Doubly Robust Conditional Independence Testing with Generative Neural Networks

TL;DR

This paper introduces a new non-parametric conditional independence test using generative neural networks, which efficiently samples from conditional distributions without explicit estimation, and is robust to approximation errors.

Contribution

It proposes a novel GNN-based sampling method for conditional independence testing that is doubly robust to approximation errors and applicable in high-dimensional settings.

Findings

The test maintains validity despite GNN approximation errors.

It demonstrates superior performance in simulations and real data.

The method is computationally efficient and broadly applicable.

Abstract

This article addresses 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 doubly robust 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.