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SHAP is a popular method for measuring variable importance in machinelearning models. In this paper, we study the algorithm used to estimate SHAPscores and outline its connection to the functional ANOVA decomposition. We usethis connection to show that challenges in SHAP approximations largely relateto the choice of a feature distribution and the number of $2^p$ ANOVA termsestimated. We argue that the connection between machine learning explainabilityand sensitivity analysis is illuminating in this case, but the immediatepractical consequences are not obvious since the two fields face a differentset of constraints. Machine learning explainability concerns models which areinexpensive to evaluate but often have hundreds, if not thousands, of features.Sensitivity analysis typically deals with models from physics or engineeringwhich may be very time consuming to run, but operate on a comparatively smallspace of inputs.

Statistical Aspects of SHAP: Functional ANOVA for Model Interpretation