# Efficient Ensemble Conditional Independence Test Framework for Causal Discovery

arXiv: https://arxiv.org/abs/2509.21021 · HTML: https://mlsanity.com/paper/2509.21021/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 57 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Builds on (most cited first, 30 of 31)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/1906.04477/) (2019)
- [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)
- [Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/2110.12036/) (2021)
- [Local permutation tests for conditional independence](https://mlsanity.com/paper/2112.11666/) (2021)
- [Double Generative Adversarial Networks for Conditional Independence Testing](https://mlsanity.com/paper/2006.02615/) (2020)
- [Cyclic Causal Discovery from Continuous Equilibrium Data](https://mlsanity.com/paper/1309.6849/) (2013)
- [A Recursive Markov Boundary-Based Approach to Causal Structure Learning](https://mlsanity.com/paper/2010.04992/) (2020)
- [Iterative Causal Discovery in the Possible Presence of Latent Confounders and Selection Bias](https://mlsanity.com/paper/2111.04095/) (2021)
- [Cauchy combination test: a powerful test with analytic p-value calculation under arbitrary dependency structures](https://mlsanity.com/paper/1808.09011/) (2018)
- [Choosing Between Methods of Combining p-values](https://mlsanity.com/paper/1707.06897/) (2017)
- [Practical Kernel Tests of Conditional Independence](https://mlsanity.com/paper/2402.13196/) (2024)
- [Causal Discovery with Fewer Conditional Independence Tests](https://mlsanity.com/paper/2406.01823/) (2024)
- [An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings](https://mlsanity.com/paper/2110.14868/) (2021)
- [Recursive Causal Discovery](https://mlsanity.com/paper/2403.09300/) (2024)
- [A Distribution Free Conditional Independence Test with Applications to Causal Discovery](https://mlsanity.com/paper/2105.07555/) (2021)
- [Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variables](https://mlsanity.com/paper/2208.06935/) (2022)
- [Nearest-Neighbor Sampling Based Conditional Independence Testing](https://mlsanity.com/paper/2304.04183/) (2023)
- [On sample complexity of conditional independence testing with Von Mises estimator with application to causal discovery](https://mlsanity.com/paper/2310.13553/) (2023)
- [The Cauchy Combination Test under Arbitrary Dependence Structures](https://mlsanity.com/paper/2107.06040/) (2021)
- [Ensemble methods for testing a global null](https://mlsanity.com/paper/2310.10407/) (2023)
- [A Fast Kernel-based Conditional Independence test with Application to Causal Discovery](https://mlsanity.com/paper/2505.11085/) (2025)
- [Stable combination tests](https://mlsanity.com/paper/2108.07876/) (2021)

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

- [DCD-PFN: A Decoupling-Aware Foundation Model for Causal Discovery](https://mlsanity.com/paper/2606.21212/) (2026)
- [Fast Flow Matching based Conditional Independence Tests for Causal Discovery](https://mlsanity.com/paper/2602.08315/) (2026)
- [Conditional Independence Tests for Constraint-Based Causal Discovery: A Survey](https://mlsanity.com/paper/2608.11156/) (2026)
- [Multi-Method Causal Evidence Synthesis: Ranking Candidate Drivers by Convergent Cross-Method Evidence from Observational Data](https://mlsanity.com/paper/2608.20187/) (2026)
- [Decoupled Causal Discovery](https://mlsanity.com/paper/2609.23535/) (2026)

## Abstract (arXiv)

Constraint-based causal discovery relies on numerous conditional independence tests (CITs), but its practical applicability is severely constrained by the prohibitive computational cost, especially as CITs themselves have high time complexity with respect to the sample size. To address this key bottleneck, we introduce the Ensemble Conditional Independence Test (E-CIT), a general-purpose and plug-and-play framework. E-CIT operates on an intuitive divide-and-aggregate strategy: it partitions the data into subsets, applies a given base CIT independently to each subset, and aggregates the resulting p-values using a novel method grounded in the properties of stable distributions. This framework reduces the computational complexity of a base CIT to linear in the sample size when the subset size is fixed. Moreover, our tailored p-value combination method offers theoretical consistency guarantees under mild conditions on the subtests. Experimental results demonstrate that E-CIT not only significantly reduces the computational burden of CITs and causal discovery but also achieves competitive performance. Notably, it exhibits an improvement in complex testing scenarios, particularly on real-world datasets.