A multiscale framework for probability measures in Wasserstein spaces is developed, including a refinement operator preserving geodesic structure and an optimality number for detecting non-geodesic dynamics across scales.
Wasserstein regression.Journal of the American Statistical Association, 118(542):869–882
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Diffeomorphisms and vector fields are uniquely identifiable from finitely many pushforward densities or weighted divergences, with the number of required observations determined by embedding theorems.
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Multiscaling in Wasserstein Spaces
A multiscale framework for probability measures in Wasserstein spaces is developed, including a refinement operator preserving geodesic structure and an optimality number for detecting non-geodesic dynamics across scales.
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On the Unique Recovery of Transport Maps and Vector Fields from Finite Measure-Valued Data
Diffeomorphisms and vector fields are uniquely identifiable from finitely many pushforward densities or weighted divergences, with the number of required observations determined by embedding theorems.