Conditional mean independence (CMI) testing is crucial for statistical tasks including model determination and variable importance evaluation. In this work, we introduce a novel population CMI measure and a bootstrap-based testing procedure that utilizes deep generative neural networks to estimate the conditional mean functions involved in the population measure. The test statistic is thoughtfully constructed to ensure that even slowly decaying nonparametric estimation errors do not affect the asymptotic accuracy of the test. Our approach demonstrates strong empirical performance in scenarios with high-dimensional covariates and response variable, can handle multivariate responses, and maintains nontrivial power against local alternatives outside an $n^{-1/2}$ neighborhood of the null hypothesis. We also use numerical simulations and real-world imaging data applications to highlight the efficacy and versatility of our testing procedure.

翻译：条件均值独立性（CMI）检验对于模型确定和变量重要性评估等统计任务至关重要。本文提出了一种新颖的总体CMI度量方法，以及一种基于自助法的检验流程，该流程利用深度生成神经网络来估计总体度量中涉及的均值函数。检验统计量的构建经过精心设计，以确保即使是非参数估计误差缓慢衰减，也不会影响检验的渐近准确性。我们的方法在高维协变量和响应变量的场景中表现出强大的实证性能，能够处理多变量响应，并且对零假设$n^{-1/2}$邻域外的局部备择假设保持非平凡功效。我们还通过数值模拟和真实世界成像数据应用，展示了该检验流程的有效性和多功能性。