25 citations · 53 across the 10 of their papers we have counts for
4 papers · 1 filter
Nearly sharp comparison results for sliced and max-sliced Wasserstein distances
Jonathan Niles-Weed, Jacob Shkrob
We prove new comparison results between the Wasserstein distance and its sliced and max-sliced counterparts. First, we show that the Hölder exponent~ obtained by Bob…
Central Limit Theorems for Smooth Optimal Transport Maps
Tudor Manole, Sivaraman Balakrishnan, Jonathan Niles-Weed +1
One of the central objects in the theory of optimal transport is the Brenier map: the unique monotone transformation which pushes forward an absolutely continuous probability law o…
Distributional Convergence of the Sliced Wasserstein Process
Jiaqi Xi, Jonathan Niles-Weed
Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasser…
Sharp Convergence Rates for Empirical Optimal Transport with Smooth Costs
Tudor Manole, Jonathan Niles-Weed
We revisit the question of characterizing the convergence rate of plug-in estimators of optimal transport costs. It is well known that an empirical measure comprising independent s…