Alternative Methods to SHAP Derived from Properties of Kernels: A Note on Theoretical Analysis

This study first derives a general and analytical expression of AFA (Additive Feature Attribution), a method that breaks down model outputs into the contributions of each feature and enables the identification of important factors from big data, in terms of the kernel in LIME (Local Interpretable Model-agnostic Explanations). Then, we propose several new AFAs that have desirable kernel properties or that align with the LS prenucleolus in cooperative game theory. Additionally, we revisit existing AFAs such as SHAP (SHapley Additive exPlanations) and re-examine the properties of their kernels.