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.
Convex Analysis and Minimization Algorithms I : Fundamentals , volume 305 of Grundlehren der mathematischen Wissenschaften
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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.