Rigorous Feature Importance Scores based on Shapley Value and Banzhaf Index

TL;DR

This paper introduces new feature importance scores based on game theory that consider non-WAXp sets, improving explanations of ML models by accounting for their role in excluding adversarial examples.

Contribution

It proposes two novel feature importance scores using Shapley value and Banzhaf index that incorporate non-WAXp sets, enhancing feature attribution in XAI.

Findings

Scores effectively quantify feature contribution in excluding adversarial examples

Properties and computational complexity of the scores are analyzed

Scores outperform existing methods in certain explanation tasks

Abstract

Feature attribution methods based on game theory are ubiquitous in the field of eXplainable Artificial Intelligence (XAI). Recent works proposed rigorous feature attribution using logic-based explanations, specifically targeting high-stakes uses of machine learning (ML) models. Typically, such works exploit weak abductive explanation (WAXp) as the characteristic function to assign importance to features. However, one possible downside is that the contribution of non-WAXp sets is neglected. In fact, non-WAXp sets can also convey important information, because of the relationship between formal explanations (XPs) and adversarial examples (AExs). Accordingly, this paper leverages Shapley value and Banzhaf index to devise two novel feature importance scores. We take into account non-WAXp sets when computing feature contribution, and the novel scores quantify how effective each feature is at excluding AExs. Furthermore, the paper identifies properties and studies the computational complexity of the proposed scores.