Paper:
In many applications labeled data is not readily available, and needs to be collected via pain-staking human supervision. We propose a rule-exemplar model for collecting human supervision to combine the scalability of rules with the quality of instance labels. The supervision is coupled such that it is both natural for humans and synergistic for learning. We propose a training algorithm that jointly denoises rules via latent coverage variables, and trains the model through a soft implication loss over the coverage and label variables. Empirical evaluation on five different tasks shows that (1) our algorithm is more accurate than several existing methods of learning from a mix of clean and noisy supervision, and (2) the coupled rule-exemplar supervision is effective in denoising rules.

Review:
The paper addresses the problem that labelled data is often unavailable in the quantities required to train effective models. It deals with classification problems, and proposes a method to obtain more (but weaker) labels data with minimal involvement from human labellers, by asking them to generalize their labelling decisions into rules and then learning restrictions on those rules to avoid learning incorrectly generalized labels. The motivating observation is that human labellers are often able to make such generalizations in much less time than it would take them to apply that rule to a large dataset themselves. This is an interesting idea, especially for cases where labelling capacity is limited. The point being made about the labelling noise not being random in this situation is an interesting one - it might be worth exploring this notion further on its own also in contexts where the source of the noise is unknown.
The presentation of the implementation the authors choose for their proposed approach is clear, and the implementation is sensible. The experimental section includes comparisons to a number of alternative methods, and the authors find that their method outperforms all others, including recent methods for combining (noisy) rule-based labels and (clean) human-sourced labels.
I would argue for accepting this paper. It studies an interesting question, which if answered has the potential to make access to machine learning solutions to certain types of problem significantly cheaper and therefore more widespread. The experiments are well-chosen and show that, depending on the data available and the task, significant gains can be made using the proposed method.
Some remarks on how the paper could become stronger: The type of problem that can be assessed with the proposed method seems to be fairly specific: most tasks studied are classification of natural language utterances. That is a natural class of tasks, since it is easy to imagine how labellers can formulate rules. However, it would have been very interesting if the authors had found ways to allow for more diversity here.  In general, I have the impression that there are more interesting ideas and results to be found in the direction explored by this paper - what about, e.g., allowing the classifier to add rules of its own?
The paper would benefit from some general editing with regards to appearance; for example, the supplementary material sections continue the regular section numbering, instead of having their own; the images are missing captions, and sometimes have somewhat unorthodox axis tick labelling.