Review for NeurIPS paper: Approximate Cross-Validation with Low-Rank Data in High Dimensions

Weaknesses: I think the significance of the results (maybe because of the delivery of the result) is below the threshold of acceptance. 1) The first weakness is that there is no discussion about whether the upper bound (mentioned in the strengths) is tight and when this upper bound implies consistency, i,e., the error goes to 0 under a certain limit. Note that the norm of the true signal, the scale of the feature matrix, and the best tuning parameter need to satisfy certain order conditions such that the problem becomes meaningful. A common approach is to apply PCA and do feature selection first. Then, the authors should compare their results with prior works on the selected features. After response: I noticed corollary 1 and corollary 2. But these two corollaries together only cover the trivial case when sample size goes to infinity while the rank of feature matrix is bounded by constant.