# Conditional Independence Tests for Constraint-Based Causal Discovery: A Survey

arXiv: https://arxiv.org/abs/2608.11156 · HTML: https://mlsanity.com/paper/2608.11156/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 118 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 29 of 29)

- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [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)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [gCastle: A Python Toolbox for Causal Discovery](https://mlsanity.com/paper/2111.15155/) (2021)
- [A fast PC algorithm for high dimensional causal discovery with multi-core PCs](https://mlsanity.com/paper/1502.02454/) (2015)
- [Multi-Agent Causal Discovery Using Large Language Models](https://mlsanity.com/paper/2407.15073/) (2024)
- [pgmpy: A Python Toolkit for Bayesian Networks](https://mlsanity.com/paper/2304.08639/) (2023)
- [The Weighted Generalised Covariance Measure](https://mlsanity.com/paper/2111.04361/) (2021)
- [A hybrid algorithm for Bayesian network structure learning with application to multi-label learning](https://mlsanity.com/paper/1506.05692/) (2015)
- [cuPC: CUDA-based Parallel PC Algorithm for Causal Structure Learning on GPU](https://mlsanity.com/paper/1812.08491/) (2018)
- [Feature Selection with the R Package MXM: Discovering Statistically-Equivalent Feature Subsets](https://mlsanity.com/paper/1611.03227/) (2016)
- [Conditional Diffusion Models Based Conditional Independence Testing](https://mlsanity.com/paper/2412.11744/) (2024)
- [Estimating and Controlling the False Discovery Rate for the PC Algorithm Using Edge-Specific P-Values](https://mlsanity.com/paper/1607.03975/) (2016)
- [Learning Discrete Bayesian Networks from Continuous Data](https://mlsanity.com/paper/1512.02406/) (2015)
- [Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discovery](https://mlsanity.com/paper/2306.11498/) (2023)
- [Directed Acyclic Graphs and causal thinking in clinical risk prediction modeling](https://mlsanity.com/paper/2002.09414/) (2020)
- [Permutation-Based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Data](https://mlsanity.com/paper/2501.18990/) (2025)
- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [A Conditional Independence Test in the Presence of Discretization](https://mlsanity.com/paper/2404.17644/) (2024)
- [Mixed Graphical Models for Causal Analysis of Multi-modal Variables](https://mlsanity.com/paper/1704.02621/) (2017)
- [Non-parametric Conditional Independence Testing for Mixed Continuous-Categorical Variables: A Novel Method and Numerical Evaluation](https://mlsanity.com/paper/2310.11132/) (2023)

## Abstract (arXiv)

Conditional Independence (CI) tests are the statistical engine of constraint-based causal discovery: in algorithms such as PC (Peter-Clark) and FCI (Fast Causal Inference), skeleton pruning and key orientations follow directly from CI decisions. This survey reviews CI testing with emphasis on assumptions, robustness, and scalability in high-dimensional and mixed-type settings common in biomedical domains. The survey organizes widely used CI methods into six families: partial-correlation, contingency-table, regression, nearest-neighbor, kernel, and machine-learning-based. Special emphasis is provided on the robustness layers that address the limitations of these families. For each family, the survey examines when CI decisions reflect the data-generating distribution and when they fail. By this, we link test-level properties, including power decay with conditioning set size and asymmetric type I/II error consequences, to graph-level errors in skeleton recovery and v-structure orientation. The survey also compares adoption across major R and Python libraries and summarizes open challenges, including mixed-type CI testing without discretization, small-sample error control, and strategies for improving scalability of CI-testing.