Statistical Inference and Learning for Shapley Additive Explanations (SHAP)

2026-02-11

AI Summary

This work addresses the lack of valid statistical inference for global SHAP value metrics, such as the $p$-th power mean. It establishes the first debiased estimation framework yielding asymptotically normal estimators: for $p \geq 2$, it employs U-statistics, while for $1 \leq p < 2$, it leverages Neyman orthogonal scores. To handle the non-smoothness of the target functional, a tunable temperature smoothing strategy is introduced. Furthermore, the SHAP curve is treated as a nuisance function, and its estimation is integrated within a semi-parametric inference framework coupled with empirical risk minimization. The resulting method provides reliable confidence intervals for global SHAP-based feature importance, thereby establishing a rigorous statistical foundation for model interpretation and feature selection.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Graphical Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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 $p$th 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 $p$th powers of SHAP. When $p \geq 2$, we show a de-biased estimator that combines U-statistics with Neyman orthogonal scores for functionals of nested regressions is asymptotically normal. When $1 \leq p<2$ (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 $p$th 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.

Problem

• SHAP
• statistical inference
• feature importance
• Shapley values
• global explanations

Innovation

• SHAP
• statistical inference
• Neyman orthogonality
• U-statistics
• semi-parametric estimation