Shapley Values: A Comparison of Definitions and Approximation Methods

Abstract

The Shapley value method is an explanatory method that describes the feature attribution of Machine Learning models. There are three different definitions of the Shapley values, namely Conditional Expectation Shapley, Marginal Expectation Shapley and Baseline Shapley. A comparison is made between the three definitions and they are applied to one statistical and two Machine Learning models that predict house transaction prices. Most existing methods to approximate Shapley values assume independence, which is in practice often violated. An existing copula-based method that tries to take into account the dependency is extended to apply to problems with continuous and discrete features. This copula-based method approximates the Shapley values more accurately than other methods. The Conditional Expectation Shapley values give unnatural explanations, therefore other definitions of the Shapley values are more suitable. The Baseline Shapley values seem to be the most promising since there is an accurate and fast approximation method and the B Shapley values are the easiest to interpret.