Title: Computing Exact Shapley Values in Polynomial Time for Product-Kernel Methods
Primary area: interpretability and explainable AI
Keywords: Interpretable machine learning;exact Shapley value; kernel methods;

Abstract: Kernel methods are widely used in machine learning due to their flexibility and expressiveness. However, their black-box nature poses significant challenges to interpretability, limiting their adoption in high-stakes applications. Shapley value-based feature attribution techniques, such as SHAP and kernel method-specific adaptation like RKHS-SHAP, offer a promising path toward explainability. Yet, computing exact Shapley values is generally intractable, leading existing methods to rely on approximations and thereby incur unavoidable error. In this work, we introduce PKeX-Shapley, a novel algorithm that utilizes the multiplicative structure of product kernels to enable the exact computation of Shapley values in polynomial time. The core of our approach is a new value function, the *functional baseline value function*, specifically designed for product-kernel models. This value function removes the influence of a feature subset by setting its functional component to the least informative state. Crucially, it allows a recursive thus efficient computation of Shapley values in polynomial time. As an important additional contribution, we show that our framework extends beyond predictive modeling to statistical inference. In particular, it generalizes to popular kernel-based discrepancy measures such as the Maximum Mean Discrepancy (MMD) and the Hilbert–Schmidt Independence Criterion (HSIC), thereby providing new tools for interpretable statistical inference.