Additional Feedback: A few other minor comments: Other methods to compare? For gene expression experiments, I've found k-means clustering using R 2 on columns to be a surprisingly good baseline for global feature clustering (and it allows for getting groups that are anti-correlated). I've also seen methods for finding groups of variables with high multivariate mutual information / total correlation / redundancy. Those ideas could be interesting for comparison or for improving the representation redundancy part to allow for groups that are not always positively correlated. Attention-based learning methods are natural comparisons for things like Figure 1.

Update: The authors have helpfully pointed out that they do provide some guidelines on setting the hyperparameters. This paper creatively combines underdamped Langevin MCMC work of Cheng et al. with the gradient estimator SPIDER of Fang et al. This allows the paper to use the theoretical result from Fang et al. to prove a better bound for achieving epsilon in 2-Wasserstein distance. Effectively it is the UL-MCMC algorithm with a better gradient estimator. This isn't meant to imply that the work is trivial as adapting any insight from the optimisation literature for use in a HMC algorithm requires careful work to yield measurable improvements.

The reviewers expressed concern on the novelty of the algorithm, but still think it is well written and should be accepted for NIPS. We encourage the authors to carefully revise the work for the final version.

Weaknesses: I have the following critical concerns about this paper: 1. The used datasets are too simple. More complex datasets such as SculptFaces in NeRV paper are required to evaluate the performance of the proposed algorithm. As detailed above, ClassNeRV could be seen as a variation of NeRV through penalizing within-class missed neighbors and between-class false neighbors with class information. Therefore, in my opinion, it is not a significant contribution. According to Sec 3.2, they derived the ClassNeRV Stress Function from NeRV Stress Function by splitting Eq. 2 into within-class and between-class relations.

Three referees indicate accept, one indicates that the paper is marginally below threshold. I agree with reviewers 1, 2 and 4 that the presented approach is insightful and useful to NeurIPS applications, and support an accept after reading the rebuttal. However, when revising the paper, please take into account reviewers' concerns about improving quantitative comparisons with other similar methods as well as providing further discussion. Please consider adding experimental support with more complex data to the the main paper or Supplementary Materials.

The paper tightens the analysis of local SGD that periodically averages the models at different nodes. It improves the bound on the communication rounds suffice to achieve linear speedups and relaxes some of the assumptions used in previous works. The authors also develop an adaptive scheme to choose the communication rounds based on the intuition from their theoretical results. They also provided empirical results on logistic regression problem with epsilon dataset to support the theoretical results. Comments: The paper is well written and east to follow.

A key quantity in the analysis is p_j, the probability of missing j-th feature. Is this quantity given in advanced? Under MCAR, it can be easily estimated. But some clarifications are needed. Essentially, this method is just SGD IPW (though it is coordinate-wise IPW not the regular IPW).

The paper addresses the issue of missing values in SGD. There was agreement that the obtained results are novel but there was no strong advocate for the paper.

Originality: The combination of sampling in areas of'greater interest' while adjusting to the underlying distribution appears in many active learning works, but the objective in (1) is novel and approaching both in a unified framework is challenging. The lower bounding of the optimization problem is also new Quality: The experimental results are very thorough and show the improvement of the proposed method over random sampling as well as several other baselines. And the exploration of effect of tuning parameters and initial sample size is excellent. However the theoretical contributions appear incomplete. The significant theoretical contribution is the (mislabelled) Theorem 2, and both the statement and proof of this is extremely informal.

The paper proposed a novel algorithm for active learning in the multi class setting. The authors present a theoretical guarantee regarding the sparseness of the model as well as empirical evaluation across 6 datasets and comparing with 5 baseline methods. All reviewers tend for vote for acceptance, but do point out several areas of improvement and the authors provide feedback for. I strongly expect the final version of the paper to include the changes that address: - Formal statement and proof outline for Theorem 2. - Include the comparison of RVM, SVM and KMC method in the passive learning setting (mentioned in the author feedback), in order to help distinguish the benefit of the novel model alone, in addition to the combination of model and active sampling. Including those results would significantly increase the value of the study.