# Statistical Aspects of SHAP: Functional ANOVA for Model Interpretation

arXiv: https://arxiv.org/abs/2208.09970 · HTML: https://mlsanity.com/paper/2208.09970/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 46 references that are in the map.
- First posted on arXiv 21 Aug 2022.

## Builds on (most cited first, 16 of 16)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Explainable Machine Learning in Deployment](https://mlsanity.com/paper/1909.06342/) (2019)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [Shapley Flow: A Graph-based Approach to Interpreting Model Predictions](https://mlsanity.com/paper/2010.14592/) (2020)
- [Unifying local and global model explanations by functional decomposition of low dimensional structures](https://mlsanity.com/paper/2208.06151/) (2022)

## Built on by (most cited first, 12 of 12)

- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions](https://mlsanity.com/paper/2405.10852/) (2024)
- [Tree Ensemble Explainability through the Hoeffding Functional Decomposition and TreeHFD Algorithm](https://mlsanity.com/paper/2510.24815/) (2025)
- [Fast Estimation of Partial Dependence Functions using Trees](https://mlsanity.com/paper/2410.13448/) (2024)
- [Disentangling Interactions and Dependencies in Feature Attribution](https://mlsanity.com/paper/2410.23772/) (2024)
- [Tensor Product Neural Networks for Functional ANOVA Model](https://mlsanity.com/paper/2502.15215/) (2025)
- [Theoretical Evaluation of Asymmetric Shapley Values for Root-Cause Analysis](https://mlsanity.com/paper/2310.09961/) (2023)
- [Generalized Functional ANOVA: A Complete Theoretical Framework](https://mlsanity.com/paper/2605.18422/) (2026)
- [CUBE: Contrastive Understanding by Balanced Experiments](https://mlsanity.com/paper/2509.10825/) (2025)
- [Bayesian Neural Networks for Functional ANOVA model](https://mlsanity.com/paper/2510.00545/) (2025)
- [Fourier Analysis on the Boolean Hypercube via Hoeffding Functional Decomposition](https://mlsanity.com/paper/2510.07088/) (2025)

## Abstract (arXiv)

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 2p 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.