Review for NeurIPS paper: Robust Density Estimation under Besov IPM Losses

Neural Information Processing Systems 

Additional Feedback: Overall, the paper addresses a very important issue into density estimation when contaminated by random outliers which is encountered in many machine learning problems. The theoretical guarantees for the linear and non-linear convergences rate and minmax bound is extremely useful for designing robust machine learning models. Unfortunately, I do not have the technical expertise to comment on the correctness of this approach. But for an out-of-area reviewer, I can see that this paper is well motivated and is written and structured well. As mentioned in my original review, experimental results with synthetic data could strengthen the paper and improve understanding of the paper, but it is not critical. The authors have explained using examples for potential applications for the theoretical results in Section 4.3 which seems good enough for me.