Abstract:
I will begin by defining the Wasserstein distance and discussing the challenges posed by the curse of dimensionality when estimating a high-dimensional distribution from i.i.d. samples thereof. I will then explain how the max-sliced Wasserstein distance overcomes these challenges. Finally, I will elaborate on the proof, which relies on a uniform version of the Dvoretzky-Kiefer-Wolfowitz inequality.
(Joint work with S. Mendelson.)