# Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discovery

arXiv: https://arxiv.org/abs/2306.11498 · HTML: https://mlsanity.com/paper/2306.11498/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 35 references that are in the map.
- First posted on arXiv 20 Jun 2023.

## Builds on (most cited first, 4 of 4)

- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)

## Built on by (most cited first, 6 of 6)

- [Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises](https://mlsanity.com/paper/2506.17065/) (2025)
- [Test-Time Learning of Causal Structure from Interventional Data](https://mlsanity.com/paper/2602.19131/) (2026)
- [RINS-T: Robust Implicit Neural Solvers for Time Series Linear Inverse Problems](https://mlsanity.com/paper/2510.17396/) (2025)
- [Closing the Expression Gap in LLM Instructions via Socratic Questioning](https://mlsanity.com/paper/2510.27410/) (2025)
- [Conditional Independence Tests for Constraint-Based Causal Discovery: A Survey](https://mlsanity.com/paper/2608.11156/) (2026)
- [GFCM: A Tail-Sensitive Mixed-Type Conditional Independence Test for Causal Discovery](https://mlsanity.com/paper/2608.15332/) (2026)

## Abstract (arXiv)

Conditional independence (CI) testing is frequently used in data analysis and machine learning for various scientific fields and it forms the basis of constraint-based causal discovery. Oftentimes, CI testing relies on strong, rather unrealistic assumptions. One of these assumptions is homoskedasticity, in other words, a constant conditional variance is assumed. We frame heteroskedasticity in a structural causal model framework and present an adaptation of the partial correlation CI test that works well in the presence of heteroskedastic noise, given that expert knowledge about the heteroskedastic relationships is available. Further, we provide theoretical consistency results for the proposed CI test which carry over to causal discovery under certain assumptions. Numerical causal discovery experiments demonstrate that the adapted partial correlation CI test outperforms the standard test in the presence of heteroskedasticity and is on par for the homoskedastic case. Finally, we discuss the general challenges and limits as to how expert knowledge about heteroskedasticity can be accounted for in causal discovery.