Review for NeurIPS paper: Geometric Dataset Distances via Optimal Transport

Additional Feedback: ###### POST REBUTTAL After reading the author's response, I increased my score by 1. I believe the general idea of using conditional distributions to compare datasets with no prior training / modeling assumptions is interesting and could lead to potentially interesting future research. Here is why I still think this is not a clear accept, and I hope these remarks will be addressed in the final version: 1) The experiments that were conducted in the paper were very clear and well illustrated, I expect that the naive methods (i), (ii), (iii) discussed in the rebuttal will be included for a quantitative comparison in transfer learning and the other applications and not just comparing the values of OTDD with different methods (fig 1 of the rebuttal) which is not informative; the order of magnitude does not tell anything on the discriminative power of a distance. Could it be explained by the fact the dimension of MNIST is large making Bures too costly to compute? Would you agree that for large d, Sinkhorn is better than OT-N and otherwise for large d? My main concern is that while these results are promising, no baseline was provided to quantify the performance gain of OTDD.