Papers › Max-sliced Wasserstein concentration and uniform ratio bounds of empirical measures on RKHS
Max-sliced Wasserstein concentration and uniform ratio bounds of empirical measures on RKHS
Ruiyu Han, Cynthia Rush, Johannes Wiesel
Optimal transport and the Wasserstein distance 𝒲ₚ have recently seen a number of applications in the fields of statistics, machine learning, data science, and the physical sciences. These applications are however severely restricted by the curse of dimensionality, meaning that the number of data points needed to estimate these problems accurately increases exponentially in the dimension. To alleviate this problem, a number of variants of 𝒲ₚ have been introduced. We focus here on one of these variants, namely the max-sliced Wasserstein metric 𝒲ₚ. This metric reduces the high-dimensional minimization problem given by 𝒲ₚ to a maximum of one-dimensional measurements in an effort to overcome the curse of dimensionality. In this note we derive concentration results and upper bounds on the expectation of 𝒲ₚ between the true and empirical measure on unbounded reproducing kernel Hilbert spaces. We show that, under quite generic assumptions, probability measures concentrate uniformly fast in one-dimensional subspaces, at (nearly) parametric rates. Our results rely on an improvement of currently known bounds for 𝒲ₚ in the finite-dimensional case.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Methods
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections