Doubly robust conditional independence testing with generative neural networks

Yi Zhang, Linjun Huang, Yun Yang, Xiaofeng Shao

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2026 · Volume 88 · Issue 1

Abstract

This article addresses the problem of testing the conditional independence of two generic random vectorsXandYgiven a third random vectorZ, 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 ofXgivenZandYgivenZ. 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.

Keywords

conditional distribution, double robustness, generative models, Kernel method, maximum mean discrepancy

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