Paper:
Broad adoption of machine learning techniques has increased privacy concerns for models trained on sensitive data such as medical records. Existing techniques for training differentially private (DP) models give rigorous privacy guarantees, but applying these techniques to neural networks can severely degrade model performance. This performance reduction is an obstacle to deploying private models in the real world. In this work, we improve the performance of DP models by fine-tuning them through active learning on public data. We introduce two new techniques -DIVERSEPUBLIC and NEARPRIVATE -for doing this fine-tuning in a privacy-aware way. For the MNIST and SVHN datasets, these techniques improve state-of-the-art accuracy for DP models while retaining privacy guarantees.

Review:
---SUMMARY---
This paper gives two methods for improving an existing differentially private model. Both methods assume a source of unlabeled data that requires no privacy guarantees. The two methods make different uses of this public data to augment the original private model. Both preserve (a degree of) privacy for the original model.
The first method is DiversePublic. DiversePublic only post-processes the original private model M -- in particular, it does not touch the original data -- and so its privacy is immediate. At a high level, DiversePublic works by picking the "best" unlabelled data points for augmenting M. First, it applies M to the unlabeled data and then applies PCA to the result. Next, it selects highly "uncertain" points, projects them onto the top k principal components, and clusters the results. Finally, it selects samples from each cluster and uses them to augment M. This augmenting process, called FineTune, is left as a black box.
The second method is NearPrivate. The given motivation for NearPrivate is that the public dataset may have a different distribution than the original private training data. To address this, NearPrivate uses DP-PCA (a pre-existing technique for differentially private PCA) on the private dataset and projects both the private and public data onto the top k principal components. Then it compares uncertain points in the public and private dataset projections and only augments M (again using the black box FineTune) using uncertain public examples with many nearby uncertain private samples. Intuitively, this should select for points that are not too different than the original private training data.
The paper then evaluates these algorithms with experiments on MNIST and SVHN under reasonable privacy parameters (I think -- see below). These experiments compare the performance of DiversePublic and NearPrivate, where both train M using vanilla DP-SGD [Abadi et al. 2016]. DiversePublic and NearPrivate trade performances on MNIST and SVHN, but NearPrivate does (as might be expected) better when the public dataset is polluted.
In summary, the paper suggests DiversePublic and NearPrivate as useful ways to augment a given differentially private model M using public data, and their experiments suggest this is reasonable.
---DECISION---
Reject.
This is an empirical paper. It proposes some algorithms and justifies these algorithms through experiments. However, the paper makes a confusing omission: it does not mention PATE [1, 2].
[1] "Semi-supervised Knowledge Transfer for Deep Learning from Private Training Data". Papernot et al. 2017.
[2] "Scalable Learning with PATE". Papernot et al. 2018.
I am more of a pure differential privacy researcher and am therefore less familiar with this line of mostly empirical work. But as far as I can tell PATE works in the same setting as that of this paper: there is a private dataset, a public unlabelled dataset, and the goal is to train a model with a differential privacy guarantee for the private dataset. As a result, PATE seems directly relevant. In particular, the claim that "there are no published examples of a differentially private SVHN classifier with both reasonable accuracy and non-trivial privacy guarantees" seems wrong, as the PATE papers include just that.
Moreover, PATE appears at least competitive with the algorithms here. For example, the comparison given as Table 1 in [2] suggests that PATE can get 98-99% accuracy on MNIST for privacy parameters at least as low as those used here with only a few hundred new labelings. In contrast, if I understand the experiments here, they are using thousands of new labelled examples to get the same accuracy and privacy. Similarly, on SVHN the experiments here get to 84% accuracy with 10,000 new labelled examples, whereas the same Table 1 puts PATE at 90% with almost identical privacy parameters and thousands fewer new labelled examples.
That comparison is my main concern. Perhaps I am missing a reason why PATE is not comparable. If it is, it should certainly appear in the experiments. If PATE is indeed comparable, then the main improvement contributed by this paper is the post-processing aspect: PATE is a way to train a private model from scratch, but these methods work on an existing model. Even then, the question of how exactly the existing model is modified (the FineTune method) is unclear.
More broadly, there are several parts of this paper that could be much clearer. I am sympathetic to paper length limitations, but I am certain many or all of these issues can be addressed in 8 pages.
1. DiversePublic description: What does it mean to "obtain the 'embeddings'...E_{public}"? How is k picked?
2. How does the private point-public point assignment in NearPrivate work? Is it just random? How many points do we pick? 
3. In general, how is FineTune meant to work? I understand it is meant to be an abstract black box in the algorithm descriptions, but the experiment description doesn't explain it either. How does FineTune work in the experiments?
4. What does 'headroom' mean in Section 4.2?
5. The way privacy parameters are specified at various points in the experiment section makes things hard to read. A concise table summarizing privacy parameters, accuracy, and additional labels would help.
But overall, I am most interested in the PATE comparison. 
---EDIT AFTER AUTHOR RESPONSE---
I missed the data-dependent aspect of PATE's privacy guarantee. That is a point in favor of this paper. As such, I've increased my score from reject to weak reject.
I actually think a revised version of this paper could reasonably appear in ICLR or similar venues. However, I think the necessary revisions are too large/numerous to accept the paper in its current form, even with promises of revisions. Here are a few revisions that I think would make the paper a much better submission to future conferences:
1. Add discussion of PATE. The data-dependence of their privacy guarantees is well-taken. But it is not clear that data-dependent privacy guarantees are as "trivial" as the paper currently claims with "there are no published examples of a differentially private SVHN classifier with both reasonable accuracy and non-trivial privacy guarantees" suggests. (In fact, I find it confusing that one of the PATE authors agrees with this claim -- they think their own work is trivial?). I agree that data-independent privacy guarantees are preferable, but this should certainly be discussed. As the authors themselves note, the original PATE paper was well-received, so if this paper wants to claim its privacy guarantees are somehow meaningless or even just unsatisfactory, that claim needs to be defended.
2. Elaborate on the fine-tuning process. Perhaps "fine tuning" is indeed "super standard in the object recognition literature", but as all three reviews here indicate, the presentation of fine tuning is unclear in this paper. The author responses also seem to simultaneously claim that fine tuning is  both "super standard" and "[not] obvious". 
3. To make room for the text above, it's not clear that the material about data pollution or even presenting both methods is necessary. I would prefer to see a thorough explanation of the active learning/post-processing paradigm through one algorithm. The authors seem to want to claim that active learning is a useful private approach because it gets data-independent privacy guarantees and performance similar to algorithms with data-dependent privacy guarantees. A paper that focuses on and thoroughly defends that claim actually sounds pretty good!