# Double Generative Adversarial Networks for Conditional Independence Testing

arXiv: https://arxiv.org/abs/2006.02615 · HTML: https://mlsanity.com/paper/2006.02615/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2020.

## Built on by (most cited first, 22 of 22)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Towards Robust and Adaptive Motion Forecasting: A Causal Representation Perspective](https://mlsanity.com/paper/2111.14820/) (2021)
- [Model-X Sequential Testing for Conditional Independence via Testing by Betting](https://mlsanity.com/paper/2210.00354/) (2022)
- [An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings](https://mlsanity.com/paper/2110.14868/) (2021)
- [Doubly Robust Alignment for Large Language Models](https://mlsanity.com/paper/2506.01183/) (2025)
- [Diffeomorphic Information Neural Estimation](https://mlsanity.com/paper/2211.10856/) (2022)
- [Conditional Independence Testing via Latent Representation Learning](https://mlsanity.com/paper/2209.01547/) (2022)
- [Conditional independence testing under misspecified inductive biases](https://mlsanity.com/paper/2307.02520/) (2023)
- [Doubly Robust Conditional Independence Testing with Generative Neural Networks](https://mlsanity.com/paper/2407.17694/) (2024)
- [Nearest-Neighbor Sampling Based Conditional Independence Testing](https://mlsanity.com/paper/2304.04183/) (2023)
- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [Testing Directed Acyclic Graph via Structural, Supervised and Generative Adversarial Learning](https://mlsanity.com/paper/2106.01474/) (2021)
- [A Free Lunch with Influence Functions? Improving Neural Network Estimates with Concepts from Semiparametric Statistics](https://mlsanity.com/paper/2202.09096/) (2022)
- [Deep Nonparametric Conditional Independence Tests for Images](https://mlsanity.com/paper/2411.06140/) (2024)
- [Statistical Inference in Reinforcement Learning: A Selective Survey](https://mlsanity.com/paper/2502.16195/) (2025)
- [From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Maps](https://mlsanity.com/paper/2504.09567/) (2025)
- [Score-based Generative Modeling for Conditional Independence Testing](https://mlsanity.com/paper/2505.23309/) (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)
- [DNA-SE: Towards Deep Neural-Nets Assisted Semiparametric Estimation](https://mlsanity.com/paper/2408.02045/) (2024)
- [Fast Flow Matching based Conditional Independence Tests for Causal Discovery](https://mlsanity.com/paper/2602.08315/) (2026)
- [Testing Conditional Distribution Equality Using Generative Models](https://mlsanity.com/paper/2610.20447/) (2026)

## Abstract (arXiv)

In this article, we study the problem of high-dimensional conditional independence testing, a key building block in statistics and machine learning. We propose an inferential procedure based on double generative adversarial networks (GANs). Specifically, we first introduce a double GANs framework to learn two generators of the conditional distributions. We then integrate the two generators to construct a test statistic, which takes the form of the maximum of generalized covariance measures of multiple transformation functions. We also employ data-splitting and cross-fitting to minimize the conditions on the generators to achieve the desired asymptotic properties, and employ multiplier bootstrap to obtain the corresponding p-value. We show that the constructed test statistic is doubly robust, and the resulting test both controls type-I error and has the power approaching one asymptotically. Also notably, we establish those theoretical guarantees under much weaker and practically more feasible conditions compared to the existing tests, and our proposal gives a concrete example of how to utilize some state-of-the-art deep learning tools, such as GANs, to help address a classical but challenging statistical problem. We demonstrate the efficacy of our test through both simulations and an application to an anti-cancer drug dataset. A Python implementation of the proposed procedure is available at https://github.com/tianlinxu312/dgcit.