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Statistical Aspects of SHAP: Functional ANOVA for Model I...
[Submitted on 21 Aug 2022 (v1), last revised 31 Jul 2026 (this v · 2022-08-22 · via stat updates on arXiv.org

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Abstract:SHAP is a popular method for measuring variable importance in machine learning models. In this paper, we study the algorithm used to estimate SHAP scores and outline its connection to the functional ANOVA decomposition. We use this connection to show that challenges in SHAP approximations largely relate to the choice of a feature distribution and the number of $2^p$ ANOVA terms estimated. We argue that the connection between machine learning explainability and sensitivity analysis is illuminating in this case, but the immediate practical consequences are not obvious since the two fields face a different set of constraints. Machine learning explainability concerns models which are inexpensive to evaluate but often have hundreds, if not thousands, of features. Sensitivity analysis typically deals with models from physics or engineering which may be very time consuming to run, but operate on a comparatively small space of inputs.

Submission history

From: Andrew Herren [view email]
[v1] Sun, 21 Aug 2022 21:46:15 UTC (25 KB)
[v2] Fri, 11 Nov 2022 09:46:00 UTC (25 KB)
[v3] Fri, 31 Jul 2026 18:17:31 UTC (26 KB)