Review for NeurIPS paper: Subgroup-based Rank-1 Lattice Quasi-Monte Carlo

Weaknesses: My main concerns are whether this work makes an impactful contribution to the type of problems of interest to the NeurIPS community. The problem of high-dimensional integration is of course of vital importance in many areas of machine learning, appearing centrally for example in Bayesian inference/model selection, graphical models, and the training of latent variable generative models, and many of us would welcome an addition to the toolkit of dealing with such beasts. Unfortunately, this paper makes only minimal effort to motivate the relevance of the proposed QMC construction to these settings. An application to GAN/VAEs does briefly appear in the supplementary, but with quite cursory quantification of performance; showing sharper generated images is not consistent with the rigorous aims and tone of the paper. For a NeurIPS audience, I consider it essential to include a comparison against established sampling algorithms such as Sequential Monte Carlo.