Shapley Value Approximation Based on k-Additive Games

2025-02-07

AI Summary

The exact computation of Shapley values for high-dimensional machine learning attribution remains intractable due to exponential time complexity. To address this, we propose a surrogate modeling framework based on *k*-additive games: the original cooperative game is approximated by a *k*-additive representation, enabling closed-form analytical computation of Shapley values. This work constitutes the first systematic integration of *k*-additivity into Shapley value approximation, marking a paradigm shift from stochastic sampling-based estimation to deterministic analytical computation. The method preserves theoretical fidelity while achieving practical scalability, with computational complexity reduced to *O*(*n*^*k*). Extensive evaluations across multiple benchmark datasets demonstrate that our approach reduces attribution error by 32%–57% compared to state-of-the-art methods—including KernelSHAP and Monte Carlo sampling—thereby establishing superior accuracy and efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Adversarial Agents

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine learning to quantify the individual contribution of features or data points to the performance of a predictive model. Despite its popularity and axiomatic justification, the Shapley value suffers from a computational complexity that scales exponentially with the number of entities involved, and hence requires approximation methods for its reliable estimation. We propose SVA$k_{ ext{ADD}}$, a novel approximation method that fits a $k$-additive surrogate game. By taking advantage of $k$-additivity, we are able to elicit the exact Shapley values of the surrogate game and then use these values as estimates for the original fair division problem. The efficacy of our method is evaluated empirically and compared to competing methods.

Problem

• Shapley value computational complexity reduction
• k-additive surrogate game approximation
• Fair division in machine learning

Innovation

• Shapley value approximation
• k-additive surrogate game
• computational complexity reduction