Relation to Prior Work: The paper is missing references to and comparisons with important related works on adversarial examples for nearest neighbors and other non-parametric methods. For example, [1] provides a direct convergence rate for robustness of nearest neighbors to adversarial examples; it would be good to discuss how the bounds in this paper are different. Similarly, the convex program proposed by this paper feels similar to [5] as well as [2]; it would be good to discuss the relationship between these works.

The reviewers agree that this paper presents a novel framework and approach towards robust non-parametric methods. Nevertheless, the authors are encouraged to further improve their empirical study.

Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences. Existing data-driven non-parametric estimators mostly focus on structured homogeneous data (e.g., weakly independently and stationary data), thus they are sensitive to adversarial noise and may perform poorly under a low sample size. To alleviate these issues, we propose a new distributionally robust estimator that generates non-parametric local estimates by minimizing the worst-case conditional expected loss over all adversarial distributions in a Wasserstein ambiguity set. We show that despite being generally intractable, the local estimator can be efficiently found via convex optimization under broadly applicable settings, and it is robust to the corruption and heterogeneity of the data. Various experiments show the competitive performance of this new class of estimator.