# A Discovery Algorithm for Directed Cyclic Graphs

arXiv: https://arxiv.org/abs/1302.3599 · HTML: https://mlsanity.com/paper/1302.3599/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2013.

## Built on by (most cited first, 30 of 34)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning](https://mlsanity.com/paper/2301.01849/) (2023)
- [Recursive Causal Discovery](https://mlsanity.com/paper/2403.09300/) (2024)
- [A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models](https://mlsanity.com/paper/2205.10083/) (2022)
- [Learning Relational Causal Models with Cycles through Relational Acyclification](https://mlsanity.com/paper/2208.12210/) (2022)
- [Establishing Markov Equivalence in Cyclic Directed Graphs](https://mlsanity.com/paper/2309.03092/) (2023)
- [Scalable and Flexible Causal Discovery with an Efficient Test for Adjacency](https://mlsanity.com/paper/2406.09177/) (2024)
- [Are Bayesian networks typically faithful?](https://mlsanity.com/paper/2410.16004/) (2024)
- [Permutation-Based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Data](https://mlsanity.com/paper/2501.18990/) (2025)
- [Relational Causal Models with Cycles:Representation and Reasoning](https://mlsanity.com/paper/2202.10706/) (2022)
- [Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data](https://mlsanity.com/paper/2310.20537/) (2023)
- [Differentiable Cyclic Causal Discovery Under Unmeasured Confounders](https://mlsanity.com/paper/2508.08450/) (2025)
- [Near-Optimal Experiment Design in Linear non-Gaussian Cyclic Models](https://mlsanity.com/paper/2509.21423/) (2025)
- [Root Cause Analysis of Outliers in Unknown Cyclic Graphs](https://mlsanity.com/paper/2510.06995/) (2025)
- [CausalVerse: Benchmarking Causal Representation Learning with Configurable High-Fidelity Simulations](https://mlsanity.com/paper/2510.14049/) (2025)
- [Fast Parallel Bayesian Network Structure Learning](https://mlsanity.com/paper/2212.04259/) (2022)
- [Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies](https://mlsanity.com/paper/2312.16815/) (2023)
- [Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles](https://mlsanity.com/paper/2507.10767/) (2025)
- [Causal Structure and Representation Learning with Biomedical Applications](https://mlsanity.com/paper/2511.04790/) (2025)
- [Comparative Study of Causal Discovery Methods for Cyclic Models with Hidden Confounders](https://mlsanity.com/paper/2401.13009/) (2024)
- [Learning Cyclic Causal Models from Incomplete Data](https://mlsanity.com/paper/2402.15625/) (2024)
- [MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Data](https://mlsanity.com/paper/2410.18918/) (2024)
- [Causal SHAP: Feature Attribution with Dependency Awareness through Causal Discovery](https://mlsanity.com/paper/2509.00846/) (2025)
- [On the Number of Conditional Independence Tests in Constraint-based Causal Discovery](https://mlsanity.com/paper/2603.21844/) (2026)
- [Identifiability of AMP chain graph models](https://mlsanity.com/paper/2106.09350/) (2021)
- [Causal Discovery for fMRI data: Challenges, Solutions, and a Case Study](https://mlsanity.com/paper/2312.12678/) (2023)
- [Dynamic causal discovery in Alzheimer's disease through latent pseudotime modelling](https://mlsanity.com/paper/2511.04619/) (2025)
- [RECLAIM: Cyclic Causal Discovery Amid Measurement Noise](https://mlsanity.com/paper/2603.20585/) (2026)

## Abstract (arXiv)

Directed acyclic graphs have been used fruitfully to represent causal strucures (Pearl 1988). However, in the social sciences and elsewhere models are often used which correspond both causally and statistically to directed graphs with directed cycles (Spirtes 1995). Pearl (1993) discussed predicting the effects of intervention in models of this kind, so-called linear non-recursive structural equation models. This raises the question of whether it is possible to make inferences about causal structure with cycles, form sample data. In particular do there exist general, informative, feasible and reliable precedures for inferring causal structure from conditional independence relations among variables in a sample generated by an unknown causal structure? In this paper I present a discovery algorithm that is correct in the large sample limit, given commonly (but often implicitly) made plausible assumptions, and which provides information about the existence or non-existence of causal pathways from one variable to another. The algorithm is polynomial on sparse graphs.