# Doubly Robust Conditional Independence Testing with Generative Neural Networks

arXiv: https://arxiv.org/abs/2407.17694 · HTML: https://mlsanity.com/paper/2407.17694/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 66 references that are in the map.
- First posted on arXiv 25 Jul 2024.

## Builds on (most cited first, 29 of 29)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Battle of the Backbones: A Large-Scale Comparison of Pretrained Models across Computer Vision Tasks](https://mlsanity.com/paper/2310.19909/) (2023)
- [Optimal Rates for Regularized Conditional Mean Embedding Learning](https://mlsanity.com/paper/2208.01711/) (2022)
- [Model-Powered Conditional Independence Test](https://mlsanity.com/paper/1709.06138/) (2017)
- [Characteristic and Universal Tensor Product Kernels](https://mlsanity.com/paper/1708.08157/) (2017)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [Distribution Approximation and Statistical Estimation Guarantees of Generative Adversarial Networks](https://mlsanity.com/paper/2002.03938/) (2020)
- [Local permutation tests for conditional independence](https://mlsanity.com/paper/2112.11666/) (2021)
- [Double Generative Adversarial Networks for Conditional Independence Testing](https://mlsanity.com/paper/2006.02615/) (2020)
- [Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence](https://mlsanity.com/paper/2012.14804/) (2020)
- [Nonparametric Conditional Density Estimation in a High-Dimensional Regression Setting](https://mlsanity.com/paper/1604.00540/) (2016)
- [Efficient Conditionally Invariant Representation Learning](https://mlsanity.com/paper/2212.08645/) (2022)
- [Deep Dimension Reduction for Supervised Representation Learning](https://mlsanity.com/paper/2006.05865/) (2020)
- [Backbones-Review: Feature Extraction Networks for Deep Learning and Deep Reinforcement Learning Approaches](https://mlsanity.com/paper/2206.08016/) (2022)
- [Practical Kernel Tests of Conditional Independence](https://mlsanity.com/paper/2402.13196/) (2024)
- [Empirical comparison between autoencoders and traditional dimensionality reduction methods](https://mlsanity.com/paper/2103.04874/) (2021)
- [Effect of Depth and Width on Local Minima in Deep Learning](https://mlsanity.com/paper/1811.08150/) (2018)
- [An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings](https://mlsanity.com/paper/2110.14868/) (2021)
- [A Distribution Free Conditional Independence Test with Applications to Causal Discovery](https://mlsanity.com/paper/2105.07555/) (2021)
- [Testing for the Markov Property in Time Series via Deep Conditional Generative Learning](https://mlsanity.com/paper/2305.19244/) (2023)
- [FONDUE: an algorithm to find the optimal dimensionality of the latent representations of variational autoencoders](https://mlsanity.com/paper/2209.12806/) (2022)
- [Nearest-Neighbor Sampling Based Conditional Independence Testing](https://mlsanity.com/paper/2304.04183/) (2023)
- [Reconciling model-X and doubly robust approaches to conditional independence testing](https://mlsanity.com/paper/2211.14698/) (2022)
- [On genetic correlation estimation with summary statistics from genome-wide association studies](https://mlsanity.com/paper/1903.01301/) (2019)

## Built on by (most cited first, 7 of 7)

- [Doubly Robust Alignment for Large Language Models](https://mlsanity.com/paper/2506.01183/) (2025)
- [Statistical Inference in Reinforcement Learning: A Selective Survey](https://mlsanity.com/paper/2502.16195/) (2025)
- [A Conditional Distribution Equality Testing Framework using Deep Generative Learning](https://mlsanity.com/paper/2509.17729/) (2025)
- [Toward Scalable and Valid Conditional Independence Testing with Spectral Representations](https://mlsanity.com/paper/2512.19510/) (2025)
- [Empirically Calibrated Conditional Independence Tests](https://mlsanity.com/paper/2602.21036/) (2026)
- [Embedding-Bias in Conditional Independence Testing](https://mlsanity.com/paper/2610.11584/) (2026)
- [Testing Conditional Distribution Equality Using Generative Models](https://mlsanity.com/paper/2610.20447/) (2026)

## Abstract (arXiv)

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.