Review for NeurIPS paper: Quantifying the Empirical Wasserstein Distance to a Set of Measures: Beating the Curse of Dimensionality

Summary and Contributions: ***** UPDATE ***** I realize I might have been harsh in my evaluation. I believe the paper would have been more suited for a more theory oriented statistics conference / journal, but this is a recurrent problem in NeurIPS and I shouldn't have taken it out on the authors. While their theoretical result is really interesting, I also didn't appreciate that the authors barely mentioned previous work on statistical learning bounds with optimal transport. There have been recent efforts on the topic by several teams, and they should at least acknowledge them. However, if other reviewers took the time to thoroughly review the proof of the main result, I'm willing to increase my score.