Reviews: Density Estimation via Discrepancy Based Adaptive Sequential Partition

Novelty: there are a fair number of adaptive partitioning density estimation methods in existence that the authors omit (Darbellay and Vajda, 1999; Petralia, Vogelstein, and Dunson, 2013; etc). Some of these are designed for high dimensions, some function in lower dimensions. In general, this space is fairly well studied but there is room for serious theoretical analysis. A much stronger result than the standard Monte Carlo integration rates would be something like rates in Hellinger or Lp distance, which are generally not dimension-free. These rates and associated traits (adaptivity to intrinsic dimension, shape constraints, etc) are generally much more predictive of how a method performs in the wild than simple MC integration rates.