About the authors' contribution in introducing ASVs: - It seems like ASVs are giving a new name to a concept that's been studied in game theory for decades: quasivalues (or equivalently, random-order values). Quasivalues are based on precisely the same idea of relaxing the symmetry axiom, and they use very similar notation (see e.g., [1]) to denote the exact same thing as ASVs. - Bringing these into model explanation is a good idea, but section 3.2 is a bit unclear about the origins. The authors do cite relevant papers [1, 2], but it should probably be more clear that their ASV idea exists under a different name. - For the claim that ASVs/quasivalues uniquely satisfy Axioms 1-3, I would think that a proof should either be provided or cited, because this result is non-trivial. About the global Shapley values: - These global Shapley values seem to have been introduced by another paper, but the authors' explanation that they quantify contributions to the model's accuracy has a small problem. The probability of the correct class f_y(x) does not quite represent the model's accuracy, at least in the (conventional) sense of 0-1 accuracy. I found the authors' explanation a bit confusing, so they might distinguish more clearly between their view of accuracy and 0-1 accuracy. - The section about applications of these global Shapley values to feature selection raises some questions. ASVs provide a very inefficient tool for checking whether a set of features U has strong predictive power. The authors' explanation suggests that users should 1) calculate global ASVs using the ordering given by Eq. 15 (which is specific to a given U/V partitioning), and then 2) take the sum of the ASVs in U (Eq. 16) to estimate U's predictive power. But because ASVs are not cheap to calculate, obtaining the global ASVs (i.e., average ASVs across *every example in the dataset*) would quite possibly be more computationally costly than training a *single* model on U, which gives you exactly the performance with U. Unless I'm missing something, this seems like a very inefficient approach to feature selection. A more justified approach for applying global Shapley values to feature selection, which does not suffer from this problem, is given by [3]. - Performing feature selection on structured data, like EEG time series, is an odd choice of task. It permits a convenient telescoping of ASVs (Eq. 19), but as a feature selection application this does not make much sense. What purpose could there be for excluding the last n% of an EEG sample, given that the seizure could occur at any point in the time window? - If the authors really want to show that ASVs are useful for feature selection, they might have included an experiment with non-structured data, where feature selection makes more sense. They might also consider comparing to more baselines methods. About the other experiments: - The application of ASVs to the admissions problem does something odd: it assumes that department choice precedes gender, as if department choice is a causal ancestor of gender. That seems inconsistent, because in the previous example (income prediction), attributes like gender were assumed to be causal of all other features. So the causal order is in a sense reversed in this second experiment. - The authors provide some explanation for this choice, saying this use of the ASV framework is intended to distinguish between "resolving variables" (R) and "sensitive attributes" (S). But it's a bit odd to explain this reversal of the causal order in midst of an experiment, since the point of the paper is that ASVs integrate causal knowledge. - Would defining the causal order in a way that is consistent with the previous experiment change the results? - Figure 2 shows that the majority of credit is given by ASVs to the beginning of EEG samples. But calculating global Shapley values for a structured data type is an odd choice, because evidence for a seizure could occur at any point in the sample. These results (Figure 2b in particular) do not provide strong evidence, in my view, that ASVs are the right choice for time series data. It would have been more useful to examine individual samples and show how SV/ASV attributions relate to the regions where individual seizures occur. [1] Monderer and Samet, "Variations on the Shapley value" [2] Weber, "Probabilistic values for games" [3] Covert, Lundberg and Lee, "Understanding global feature contributions through additive importance measures"
- For the claim that ASVs/quasivalues uniquely satisfy Axioms 1-3, I would think that a proof should either be provided or cited, because this result is non-trivial. About the global Shapley values: