Regression-adjusted Monte Carlo Estimators for Shapley Values and Probabilistic Values

2025-06-13

AI Summary

Efficient, unbiased estimation of probabilistic values—such as the Shapley value, Banzhaf value, and semivalues—in explainable AI remains challenging due to high computational complexity and reliance on restrictive linear regression assumptions. Method: This paper proposes a novel decoupled framework integrating Monte Carlo sampling with flexible regression modeling. It orthogonally combines any analytically tractable probabilistic value with expressive regression models (e.g., XGBoost), eliminating the need for linear approximations while preserving unbiasedness; variance reduction techniques are further incorporated to enhance estimation accuracy. Contribution/Results: Evaluated on eight benchmark datasets, our method reduces Shapley value estimation error by 6.5×, 3.8×, and 2.6× compared to Permutation SHAP, Kernel SHAP, and Leverage SHAP, respectively. For generalized probabilistic values, error reduction reaches up to 215×. The framework achieves a significant balance between computational efficiency and statistical precision, enabling scalable, model-agnostic, and theoretically sound attribution.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Calibration & Uncertainty Quantification
• Humans and AI: Explainable AI (XAI) for Human Understanding

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more. Since all of these values require exponential time to compute exactly, research has focused on efficient approximation methods using two techniques: Monte Carlo sampling and linear regression formulations. In this work, we present a new way of combining both of these techniques. Our approach is more flexible than prior algorithms, allowing for linear regression to be replaced with any function family whose probabilistic values can be computed efficiently. This allows us to harness the accuracy of tree-based models like XGBoost, while still producing unbiased estimates. From experiments across eight datasets, we find that our methods give state-of-the-art performance for estimating probabilistic values. For Shapley values, the error of our methods can be $6.5 imes$ lower than Permutation SHAP (the most popular Monte Carlo method), $3.8 imes$ lower than Kernel SHAP (the most popular linear regression method), and $2.6 imes$ lower than Leverage SHAP (the prior state-of-the-art Shapley value estimator). For more general probabilistic values, we can obtain error $215 imes$ lower than the best estimator from prior work.

Problem

• Efficiently estimating Shapley and probabilistic values
• Combining Monte Carlo sampling with regression techniques
• Improving accuracy over existing Shapley value estimators

Innovation

• Combines Monte Carlo sampling with regression
• Uses flexible function families like XGBoost
• Achieves state-of-the-art error reduction