A Refutation of Shapley Values for Explainability

Xuanxiang Huang, Joao Marques-Silva

Keywords: Shapley values, Explainability

TL;DR: The paper proves the existence of classifiers, for arbitrarily large number of features, for which Shapley values yield misleading information about the relative order of importance of features.

Abstract:

Recent work demonstrated the existence of Boolean functions for which Shapley values provide misleading information about the
relative importance of features in rule-based explanations. Such misleading information was broadly categorized into a number of
possible issues. Each of those issues relates with features being relevant or irrelevant for a prediction, and all are significant
regarding the inadequacy of Shapley values for rule-based explainability. This earlier work devised a brute-force approach to identify Boolean functions, defined on small numbers of features, and also associated instances, which displayed such inadequacy-revealing issues, and so served as evidence to the inadequacy of Shapley values for rule-based explainability. However, an outstanding question is how frequently such inadequacy-revealing issues can occur for Boolean functions with arbitrary large numbers of features. It is plain that a brute-force approach would be unlikely to provide insights on how to tackle this question. This paper answers the above question by proving that, for any number of features, there exist Boolean functions that exhibit one or more inadequacy-revealing issues, thereby contributing decisive arguments against the use of Shapley values as the theoretical underpinning of feature-attribution methods in explainability.

Submission Number: 13665