Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 6: Weak Accept
review_content: The paper studies theoretical perspective of double descent phenomenon for the interpolated K-NN classifier.

The paper is works in several interesting directions and gives theoretical reasoning to how interpolated K-NN could exhibit the double descent phenomenon. They give theoretical justifications albeit with strong assumptions.

I think the paper is a good paper. However, I have concerns with the presentation quality of the paper. It is very tough to get through the paper till the end. 

In my view, it would have been an Accept if the paper was well written.
review_title: Official Blind Review #2

final_score: rating: 3: Weak Reject
review_content: This paper studies the interpolated k-nearest neighbors algorithm from a theoretical perspective. Specifically, it studies how the performance of the algorithm is affected by reweighting the k nearest neighbors according to their relative distance. This regime has been considered in prior work, particularly Belkin et al. (2018).

Under various niceness conditions, the paper proves error bounds for interpolated k-nearest neighbors for both regression (i.e. squared loss) and classification (i.e. 0-1 loss after thresholding).

Overall, I have the impression that this paper contains interesting ideas, but the presentation is very poor. It should be revised and resubmitted before it can be accepted.

In particular, the paper does not make its contribution clear. The main theorem only appears on page 4 and the reader must consult the appendix to see the definition of all the terms that appear in the theorem. I have no idea how to interpret the (complicated) expression in the theorem. The theorem needs to be explained in intuitive terms. More context needs to be given by comparing the main theorem to prior works (which I am not familiar with). 



review_title: Official Blind Review #3

final_score: rating: 1: Reject
review_content: This paper is about interpolation schemes in the particular case of the
Nearest Neighbor algorithm. The authors investigate the benet, mainly
theoretical, of the proposed interpolation. They study minimax rates of
the proposed interpolated-NN for both classication and regression. The
statistical stability of the Interpolated-NN is adressed.
The paper is easy to understand and correctly written. Nevertheless,
It is a particular case of ( \Overtting or perfect tting? Risk bounds for
classication and regression rules that interpolate", Belkin, M., Hsu, D.,
and Mitra, P. (2018a)) with an explicit interpolation schemes given by the
euclidien distance power gamma. It appears as an application of the above
paper which brings only few theoretical advantages and not enough to justify,
although intuitive, the choice of these weights. Only few discussions and
no comparison to others bounds (as those in the above paper) of the main
theorem are given. The paper is too much incremental from the papers of
Belkin et al. (2018) and Xing et al. (2018) and the benets of the proposed
interpolation are limited. Furthermore, the empirical performance of the
interpolate-NN is clearly not convincing and show no signicant practical
advantages of the proposed method. As the goal of the paper is clearly
theoretical, the 'real data analysis' part is not necessary in my opinion.
review_title: Official Blind Review #1

Meta-review: The authors show that data interpolation in the context of nearest neighbor algorithms, can sometime strictly improve performance. The paper is poorly written for an ICLR audience and the added value compared to extensive prior work in the area is not clearly demonstrated.
Decision: Reject