Testing Conditional Mean Independence Using Generative Neural Networks
Journal:
arXiv
Published Date:
Jan 28, 2025
Abstract
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.
