Antithetic Sampling for Top-k Shapley Identification

Abstract: Additive feature explanations rely primarily on game-theoretic notions such as the Shapley value by viewing features as cooperating players. The Shapley value's popularity in and outside of explainable AI stems from its axiomatic uniqueness. However, its computational complexity severely limits practicability. Most works investigate the uniform approximation of all features' Shapley values, needlessly consuming samples for insignificant features. In contrast, identifying the $k$ most important features can already be sufficiently insightful and yields the potential to leverage algorithmic opportunities connected to the field of multi-armed bandits. We propose Comparable Marginal Contributions Sampling (CMCS), a method for the top-$k$ identification problem utilizing a new sampling scheme taking advantage of correlated observations. We conduct experiments to showcase the efficacy of our method in compared to competitive baselines. Our empirical findings reveal that estimation quality for the approximate-all problem does not necessarily transfer to top-$k$ identification and vice versa.