# Discovering Cyclic Causal Models with Latent Variables: A General SAT-Based Procedure

arXiv: https://arxiv.org/abs/1309.6836 · HTML: https://mlsanity.com/paper/1309.6836/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2013.

## Built on by (most cited first, 18 of 18)

- [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)
- [Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions](https://mlsanity.com/paper/2201.05666/) (2022)
- [Deep Causal Learning: Representation, Discovery and Inference](https://mlsanity.com/paper/2211.03374/) (2022)
- [When Selection Meets Intervention: Additional Complexities in Causal Discovery](https://mlsanity.com/paper/2503.07302/) (2025)
- [Obtaining Causal Information by Merging Datasets with MAXENT](https://mlsanity.com/paper/2107.07640/) (2021)
- [Learning MAX-SAT from Contextual Examples for Combinatorial Optimisation](https://mlsanity.com/paper/2202.03888/) (2022)
- [Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning](https://mlsanity.com/paper/2405.04715/) (2024)
- [Gene Regulatory Network Inference in the Presence of Selection Bias and Latent Confounders](https://mlsanity.com/paper/2501.10124/) (2025)
- [Visual Analysis of Multi-outcome Causal Graphs](https://mlsanity.com/paper/2408.02679/) (2024)
- [Realizing LLMs' Causal Potential Requires Science-Grounded, Novel Benchmarks](https://mlsanity.com/paper/2510.16530/) (2025)
- [Universal Lower Bound for Learning Causal DAGs with Atomic Interventions](https://mlsanity.com/paper/2111.05070/) (2021)
- [GRACE-C: Generalized Rate Agnostic Causal Estimation via Constraints](https://mlsanity.com/paper/2205.09235/) (2022)
- [Enabling Runtime Verification of Causal Discovery Algorithms with Automated Conditional Independence Reasoning (Extended Version)](https://mlsanity.com/paper/2309.05264/) (2023)
- [Characterization and Learning of Causal Graphs with Latent Confounders and Post-treatment Selection from Interventional Data](https://mlsanity.com/paper/2509.25800/) (2025)
- [Dynamic Expert-Guided Model Averaging for Causal Discovery](https://mlsanity.com/paper/2601.16715/) (2026)
- [Graph Structure Inference with BAM: Introducing the Bilinear Attention Mechanism](https://mlsanity.com/paper/2402.07735/) (2024)
- [ION-C: Integration of Overlapping Networks via Constraints](https://mlsanity.com/paper/2411.04243/) (2024)

## Abstract (arXiv)

We present a very general approach to learning the structure of causal models based on d-separation constraints, obtained from any given set of overlapping passive observational or experimental data sets. The procedure allows for both directed cycles (feedback loops) and the presence of latent variables. Our approach is based on a logical representation of causal pathways, which permits the integration of quite general background knowledge, and inference is performed using a Boolean satisfiability (SAT) solver. The procedure is complete in that it exhausts the available information on whether any given edge can be determined to be present or absent, and returns "unknown" otherwise. Many existing constraint-based causal discovery algorithms can be seen as special cases, tailored to circumstances in which one or more restricting assumptions apply. Simulations illustrate the effect of these assumptions on discovery and how the present algorithm scales.