用生成神经网络测试条件均值独立性，高效处理高维数据。
Testing Conditional Mean Independence Using Generative Neural Networks
- 用生成网络估计条件均值函数，构建稳健检验统计量。
- 在高维和多维响应下仍保持检验功效，对局部替代有检测力。
- 适合变量重要性评估与模型选择，适用于复杂真实数据。
条件均值独立性（CMI）检验在模型确定和变量重要性评估等统计任务中至关重要。本文提出一种新的总体CMI度量及基于自助法的检验方法，利用深度生成神经网络估计总体度量中的条件均值函数。检验统计量设计精巧，即使非参数估计误差缓慢衰减，也不影响检验的渐近准确性。该方法在高维协变量和响应变量场景下表现出色，可处理多维响应，并对超出n^{-1/2}邻域的局部替代保持非平凡功效。通过数值模拟和真实影像数据应用，验证了方法的有效性与通用性。
原文摘要 · Abstract (English)
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.
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