In this paper we define a population parameter, ``Generalized Variable Importance Metric (GVIM)'', to measure importance of predictors for black box machine learning methods, where the importance is not represented by model-based parameter. GVIM is defined for each input variable, using the true conditional expectation function, and it measures the variable's importance in affecting a continuous or a binary response. We extend previously published results to show that the defined GVIM can be represented as a function of the Conditional Average Treatment Effect (CATE) for any kind of a predictor, which gives it a causal interpretation and further justification as an alternative to classical measures of significance that are only available in simple parametric models. Extensive set of simulations using realistically complex relationships between covariates and outcomes and number of regression techniques of varying degree of complexity show the performance of our proposed estimator of the GVIM.

翻译：本文定义了一个总体参数——“广义变量重要性度量（GVIM）”，用于衡量黑箱机器学习方法中预测变量的重要性，该重要性不以模型参数形式呈现。GVIM针对每个输入变量基于真实条件期望函数进行定义，并度量该变量对连续型或二元型响应变量影响的重要性。我们扩展了先前发表的研究成果，证明了定义的GVIM可表示为任意预测变量条件平均处理效应（CATE）的函数，这赋予了其因果解释，并进一步论证了其作为经典显著性度量（仅适用于简单参数模型）替代方案的合理性。通过使用协变量与结局变量之间复杂现实关系以及多种复杂程度不同的回归技术进行的大量模拟实验，展示了所提出的GVIM估计量的性能。