# Statistical Inference and Learning for Shapley Additive Explanations (SHAP)

arXiv: https://arxiv.org/abs/2602.10532 · HTML: https://mlsanity.com/paper/2602.10532/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 69 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Builds on (most cited first, 30 of 32)

- [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)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Efficient nonparametric statistical inference on population feature importance using Shapley values](https://mlsanity.com/paper/2006.09481/) (2020)
- [Orthogonal Random Forest for Causal Inference](https://mlsanity.com/paper/1806.03467/) (2018)
- [A general framework for inference on algorithm-agnostic variable importance](https://mlsanity.com/paper/2004.03683/) (2020)
- [RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests](https://mlsanity.com/paper/2110.03031/) (2021)
- [Amazon SageMaker Clarify: Machine Learning Bias Detection and Explainability in the Cloud](https://mlsanity.com/paper/2109.03285/) (2021)
- [Decomposing Global Feature Effects Based on Feature Interactions](https://mlsanity.com/paper/2306.00541/) (2023)
- [Automatic Debiased Machine Learning for Covariate Shifts](https://mlsanity.com/paper/2307.04527/) (2023)
- [Covariate-assisted bounds on causal effects with instrumental variables](https://mlsanity.com/paper/2301.12106/) (2023)
- [Powershap: A Power-full Shapley Feature Selection Method](https://mlsanity.com/paper/2206.08394/) (2022)
- [A feature selection method based on Shapley values robust to concept shift in regression](https://mlsanity.com/paper/2304.14774/) (2023)
- [Orthogonal Causal Calibration](https://mlsanity.com/paper/2406.01933/) (2024)
- [Inference on Optimal Dynamic Policies via Softmax Approximation](https://mlsanity.com/paper/2303.04416/) (2023)
- [Shapley Curves: A Smoothing Perspective](https://mlsanity.com/paper/2211.13289/) (2022)
- [Inference on Variable Importance for Treatment Effect Heterogeneity: Shapley Values and Beyond](https://mlsanity.com/paper/2510.18843/) (2025)

## Built on by (most cited first, 1 of 1)

- [Semiparametric Inference for Conditional Shapley Feature Importance](https://mlsanity.com/paper/2609.10313/) (2026)

## Abstract (arXiv)

The SHAP (short for Shapley additive explanation) framework has become an essential tool for attributing importance to variables in predictive tasks. In model-agnostic settings, SHAP uses the concept of Shapley values from cooperative game theory to fairly allocate credit to the features in a vector X based on their contribution to an outcome Y. While the explanations offered by SHAP are local by nature, learners often need global measures of feature importance in order to improve model explainability and perform feature selection. The most common approach for converting these local explanations into global ones is to compute either the mean absolute SHAP or mean squared SHAP. However, despite their ubiquity, there do not exist approaches for performing statistical inference on these quantities. In this paper, we take a semi-parametric approach for calibrating confidence in estimates of the pth powers of Shapley additive explanations. We show that, by treating the SHAP curve as a nuisance function that must be estimated from data, one can reliably construct asymptotically normal estimates of the pth powers of SHAP. When p ≥ 2, we show a de-biased estimator that combines U-statistics with Neyman orthogonal scores for functionals of nested regressions is asymptotically normal. When 1 ≤ p < 2 (and the hence target parameter is not twice differentiable), we construct de-biased U-statistics for a smoothed alternative. In particular, we show how to carefully tune the temperature parameter of the smoothing function in order to obtain inference for the true, unsmoothed pth power. We complement these results by presenting a Neyman orthogonal loss that can be used to learn the SHAP curve via empirical risk minimization and discussing excess risk guarantees for commonly used function classes.