Is Shapley Explanation for a model unique?

TL;DR

This paper investigates the factors influencing Shapley value explanations in machine learning models, revealing that Shapley explanations are not unique and depend on model outcomes and application context.

Contribution

It provides a detailed analysis of how feature distribution and model outcome types affect Shapley explanations, highlighting their non-uniqueness.

Findings

Shapley values depend on feature moments beyond mean.

Disagreements occur in baseline, sign, and importance across outcomes.

Shapley explanations vary with model output type and application.

Abstract

Shapley value has recently become a popular way to explain the predictions of complex and simple machine learning models. This paper is discusses the factors that influence Shapley value. In particular, we explore the relationship between the distribution of a feature and its Shapley value. We extend our analysis by discussing the difference that arises in Shapley explanation for different predicted outcomes from the same model. Our assessment is that Shapley value for particular feature not only depends on its expected mean but on other moments as well such as variance and there are disagreements for baseline prediction, disagreements for signs and most important feature for different outcomes such as probability, log odds, and binary decision generated using same linear probability model (logit/probit). These disagreements not only stay for local explainability but also affect the global feature importance. We conclude that there is no unique Shapley explanation for a given model. It varies with model outcome (Probability/Log-odds/binary decision such as accept vs reject) and hence model application.