Shapley values for feature selection: The good, the bad, and the axioms

TL;DR

This paper critically examines the use of Shapley values in feature selection, highlighting potential conflicts with its axiomatic foundations through theoretical examples and simulations.

Contribution

It questions the suitability of Shapley values for feature selection and provides insights through theoretical counterexamples and empirical simulations.

Findings

Shapley axioms may conflict with feature selection goals.

Counterexamples show limitations of Shapley-based methods.

Simulations compare different Shapley formulations like SHAP and SAGE.

Abstract

The Shapley value has become popular in the Explainable AI (XAI) literature, thanks, to a large extent, to a solid theoretical foundation, including four "favourable and fair" axioms for attribution in transferable utility games. The Shapley value is provably the only solution concept satisfying these axioms. In this paper, we introduce the Shapley value and draw attention to its recent uses as a feature selection tool. We call into question this use of the Shapley value, using simple, abstract "toy" counterexamples to illustrate that the axioms may work against the goals of feature selection. From this, we develop a number of insights that are then investigated in concrete simulation settings, with a variety of Shapley value formulations, including SHapley Additive exPlanations (SHAP) and Shapley Additive Global importancE (SAGE).