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.
Lifting functionals defined on maps to measure-valued maps via optimal transport
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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.