用k-加性博弈近似计算博弈论中的公平分配值，加速模型特征重要性分析。
Shapley Value Approximation Based on k-Additive Games
- 构建k-加性代理博弈，利用其结构特性精确求解近似值
- 在多个数据集上相比现有方法更准确且计算更快
- 适合需要高效、精准特征归因的机器学习可解释性场景
Shapley值是解决多主体间收益公平分配问题的主流方法。从博弈论视角出发，该方法也可用于机器学习中量化特征或数据点对预测模型性能的贡献。尽管其理论基础坚实且具有公理化优势，但其计算复杂度随参与实体数量呈指数增长，因此需依赖近似方法实现可靠估计。本文提出SVA$k_{\text{ADD}}$，一种基于k-加性代理博弈的新近似方法。通过利用k-加性的结构特性，能够精确求解代理博弈的Shapley值，并将其作为原始公平分配问题的估计值。实验验证了该方法的有效性，并与现有方法进行了对比。
原文摘要 · Abstract (English)
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$k_{\text{ADD}}$, 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.
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