1. Optimal quantization is not scalable (which is mentioned in the paper as well). Even with clustering before, it is costly to both N(number of data) and M(the dimension). The paper (in abstract and intro) aims to speed up VI by fast convergence which is needed for big data/big model setting, which the quantization is a bottleneck for it, which makes the method loses its point. 2. Apart form the scalability, I wonder about the effectiveness in high dimensional space as well where everything is far away from each other. 3. The experiments are only with very simple small UCI datasets and very simple/small models (linear regression). I would be great to see with more "real-life" experiments. 4. There is also limited baselines. [a] is discussed in the paper but not compared. Only the basic BBVI is compared. It would be good to see at least baselines such as [a] and [b] in the experiments. 5. For algorithm 2, it would be insanely expensive if quantization needs be to computed every round. but it is explained with exponential family, it only need once. But if it limits to be exponential family, then the point of whole BBVI is lost. 5. Small things: line 2, minimize->maximize; can you explicitly discuss about the optimal quantization computational complexity. [a]Alexander Buchholz, Florian Wenzel, and Stephan Mandt. “Quasi-Monte Carlo Variational 238 Inference”. [b] Stochastic Learning on Imbalanced Data: Determinantal Point Processes for Mini-batch Diversification
1. Optimal quantization is not scalable (which is mentioned in the paper as well). Even with clustering before, it is costly to both N(number of data) and M(the dimension). The paper (in abstract and intro) aims to speed up VI by fast convergence which is needed for big data/big model setting, which the quantization is a bottleneck for it, which makes the method loses its point.