Review for NeurIPS paper: Gradient Boosted Normalizing Flows

Weaknesses: No increase in theoretical flow expressivity: Unlike traditional boosting in which an ensemble of weak learners is provably more expressive, the paper doesn't provide such a proof for the proposed NF boosting procedure. Moreover, I conjecture that this methodology (in the general case, under NN / polynomial universal approximation assumptions) *cannot* build an ensemble that is more expressive than a single constituent component. There are two bottlenecks in NF expressivity---the base distribution and the class of transformation function [Papamakarios et al., 2019]---and the proposed method does not fundamentally change either of these. For example, the base distribution is simple and shared across all components (line 99). Recent work that does improve flow expressivity must use mixture formulations [Papamakarios et al., 2019] (discrete [Dinh et al., 2019] or continuous [Cornish et al., 2020] indices) whose base distribution (or support) and transformation change according to the index.