Testing Conditional Mean Independence Using Generative Neural Networks
This work addresses a crucial statistical problem for model determination and variable importance evaluation, offering a versatile testing method with incremental improvements in handling high-dimensional and multivariate scenarios.
The paper tackles conditional mean independence testing by introducing a novel population measure and a bootstrap-based procedure using deep generative neural networks to estimate conditional mean functions, achieving strong empirical performance with high-dimensional covariates and responses, nontrivial power against local alternatives, and validation through simulations and real-world imaging data.
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.