiscale Supervised Unbalanced Optimal Transport Flow Matching
MUST-FM is a simulation-free multiscale supervised framework that scales unbalanced optimal transport flow matching for trajectory inference in single-cell data by exploiting hierarchical structure and transition priors.