Paper:
Inferring Generative Model Structure with Static Analysis
Obtaining enough labeled data to robustly train complex discriminative models is a major bottleneck in the machine learning pipeline. A popular solution is combining multiple sources of weak supervision using generative models. The structure of these models affects the quality of the training labels, but is difficult to learn without any ground truth labels. We instead rely on weak supervision sources having some structure by virtue of being encoded programmatically. We present Coral, a paradigm that infers generative model structure by statically analyzing the code for these heuristics, thus significantly reducing the amount of data required to learn structure. We prove that Coral's sample complexity scales quasilinearly with the number of heuristics and number of relations identified, improving over the standard sample complexity, which is exponential in n for learning n th degree relations. Empirically, Coral matches or outperforms traditional structure learning approaches by up to 3.81 F1 points. Using Coral to model dependencies instead of assuming independence results in better performance than a fully supervised model by 3.07 accuracy points when heuristics are used to label radiology data without ground truth labels.

Review:
The authors propose using static analysis to improve the synthesis of generative models designed to combine multiple heuristic functions. They leverage the fact that expressing heuristics as programs often encodes information about their relationship to other heuristics. In particular, this occurs when multiple heuristics depend (directly or indirectly) on the same value, such as the perimeter of a bounding box in a vision application. The proposed system, Coral, infers and explicitly encodes these relationships in a factor graph model. The authors show empirically how Coral leads to improvements over other related techniques.
I believe the idea is interesting and worth considering for acceptance. However, I have various queries, and points that might strengthen the paper:
* I found it difficult at first to see how Coral relates to other work in this area. It might be useful to position the "Related Work" section earlier in the paper. It might also help to more explicitly describe how Coral relates to [2] (Bach et al.), which seems closest to this work -- in particular, there is quite a lot of similarity between the factor graphs considered by the two models. (Coral seems to be obtained by inserting the phi_i^HF and p_i nodes between the lambda_i and phi^DSP nodes, and by restricting only to pairwise terms in the phi^DSP factor.)
* It isn't stated anywhere I could see that lambda_i \in {-1, 1}, but based on the definition of phi^Acc_i (line 147), this must be the case, right? If so, the "True" and "False" values in Figure 3 (a) should potentially be replaced with 1 and -1 for clarity.
* Why does (i) (line 156) constitute a problem for the model? Surely over-specification is OK? (I can definitely see how under-specification in (ii) is an issue, on the other hand.)
* What is the justification for using the indicator function I[p_i = p_j] for phi_ij^Sim? I would expect this hardly ever to have the value 1 for most primitives of interest. It is mentioned that, for instance, we might expect the area and perimeter of a tumour to be related, but surely we do not expect these values to be identical? (I note that similar correlation dependencies occur in [2] (Bach et al.), but these compare the heuristic functions rather than the primitives as here. Since the heuristic functions return an estimate of the label Y, it seems much more reasonable to expect their values might be equal.)
* It is stated in line 176 that the supplementary materials contains a proof that "if any additional factor would have improved the accuracy of the model, then the provided primitive dependencies would have to be incorrect". However, I couldn't find this -- where exactly can it be found?
Finally, some minor (possible) typos:
* Line 133: "if an edge point" should be "if an edge points"
* Figure 3 (a): The first "return False" has an extra indent
* The double summation in the definition of P between lines 170 and 171 seems to double count certain terms, and is slightly different from the definition of phi^DSP between lines 169 and 170
* Line 227: "structure learning structure learning"
* Line 269: "structure learning performed better than Coral when we looked only used static analysis to infer dependencies"