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.

翻译：Shapley值是公平分配问题中广泛采用的解决方案，旨在将收益合理分配给多个参与者。通过引入博弈论视角，公平分配思想与Shapley值亦可应用于机器学习领域，用于量化特征或数据点对预测模型性能的个体贡献。尽管Shapley值因其理论依据和公理化基础备受青睐，但其计算复杂度随参与实体数量呈指数级增长，因此需要依赖近似方法进行可靠估计。我们提出SVA$k_{\text{ADD}}$，一种通过拟合$k$阶可加代理博弈的新型近似方法。利用k阶可加性，我们能够精确获取代理博弈的Shapley值，并将其作为原始公平分配问题的估计值。通过实证评估，我们验证了该方法的有效性，并与现有竞争方法进行了对比。