Testing Conditional Mean Independence Using Generative Neural Networks

2025-01-28

AI Summary

This paper addresses the challenge of conditional mean independence (CMI) testing in high-dimensional settings. Methodologically, it introduces a novel nonparametric testing framework featuring: (i) the first CMI measure robust to nonparametric estimation error—overcoming the conventional (n^{-1/2}) local-neighborhood limitation; (ii) precise modeling of the conditional mean function via generative neural networks; and (iii) a bootstrap-based test statistic accommodating multivariate responses and high-dimensional covariates. Theoretically, the test is proven to possess nontrivial local power under local alternatives. Empirical evaluations—including simulations and real neuroimaging data—demonstrate that the proposed method substantially outperforms existing CMI testers, maintaining both robustness and high statistical power in high dimensions. This advances reliable model interpretability and variable importance assessment.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Graphical Models

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Conditionally Mean Independence
• Model Evaluation
• Multivariate Data

Innovation

• Conditional Mean Independence
• Generative Neural Networks
• Complex Function Estimation