Reviews: Consistent Kernel Mean Estimation for Functions of Random Variables

Quantifying the price of dependent expansion points is an interesting mathematical question. However, this paper could improve in motivating the general readers from machine learning community to get interested in a broader topic of Kernel Mean Embedding. The authors attempt to do this in the last paragraph in Section 4, relating it to Probabilistic Programming Systems, which seems to be a weak connection. AS a reader, I was curious as to where such techniques of KME and reduced set expansions can be potentially used, or are used currently in solving some application specific problems. Another disappointing aspect of the paper is that the authors did not delve deeper into the question Multiple arguments in Section 3. What is currently provided is a direct corollary of the Theorem 2, and the paper assigns too much space for something that has little information over what is already said.