# Iterative Causal Discovery in the Possible Presence of Latent Confounders and Selection Bias

arXiv: https://arxiv.org/abs/2111.04095 · HTML: https://mlsanity.com/paper/2111.04095/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 20 references that are in the map.
- First posted on arXiv 7 Nov 2021.

## Builds on (most cited first, 5 of 5)

- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Learning Sparse Causal Models is not NP-hard](https://mlsanity.com/paper/1309.6824/) (2013)
- [Causal Identification under Markov Equivalence](https://mlsanity.com/paper/1812.06209/) (2018)
- [Bayesian Structure Learning by Recursive Bootstrap](https://mlsanity.com/paper/1809.04828/) (2018)
- [Improving Efficiency and Accuracy of Causal Discovery Using a Hierarchical Wrapper](https://mlsanity.com/paper/2107.05001/) (2021)

## Built on by (most cited first, 21 of 21)

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Causal Interpretation of Self-Attention in Pre-Trained Transformers](https://mlsanity.com/paper/2310.20307/) (2023)
- [From Temporal to Contemporaneous Iterative Causal Discovery in the Presence of Latent Confounders](https://mlsanity.com/paper/2306.00624/) (2023)
- [Gene Regulatory Network Inference in the Presence of Selection Bias and Latent Confounders](https://mlsanity.com/paper/2501.10124/) (2025)
- [A Survey of Methods, Challenges and Perspectives in Causality](https://mlsanity.com/paper/2302.00293/) (2023)
- [Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)](https://mlsanity.com/paper/2406.10537/) (2024)
- [A Causal World Model Underlying Next Token Prediction: Exploring GPT in a Controlled Environment](https://mlsanity.com/paper/2412.07446/) (2024)
- [An Explainable AI Approach to Large Language Model Assisted Causal Model Auditing and Development](https://mlsanity.com/paper/2312.16211/) (2023)
- [Causal Climate Emulation with Bayesian Filtering](https://mlsanity.com/paper/2506.09891/) (2025)
- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [CLEAR: Causal Explanations from Attention in Neural Recommenders](https://mlsanity.com/paper/2210.10621/) (2022)
- [On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models](https://mlsanity.com/paper/2502.08531/) (2025)
- [GT-CausIn: a novel causal-based insight for traffic prediction](https://mlsanity.com/paper/2212.05782/) (2022)
- [Interpretability and causal discovery of the machine learning models to predict the production of CBM wells after hydraulic fracturing](https://mlsanity.com/paper/2212.10718/) (2022)
- [Characterization and Learning of Causal Graphs with Latent Confounders and Post-treatment Selection from Interventional Data](https://mlsanity.com/paper/2509.25800/) (2025)
- [Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Models](https://mlsanity.com/paper/2510.04378/) (2025)
- [Recovering Linear Causal Models with Latent Variables via Cholesky Factorization of Covariance Matrix](https://mlsanity.com/paper/2311.00674/) (2023)
- [Demystifying the Physics of Deep Reinforcement Learning-Based Autonomous Vehicle Decision-Making](https://mlsanity.com/paper/2403.11432/) (2024)
- [Efficient Differentiable Causal Discovery via Reliable Super-Structure Learning](https://mlsanity.com/paper/2601.05474/) (2026)
- [A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2605.10651/) (2026)
- [CausalSteward: An Agentic Divide-Conquer-Combine Copilot for Causal Discovery](https://mlsanity.com/paper/2607.01936/) (2026)

## Abstract (arXiv)

We present a sound and complete algorithm, called iterative causal discovery (ICD), for recovering causal graphs in the presence of latent confounders and selection bias. ICD relies on the causal Markov and faithfulness assumptions and recovers the equivalence class of the underlying causal graph. It starts with a complete graph, and consists of a single iterative stage that gradually refines this graph by identifying conditional independence (CI) between connected nodes. Independence and causal relations entailed after any iteration are correct, rendering ICD anytime. Essentially, we tie the size of the CI conditioning set to its distance on the graph from the tested nodes, and increase this value in the successive iteration. Thus, each iteration refines a graph that was recovered by previous iterations having smaller conditioning sets -- a higher statistical power -- which contributes to stability. We demonstrate empirically that ICD requires significantly fewer CI tests and learns more accurate causal graphs compared to FCI, FCI+, and RFCI algorithms (code is available at https://github.com/IntelLabs/causality-lab).