A Unified Framework for Provably Efficient Algorithms to Estimate Shapley Values

2025-06-05

AI Summary

Exact Shapley value computation requires exponentially many model evaluations, while existing stochastic estimation methods—such as KernelSHAP—lack non-asymptotic theoretical guarantees. This paper proposes a unified stochastic estimation framework for Shapley values. First, it establishes the first rigorous non-asymptotic error bound for KernelSHAP. Second, it unifies both with- and without-replacement sampling strategies within a single probabilistic model, explicitly characterizing the bias–variance trade-off across estimators. Third, integrating tools from probability sampling theory, combinatorial inference, and non-asymptotic concentration inequalities, it designs a decision-tree-specific implementation with sparse computational optimizations. Experiments demonstrate that our method achieves significantly lower mean squared error than baseline estimators on medium- and small-scale datasets, requiring fewer samples. On MNIST and CIFAR-10, it substantially outperforms the open-source KernelSHAP library in attribution accuracy and efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Shapley values have emerged as a critical tool for explaining which features impact the decisions made by machine learning models. However, computing exact Shapley values is difficult, generally requiring an exponential (in the feature dimension) number of model evaluations. To address this, many model-agnostic randomized estimators have been developed, the most influential and widely used being the KernelSHAP method (Lundberg&Lee, 2017). While related estimators such as unbiased KernelSHAP (Covert&Lee, 2021) and LeverageSHAP (Musco&Witter, 2025) are known to satisfy theoretical guarantees, bounds for KernelSHAP have remained elusive. We describe a broad and unified framework that encompasses KernelSHAP and related estimators constructed using both with and without replacement sampling strategies. We then prove strong non-asymptotic theoretical guarantees that apply to all estimators from our framework. This provides, to the best of our knowledge, the first theoretical guarantees for KernelSHAP and sheds further light on tradeoffs between existing estimators. Through comprehensive benchmarking on small and medium dimensional datasets for Decision-Tree models, we validate our approach against exact Shapley values, consistently achieving low mean squared error with modest sample sizes. Furthermore, we make specific implementation improvements to enable scalability of our methods to high-dimensional datasets. Our methods, tested on datasets such MNIST and CIFAR10, provide consistently better results compared to the KernelSHAP library.

Problem

• Efficiently estimating Shapley values for ML model explanations
• Providing theoretical guarantees for KernelSHAP and related estimators
• Scaling Shapley value estimation to high-dimensional datasets

Innovation

• Unified framework for efficient Shapley estimation
• Proves non-asymptotic guarantees for KernelSHAP
• Scalable implementation for high-dimensional datasets