# Nearest-Neighbor Sampling Based Conditional Independence Testing

arXiv: https://arxiv.org/abs/2304.04183 · HTML: https://mlsanity.com/paper/2304.04183/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 9 Apr 2023.

## Builds on (most cited first, 13 of 13)

- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)
- [Model-Powered Conditional Independence Test](https://mlsanity.com/paper/1709.06138/) (2017)
- [CCMI : Classifier based Conditional Mutual Information Estimation](https://mlsanity.com/paper/1906.01824/) (2019)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [Double Generative Adversarial Networks for Conditional Independence Testing](https://mlsanity.com/paper/2006.02615/) (2020)
- [Demystifying Fixed k-Nearest Neighbor Information Estimators](https://mlsanity.com/paper/1604.03006/) (2016)
- [A Distribution Free Conditional Independence Test with Applications to Causal Discovery](https://mlsanity.com/paper/2105.07555/) (2021)
- [Breaking the Bandwidth Barrier: Geometrical Adaptive Entropy Estimation](https://mlsanity.com/paper/1609.02208/) (2016)

## Built on by (most cited first, 5 of 5)

- [Doubly Robust Conditional Independence Testing with Generative Neural Networks](https://mlsanity.com/paper/2407.17694/) (2024)
- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [Diffusion Models with Double Guidance: Generate with aggregated datasets](https://mlsanity.com/paper/2505.13213/) (2025)
- [Score-based Generative Modeling for Conditional Independence Testing](https://mlsanity.com/paper/2505.23309/) (2025)
- [Fast Flow Matching based Conditional Independence Tests for Causal Discovery](https://mlsanity.com/paper/2602.08315/) (2026)

## Abstract (arXiv)

The conditional randomization test (CRT) was recently proposed to test whether two random variables X and Y are conditionally independent given random variables Z. The CRT assumes that the conditional distribution of X given Z is known under the null hypothesis and then it is compared to the distribution of the observed samples of the original data. The aim of this paper is to develop a novel alternative of CRT by using nearest-neighbor sampling without assuming the exact form of the distribution of X given Z. Specifically, we utilize the computationally efficient 1-nearest-neighbor to approximate the conditional distribution that encodes the null hypothesis. Then, theoretically, we show that the distribution of the generated samples is very close to the true conditional distribution in terms of total variation distance. Furthermore, we take the classifier-based conditional mutual information estimator as our test statistic. The test statistic as an empirical fundamental information theoretic quantity is able to well capture the conditional-dependence feature. We show that our proposed test is computationally very fast, while controlling type I and II errors quite well. Finally, we demonstrate the efficiency of our proposed test in both synthetic and real data analyses.