1. Larry Wasserman is Professor, Department of Statistics and Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA 15213 . Shuheng Zhou is Post-Doctoral Fellow, Seminar für Statistik, ETH Zürich, CH 8092, Switzerland. We thank Avrim Blum, Katrina Ligett, Steve Fienberg, Alessandro Rinaldo, and Yuval Nardi for many helpful discussions. We thank Wenbo Li and Mikhail Lifshits for helpful pointers and discussions on small ball probabilities. We thank the Associate Editor and three referees...