Causal Analysis of Shapley Values: Conditional vs. Marginal

Shapley values, a game theoretic concept, has been one of the most popular tools for explaining Machine Learning (ML) models in recent years. Unfortunately, the two most common approaches, conditional and marginal, to calculating Shapley values can lead to different results along with some undesirable side effects when features are correlated. This in turn has led to the situation in the literature where contradictory recommendations regarding choice of an approach are provided by different authors. In this paper we aim to resolve this controversy through the use of causal arguments. We show that the differences arise from the implicit assumptions that are made within each method to deal with missing causal information. We also demonstrate that the conditional approach is fundamentally unsound from a causal perspective. This, together with previous work in [1], leads to the conclusion that the marginal approach should be preferred over the conditional one.