NeurIPS 2019
Sun Dec 8th through Sat the 14th, 2019 at Vancouver Convention Center
Paper ID: 387 Selecting Optimal Decisions via Distributionally Robust Nearest-Neighbor Regression

### Reviewer 1

prediction-based prescriptive method is developed in the paper

### Reviewer 2

Major concerns: The data described from the paper are with labeling (response y_m) for each action m \in M. Therefore it seems to me the counterfactual effects can also be predicted by just using the regression based method (either parametric or nonparametric). The KNN method is more of an unsupervised method to do a re-weighting, than a nonparametric component in the model. I am not fully convinced of the benefits of using KNN. On the other hand, I see potential problems: for example, this method could be sensitive to the choice of number of neighbors K; it treats all the neighbors with the same weight in the final response prediction.

### Reviewer 3

This paper has potential, but a significant rewrite is needed to discuss the related literature and clarify the results in context.

### Reviewer 4

The paper tackles the problem of predicting the outcome of an action chosen from a set of possible actions, The outcome is a function of the action, having a linear component, non-linear component and some additive noise. The idea is first finding a linear function minimizing the deviation from the outcomes, for every distribution which is "close" to the empirical distribution (by the Wasserstein distance). Idea which was analyzed before. The idea added in the paper is using the resulting linear-regression coefficient to build a metric upon samples from the same group and then produce prediction which is the average of the outcomes for the K-nearest neighbors. This way the prediction can leverage not only the private history of the specific instance but also the outcomes of "close" instances. The paper provide bound on the resulting error under several assumptions. The idea is interesting and seems novel. The analysis isn't trivial. The paper is written in a relative clear manner.

### Reviewer 5

Originality - The work nicely combines two methods to calculate an estimator with good prediction. However, it is not clear from the paper why this combination of methods provides the optimal performance. Quality - The claimes are well suported by theoritical analysis and experimntal results. Clarity - The submission is clearly written. Significance - This paper offers an interesting approach for feature selecting for knn regression, based on weighted metric. This is an interesting research direction, on the theoretical and applicative areas.