After discussion, the reviewers agreed that the paper was written clearly and the theoretical contributions were sound and interesting; enough so that the paper was worth accepting on those merits. But they also agreed that, despite the rebuttal, there is still uncertainty in the practicality of the algorithm and empirical results. The results (in the paper + rebuttal) appear to be limited to cases where ABC isn't necessary, and the comparison to significantly simpler kernel methods is not really comprehensive. For the final draft, please be sure to add the results from the rebuttal, as well as more thorough evidence that the method performs well against common kernel methods and in settings where ABC is required.