Kernel Banzhaf: A Fast and Robust Estimator for Banzhaf Values

Banzhaf values offer a simple and interpretable alternative to the widely-used Shapley values. We introduce Kernel Banzhaf, a novel algorithm inspired by KernelSHAP, that leverages an elegant connection between Banzhaf values and linear regression. Through extensive experiments on feature attribution tasks, we demonstrate that Kernel Banzhaf substantially outperforms other algorithms for estimating Banzhaf values in both sample efficiency and robustness to noise. Furthermore, we prove theoretical guarantees on the algorithm's performance, establishing Kernel Banzhaf as a valuable tool for interpretable machine learning. The increasing complexity of AI models has intensified the challenges associated with model interpretability. Modern machine learning models, such as deep neural networks and complex ensemble methods, often operate as "opaque boxes." This opacity makes it difficult for users to understand and trust model predictions, especially in decision-making scenarios like healthcare, finance, and legal applications, which require rigorous justifications. Thus, there is a pressing need for reliable explainability tools to bridge the gap between complex model behaviors and human understanding. Among the various methods employed within explainable AI, game-theoretic approaches have gained prominence for quantifying the contribution of features in predictive modeling and enhancing model interpretability. While primarily associated with feature attribution (Lundberg & Lee, 2017; Karczmarz et al., 2022), these methods also contribute to broader machine learning tasks such as feature selection (Covert et al., 2020) and data valuation (Ghorbani & Zou, 2019; Wang & Jia, 2023). Such applications extend the utility of explainable AI, fostering greater trust in AI systems by providing insights beyond traditional explanations.