Reviews: Nearest-Neighbor Sample Compression: Efficiency, Consistency, Infinite Dimensions

This work develops a compression-based algorithm for multiclass learning; the authors claim the method is both efficient and strongly Bayes-consistent in spaces of finite doubling dimension. They also provide one example of a space of infinite doubling dimension with a particular measure for which their method is weakly Bayes consistent, whereas the same construction leads to inconsistency of k-NN rules. Overall, I think this paper is technically strong and seems to develop interesting results, but I have a few concerns about the significance of this paper which I will discuss below. If the authors can address these concerns, I would support this paper for acceptance. Detailed comments: I did not check the proofs in the appendix in detail but the main ideas appear to be correct.