Reviews: The power of absolute discounting: all-dimensional distribution estimation

This paper presents a theoretical examination of the optimality of absolute discounting similar to the examination of optimality of Good Turing in Orlitsky and Suresh (2015). Results for minimax optimality, adaptivity and competitiveness are presented, as well as an equivalence between absolute discounting and Good Turing in certain scenarios, which suggests a choice of discount. Experimental results demonstrate the quality of the approach, along with some interesting results on predicting terror attacks in classes of cities (e.g., cities with zero prior attacks) given prior data. The paper is very well written and crystal clear, and the results are quite interesting. This is an excellent addition to the literature on these methods.