Testing Conditional Mean Independence Using Generative Neural Networks

TL;DR

This paper introduces a new method for testing conditional mean independence using deep generative neural networks, providing accurate, high-dimensional, and multivariate analysis with strong empirical results.

Contribution

It proposes a novel population CMI measure and a bootstrap testing procedure leveraging deep generative neural networks for improved estimation and testing accuracy.

Findings

Strong empirical performance in high-dimensional settings

Effective handling of multivariate responses

Maintains power against local alternatives

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.