Establishes an explicit strong-convexity modulus for the barycentric variance functional on Alexandrov spaces, implying Hölder stability of barycenters and empirical consistency bounds without using linear structure.
Theory Related Fields 177 (2020), no
2 Pith papers cite this work. Polarity classification is still indexing.
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Wasserstein least squares extends Euclidean least squares to distribution-valued responses via convex analysis, yielding n^{-1/2} rates under template deformation and faster barycenter rates than prior work.
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Quantitative Stability of Wasserstein Barycenters over Alexandrov Spaces with Lower Curvature Bounds
Establishes an explicit strong-convexity modulus for the barycentric variance functional on Alexandrov spaces, implying Hölder stability of barycenters and empirical consistency bounds without using linear structure.
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Wasserstein Least Squares: A Canonical Regression Method for Probability Distributions
Wasserstein least squares extends Euclidean least squares to distribution-valued responses via convex analysis, yielding n^{-1/2} rates under template deformation and faster barycenter rates than prior work.