Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.
and Zemel, Yoav , year =
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Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.
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Absolute continuity of generalized Wasserstein barycenters of finitely many measures
Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.
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Scale selection for geometric medians on product manifolds
Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.