Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: The authors propose a heuristic, deep learning approach to computing agent/feature importance in complex cooperative game theoretic settings. Such setting are known to be hard to solve and understand exactly (for example computing the Shapley value in voting games is #P-complete), motivating the study of the paper. 
strengths_and_weaknesses: - The authors’ algorithms seem to perform well according to the experiments
- The authors’ proposed framework has several proposed and illustrated applications, including solving voting games and understanding feature importance in hard-to-understand models
- The authors look at several metrics of interest for measure contribution/importance, including shapley values, Banzhaf indexes, and cores. The flexibility provided by the framework seems nice and useful. 

Weaknesses:
- My main question and “issue” with the paper is that I do not get a good sense here of whether the neural net approach is actually necessary, or if it is actually overkill. For example, if the goal were just to compute Shapley values fast, approaches based on sampling are known and seem to be relatively efficient. How does the current work compare to those? 
- Maybe things are more complicated when it comes to compute the actual outcomes rather than just computing shapley values, but this needs to be discussed more. There is indeed motivation for a heuristic approach in that these problems are hard to solve exactly, but it seems the authors jumped to a neural net before exploring simpler heuristics on very structured problems/it is not clear to me why this brings compared to possible simpler approaches. 
- Related to the point above, the paper makes no comparison with previous work, when other heuristics I believe exist for at least some of the questions asked in the paper

questions: - Can the authors compare their results to previous work/non deep learning based results? Does the deep learning approach lead to significant improvement which warrants the downsides of having to use a black-box, hard to understand algorithm?
limitations: In terms of societal impact, I think it is nice that the authors have applications to interpretability. Limitations are discussed in Section 4.1.2.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: The paper discusses using neural computation to compute values of cooperative game theory in weighted voting games and feature importance games.  For weighted voting games, models for both fixed and variable numbers of players are given.  While fixed models outperformed variable models, results on random games indicates that both models do relatively well.  Furthermore, predictions fro feature importance games are quite good after training on only a small amount of training data.
strengths_and_weaknesses: Strengths:

+ The paper does a good job of describing and introducing the problem.

+ The presentation of the paper is clear and clean.

+ This paper implements and tests a good, simple, and useful idea: Can neural computation to computer values of cooperative game theory.  

+ The analysis of the results is good and detailed.

Weaknesses:

- It would be fun to illustrate how well the trained neural networks perform on known problems rather than on just random games.

- (Table 1) Suggestion: I think it would be good to understand how significant the failures are when the neural network fails (e.g., significantly out of distribution).  Is there any way to detect when it would fail?

A few minor nitpicks:

- It’s probably right in front of my eyes, but I could see where p(C) was defined on line 111

- Line 260: fix “at a the cost” — there’s clearly an extra word

questions: See comments in the previous section.
limitations: I think further exploration of failure cases would be appropriate at some point
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: This paper applies a multi-layer perceptron to learning to approximate the Shapley value of a weighted voting game (where the input is a description of the voting weights of each player, and the output is a vector of Shapley values for each voter).  The fixed-dimension case (for which the number of voters is constant) and variable dimension case are both considered; the variable dimension case is handled simply by zero-padding (i.e., non-players are added with weight 0 to every empty slot).

Although weighted voting games are simple, approximating their Shapley value within a multiplicative factor is known to be intractable in the worst case.

strengths_and_weaknesses: The basic idea is sound: we sometimes want the Shapley value (to estimate the relative influence of different input features on the output of an ML model, or to estimate the relative power of different voters).  However, it's intractable to compute exactly.  So let's try approximating it by training a neural network on small instances.  It seems to work pretty well on the instances that they test on.

One of the main motivations for this work is scalability.  It can be exponentially expensive to compute the Shapley value as the number of participants increases, making an approximation approach valuable.  Clearly the network with a fixed number of participants won't be much use in large-scale situations, since the training data needs to be as large as the test data.  On the other hand, the paper shows that you can get decent performance by training on a dataset with about half as many participants as in the test set (using the zero-padding variable-dimension approach).  This is of course better than nothing, but I'm skeptical that an approximate doubling of the feasible size of input is going to be sufficient in settings that actually need scale.

The paper is clearly written, with the exception of the material on explainable AI.  This domain is an important part of the paper's motivation, but its treatment feels like something of an afterthought.   I can take a guess at what is going on here (the "value" created by a given agent is going to be either the average change in a binary classification, or the average change in regression output, averaged over all orderings), but it would be nice if this were somehow made explicit.  Section 3.2 doesn't really give any details about the actual procedure (what is a "sampled sub-dataset"?  Are you sampling rows (instances) or columns (features)?  Appendix D.2 doesn't refer to this at all.).  Section 2.2 is similarly vague.

Overall, I don't think this work clears the significance bar for publication at NeurIPS.  It proposes a standard feedforward architecture for prediction in a specific scenario.  The scenario is interesting but not really deeply explored.  There is no explicit comparison to baselines, so it's hard to tell what we actually gain.  In particular, we don't see any performance numbers at all.  How large is the performance difference vs standard techniques?  Are you able to do well on instances that take SHAP weeks, for example?

__minor comments__

- p.5: "we redistribute the payoffs allocated to non-player entries": How necessary does this turn out to be?  (I.e., is a substantial fraction of payoff often allocated to non-players?)

- p.6: The first paragraph of s.3.2 is very repetitive

- On a related note, it's not clear from the main text what the ground truth for figure 7 is meant to be.

- Figure 2 is unreadably small, and also seems to make the PDF very slow to render.

questions: Do you have performance numbers (both timing and prediction quality) for any scenario where the use of something like SHAP would be intractable?
limitations: see strengths/weaknesses
review_title: null

Meta-review: metareview: This paper proposes a deep learning approach to computing agent/feature importance in complex cooperative game theoretic settings.  The reviewers are overall positive, albeit some are a bit lukewarm, about the paper.  Overall, the consensus after the discussion is that the idea of studying how well neural computation can be used to approximate the relevant quantities (hard to solve exactly) in cooperative game theory is itself a contribution, and this paper has done a decent job in analyzing the approach and establishing its validity. We would encourage the authors to incorporate the reviewer comments (e.g., move the many vs one discussion to the main paper to strengthen the motivation, include comparisons with more baselines, etc) into the final version and produce a stronger paper.
confidence: Less certain
Decision: Accept