# Causal Discovery via Conditional Independence Testing with Proxy Variables

arXiv: https://arxiv.org/abs/2305.05281 · HTML: https://mlsanity.com/paper/2305.05281/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 62 references that are in the map.
- First posted on arXiv 9 May 2023.

## Builds on (most cited first, 19 of 19)

- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [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)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [CCMI : Classifier based Conditional Mutual Information Estimation](https://mlsanity.com/paper/1906.01824/) (2019)
- [Causal Inference via Kernel Deviance Measures](https://mlsanity.com/paper/1804.04622/) (2018)
- [Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference](https://mlsanity.com/paper/2104.02929/) (2021)
- [Optimal transport for causal discovery](https://mlsanity.com/paper/2201.09366/) (2022)
- [Identifying effects of multiple treatments in the presence of unmeasured confounding](https://mlsanity.com/paper/2011.04504/) (2020)
- [Proximal mediation analysis](https://mlsanity.com/paper/2109.11904/) (2021)
- [Causal Inference and Mechanism Clustering of A Mixture of Additive Noise Models](https://mlsanity.com/paper/1809.08568/) (2018)
- [Wasserstein Conditional Independence Testing](https://mlsanity.com/paper/2107.14184/) (2021)
- [Nonparametric Conditional Local Independence Testing](https://mlsanity.com/paper/2203.13559/) (2022)
- [Partial Identification of Causal Effects Using Proxy Variables](https://mlsanity.com/paper/2304.04374/) (2023)
- [Many Proxy Controls](https://mlsanity.com/paper/2110.03973/) (2021)
- [Causal Discovery Using Proxy Variables](https://mlsanity.com/paper/1702.07306/) (2017)
- [Estimation of Bivariate Structural Causal Models by Variational Gaussian Process Regression Under Likelihoods Parametrised by Normalising Flows](https://mlsanity.com/paper/2109.02521/) (2021)

## Built on by (most cited first, 3 of 3)

- [The Blessings of Multiple Treatments and Outcomes in Treatment Effect Estimation](https://mlsanity.com/paper/2309.17283/) (2023)
- [When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discovery](https://mlsanity.com/paper/2506.23374/) (2025)
- [Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independence](https://mlsanity.com/paper/2604.07191/) (2026)

## Abstract (arXiv)

Distinguishing causal connections from correlations is important in many scenarios. However, the presence of unobserved variables, such as the latent confounder, can introduce bias in conditional independence testing commonly employed in constraint-based causal discovery for identifying causal relations. To address this issue, existing methods introduced proxy variables to adjust for the bias caused by unobserveness. However, these methods were either limited to categorical variables or relied on strong parametric assumptions for identification. In this paper, we propose a novel hypothesis-testing procedure that can effectively examine the existence of the causal relationship over continuous variables, without any parametric constraint. Our procedure is based on discretization, which under completeness conditions, is able to asymptotically establish a linear equation whose coefficient vector is identifiable under the causal null hypothesis. Based on this, we introduce our test statistic and demonstrate its asymptotic level and power. We validate the effectiveness of our procedure using both synthetic and real-world data.