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

TL;DR

This paper provides a theoretical analysis of kernel properties in additive feature attribution methods, proposing new AFAs and re-evaluating existing ones like SHAP within a unified kernel framework.

Contribution

It derives a general expression for AFA in LIME, introduces new AFAs based on kernel properties, and re-examines SHAP's kernel properties for better interpretability.

Findings

Derived a general analytical expression of AFA in terms of kernels

Proposed new AFAs with desirable kernel properties

Re-examined the kernel properties of SHAP

Abstract

This study first derives a general and analytical expression of AFA (Additive Feature Attribution) in terms of the kernel in LIME (Local Interpretable Model-agnostic Explanations). Then, we propose some new AFAs that have appropriate properties of kernels or that coincide with the LS prenucleolus in cooperative game theory. We also revisit existing AFAs such as SHAP (SHapley Additive exPlanations) and re-examine the properties of their kernels.