Establishes a unified temporal-spatial minimax lower bound of order M to the power of minus gamma_d times (k+1) over (k+1 plus gamma_d) for W2-risk of future distribution estimates under k-th order adiabatic smoothness on the velocity field.
Plugin estimation of smooth optimal transport maps
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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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A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space
Establishes a unified temporal-spatial minimax lower bound of order M to the power of minus gamma_d times (k+1) over (k+1 plus gamma_d) for W2-risk of future distribution estimates under k-th order adiabatic smoothness on the velocity field.
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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.