# A Constraint-Based Algorithm For Causal Discovery with Cycles, Latent Variables and Selection Bias

arXiv: https://arxiv.org/abs/1805.02087 · HTML: https://mlsanity.com/paper/1805.02087/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2018.

## Built on by (most cited first, 16 of 16)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/2110.12036/) (2021)
- [GFlowCausal: Generative Flow Networks for Causal Discovery](https://mlsanity.com/paper/2210.08185/) (2022)
- [Learning Relational Causal Models with Cycles through Relational Acyclification](https://mlsanity.com/paper/2208.12210/) (2022)
- [Sample-Specific Root Causal Inference with Latent Variables](https://mlsanity.com/paper/2210.15340/) (2022)
- [Establishing Markov Equivalence in Cyclic Directed Graphs](https://mlsanity.com/paper/2309.03092/) (2023)
- [Are Bayesian networks typically faithful?](https://mlsanity.com/paper/2410.16004/) (2024)
- [Causality and independence in perfectly adapted dynamical systems](https://mlsanity.com/paper/2101.11885/) (2021)
- [Relational Causal Models with Cycles:Representation and Reasoning](https://mlsanity.com/paper/2202.10706/) (2022)
- [Trying to Outrun Causality with Machine Learning: Limitations of Model Explainability Techniques for Identifying Predictive Variables](https://mlsanity.com/paper/2202.09875/) (2022)
- [Relational Causal Discovery with Latent Confounders](https://mlsanity.com/paper/2507.01700/) (2025)
- [Comparative Study of Causal Discovery Methods for Cyclic Models with Hidden Confounders](https://mlsanity.com/paper/2401.13009/) (2024)
- [σ-Maximal Ancestral Graphs](https://mlsanity.com/paper/2507.00093/) (2025)
- [Algorithmic Fairness Over Time: Advances & Prospects](https://mlsanity.com/paper/2610.15015/) (2026)

## Abstract (arXiv)

Causal processes in nature may contain cycles, and real datasets may violate causal sufficiency as well as contain selection bias. No constraint-based causal discovery algorithm can currently handle cycles, latent variables and selection bias (CLS) simultaneously. I therefore introduce an algorithm called Cyclic Causal Inference (CCI) that makes sound inferences with a conditional independence oracle under CLS, provided that we can represent the cyclic causal process as a non-recursive linear structural equation model with independent errors. Empirical results show that CCI outperforms CCD in the cyclic case as well as rivals FCI and RFCI in the acyclic case.