题目：Testing conditional independence via generative neural networks

主讲人：圣路易斯华盛顿大学 邵晓峰教授

主持人：西南财经大学统计与数据科学学院 常晋源教授

时间：2025年06月20日（周五）上午09:00-11:45

地点：西南财经大学光华校区光华楼1003会议室

报告摘要：

In this talk, I will present some recent work on the problem of testing the conditional independence of two generic random vectors X and Y given a third random vector Z, which plays an important role in statistical and machine learning applications. We propose a new non-parametric testing procedure that avoids explicitly estimating any conditional distributions but instead requires sampling from the two marginal conditional distributions of X given Z and Y given Z. We further propose using a generative neural network (GNN) framework to sample from these approximated marginal conditional distributions, which tends to mitigate the curse of dimensionality due to its adaptivity to any low-dimensional structures and smoothness underlying the data. Theoretically, our test statistic is shown to enjoy a double robustness property against GNN approximation errors, meaning that the test statistic retains all desirable properties of the oracle test statistic utilizing the true marginal conditional distributions, as long as the product of the two approximation errors decays to zero faster than the parametric rate. Asymptotic properties of our statistic and the consistency of a bootstrap procedure are derived under both null and local alternatives. Extensive numerical experiments and real data analysis illustrate the effectiveness and broad applicability of our proposed test. An extension to test the conditional mean independence will also be presented.

主讲人简介：

Xiaofeng Shao received his PhD in Statistics from the University of Chicago in 200. He is currently Professor of Statistics and Data Science at Washington University in St. Louis. His current research interests include time series analysis, change-point analysis, functional data analysis, high dimensional data analysis and their applications. He is a fellow of Institute of Mathematical Statistics (IMS) and American Statistical Association (ASA). He currently serves as an associate editor for Journal of Royal Statistical Society, Series B and Journal of Time Series Analysis.