Tree ensemble methods provide promising predictions with models difficult to interpret. Recent introduction of Shapley values for individualized feature contributions, accompanied with several fast computing algorithms for predicted values, shows intriguing results. However, individualizing coefficients of determination, aka $R^2$, for each feature is challenged by the underlying quadratic losses, although these coefficients allow us to comparatively assess single feature's contribution to tree ensembles. Here we propose an efficient algorithm, Q-SHAP, that reduces the computational complexity to polynomial time when calculating Shapley values related to quadratic losses. Our extensive simulation studies demonstrate that this approach not only enhances computational efficiency but also improves estimation accuracy of feature-specific coefficients of determination.

翻译：树集成方法通过难以解释的模型提供了有前景的预测结果。近期引入的用于个体化特征贡献的Shapley值，以及几种针对预测值的快速计算算法，展示了引人注目的成果。然而，为每个特征个体化决定系数（即$R^2$）因其背后的二次损失而面临挑战，尽管这些系数使我们能够比较评估单个特征对树集成的贡献。本文提出了一种高效算法Q-SHAP，在计算与二次损失相关的Shapley值时，将计算复杂度降低至多项式时间。我们广泛的模拟研究表明，该方法不仅提高了计算效率，而且改善了特征特异性决定系数的估计精度。