Title: ShaplEIG: A Bayesian Framework for Estimating Shapley Values

Abstract:

While Shapley values serve as a robust attribution metric in interpretable machine learning, their precise calculation becomes computationally infeasible as the number of participants increases due to exponential scaling. Consequently, numerous approximation techniques have emerged that rely on evaluating value functions for sampled coalitions. This leads to a critical inquiry: can the accuracy of these approximations be enhanced by intelligently choosing which coalitions to evaluate, leveraging insights from prior assessments? Such adaptive strategies are especially valuable in scenarios where the value function is expensive to compute and evaluation budgets are tight, including applications like hyperparameter importance analysis, data valuation, and retraining-based feature importance.

To address this challenge, we introduce ShaplEIG, a Bayesian experimental design method. This approach utilizes a Gaussian process surrogate to model the costly value function and dynamically selects coalitions that maximize the expected information gain regarding the Shapley values. Leveraging the linearity of Shapley values with respect to the value function, we demonstrate that this expected information gain can be derived in closed form. Additionally, we develop a computational strategy that lowers the complexity from exponential to polynomial relative to the number of players, utilizing elementary symmetric polynomials. Our extensive experimental results across various high-cost applications demonstrate that ShaplEIG consistently outperforms current state-of-the-art baselines in terms of sample efficiency, particularly within low-budget constraints.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC