Provably Accurate Shapley Value Estimation via Leverage Score Sampling

Originally introduced in game theory, Shapley values have emerged as a central tool in explainable machine learning, where they are used to attribute model predictions to specific input features. However, computing Shapley values exactly is expensive: for a model with $n$ features, $O(2^n)$ model evaluations are necessary. To address this issue, approximation algorithms are widely used. One of the most popular is the Kernel SHAP algorithm, which is model agnostic and remarkably effective in practice. However, to the best of our knowledge, Kernel SHAP has no strong non-asymptotic complexity guarantees. We address this issue by introducing *Leverage SHAP*, a light-weight modification of Kernel SHAP that provides provably accurate Shapley value estimates with just $O(n\log n)$ model evaluations. Our approach takes advantage of a connection between Shapley value estimation and agnostic active learning by employing *leverage score sampling*, a powerful regression tool. Beyond theoretical guarantees, we show that Leverage SHAP consistently outperforms even the highly optimized implementation of Kernel SHAP available in the ubiquitous SHAP library [Lundberg \& Lee, 2017].