# Wasserstein Conditional Independence Testing

arXiv: https://arxiv.org/abs/2107.14184 · HTML: https://mlsanity.com/paper/2107.14184/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2021.

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

- [An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings](https://mlsanity.com/paper/2110.14868/) (2021)
- [Conditional Independence Testing via Latent Representation Learning](https://mlsanity.com/paper/2209.01547/) (2022)
- [Causal Discovery via Conditional Independence Testing with Proxy Variables](https://mlsanity.com/paper/2305.05281/) (2023)
- [A Geometric Approach to Optimal Experimental Design](https://mlsanity.com/paper/2510.14848/) (2025)
- [Score-based Generative Modeling for Conditional Independence Testing](https://mlsanity.com/paper/2505.23309/) (2025)
- [The Blessings of Multiple Treatments and Outcomes in Treatment Effect Estimation](https://mlsanity.com/paper/2309.17283/) (2023)
- [Amortized Conditional Independence Testing](https://mlsanity.com/paper/2502.20925/) (2025)

## Abstract (arXiv)

We introduce a test for the conditional independence of random variables X and Y given a random variable Z, specifically by sampling from the joint distribution (X,Y,Z), binning the support of the distribution of Z, and conducting multiple p-Wasserstein two-sample tests. Under a p-Wasserstein Lipschitz assumption on the conditional distributions LX|Z, LY|Z, and L(X,Y)|Z, we show that it is possible to control the Type I and Type II error of this test, and give examples of explicit finite-sample error bounds in the case where the distribution of Z has compact support.