Shapley values originated in cooperative game theory but are extensively used today as a model-agnostic explanation framework to explain predictions made by complex machine learning models in the industry and academia. There are several algorithmic approaches for computing different versions of Shapley value explanations. Here, we focus on conditional Shapley values for predictive models fitted to tabular data. Estimating precise conditional Shapley values is difficult as they require the estimation of non-trivial conditional expectations. In this article, we develop new methods, extend earlier proposed approaches, and systematize the new refined and existing methods into different method classes for comparison and evaluation. The method classes use either Monte Carlo integration or regression to model the conditional expectations. We conduct extensive simulation studies to evaluate how precisely the different method classes estimate the conditional expectations, and thereby the conditional Shapley values, for different setups. We also apply the methods to several real-world data experiments and provide recommendations for when to use the different method classes and approaches. Roughly speaking, we recommend using parametric methods when we can specify the data distribution almost correctly, as they generally produce the most accurate Shapley value explanations. When the distribution is unknown, both generative methods and regression models with a similar form as the underlying predictive model are good and stable options. Regression-based methods are often slow to train but produce the Shapley value explanations quickly once trained. The vice versa is true for Monte Carlo-based methods, making the different methods appropriate in different practical situations.

翻译：Shapley值起源于合作博弈理论，如今被广泛用作模型无关的解释框架，用于解释学术界和工业界复杂机器学习模型做出的预测。已有多种算法可用于计算不同版本的Shapley值解释。本文聚焦于应用于表格数据的预测模型中条件Shapley值，其精确估计面临挑战，因为需要估算复杂的条件期望。我们开发了新方法、拓展了先前提出的方法，并将这些新型改进方法与现有方法系统归类为不同方法类以进行比较评估。这些方法类分别采用蒙特卡洛积分或回归模型来刻画条件期望。通过开展大量模拟实验，我们系统评估了不同方法类在多种设定下对条件期望（进而对条件Shapley值）的估计精度。同时我们将这些方法应用于多个真实数据实验，并就不同方法类及算法的适用场景提出建议。总体而言，当数据分布可近似准确指定时，推荐使用参数化方法——这类方法通常能提供最精确的Shapley值解释；当分布未知时，生成式方法与底层预测模型结构相似的回归模型均为稳定可靠的选择。基于回归的方法训练耗时较长，但训练完成后可快速生成Shapley值解释，而基于蒙特卡洛的方法则相反，这使得不同方法在不同实际场景中各有其适用性。