# Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders

arXiv: https://arxiv.org/abs/1807.03024 · HTML: https://mlsanity.com/paper/1807.03024/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2018.

## Built on by (most cited first, 30 of 35)

- [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)
- [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)
- [Discovering Agents](https://mlsanity.com/paper/2208.08345/) (2022)
- [Passive learning of active causal strategies in agents and language models](https://mlsanity.com/paper/2305.16183/) (2023)
- [Obtaining Causal Information by Merging Datasets with MAXENT](https://mlsanity.com/paper/2107.07640/) (2021)
- [Identifying Macro Conditional Independencies and Macro Total Effects in Summary Causal Graphs with Latent Confounding](https://mlsanity.com/paper/2407.07934/) (2024)
- [A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models](https://mlsanity.com/paper/2205.10083/) (2022)
- [Intervention Generalization: A View from Factor Graph Models](https://mlsanity.com/paper/2306.04027/) (2023)
- [Simulations in Recommender Systems: An industry perspective](https://mlsanity.com/paper/2109.06723/) (2021)
- [A Survey of Methods, Challenges and Perspectives in Causality](https://mlsanity.com/paper/2302.00293/) (2023)
- [Establishing Markov Equivalence in Cyclic Directed Graphs](https://mlsanity.com/paper/2309.03092/) (2023)
- [Causality and independence in perfectly adapted dynamical systems](https://mlsanity.com/paper/2101.11885/) (2021)
- [Identifying Macro Causal Effects in a C-DMG over ADMGs](https://mlsanity.com/paper/2504.01551/) (2025)
- [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)
- [Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies](https://mlsanity.com/paper/2312.16815/) (2023)
- [Identifying Macro Causal Effects in C-DMGs over DMGs](https://mlsanity.com/paper/2506.19650/) (2025)
- [An Asymmetric Independence Model for Causal Discovery on Path Spaces](https://mlsanity.com/paper/2503.09859/) (2025)
- [Coarsening Linear Non-Gaussian Causal Models with Cycles](https://mlsanity.com/paper/2605.10163/) (2026)
- [LLM Explainability with Counterfactual Chains and Causal Graphs](https://mlsanity.com/paper/2606.05972/) (2026)
- [Comparative Study of Causal Discovery Methods for Cyclic Models with Hidden Confounders](https://mlsanity.com/paper/2401.13009/) (2024)
- [Algorithmic Identification of Essential Exogenous Nodes for Causal Sufficiency in Brain Networks](https://mlsanity.com/paper/2403.05407/) (2024)
- [Efficient Counterfactual Reasoning in ProbLog via Single World Intervention Programs](https://mlsanity.com/paper/2603.20505/) (2026)
- [Language-Based Causal Representation Learning](https://mlsanity.com/paper/2207.05259/) (2022)
- [Causal identification with Y0](https://mlsanity.com/paper/2508.03167/) (2025)
- [Dynamic causal discovery in Alzheimer's disease through latent pseudotime modelling](https://mlsanity.com/paper/2511.04619/) (2025)
- [Partially Observed Structural Causal Models](https://mlsanity.com/paper/2605.03268/) (2026)

## Abstract (arXiv)

We address the problem of causal discovery from data, making use of the recently proposed causal modeling framework of modular structural causal models (mSCM) to handle cycles, latent confounders and non-linearities. We introduce σ-connection graphs (σ-CG), a new class of mixed graphs (containing undirected, bidirected and directed edges) with additional structure, and extend the concept of σ-separation, the appropriate generalization of the well-known notion of d-separation in this setting, to apply to σ-CGs. We prove the closedness of σ-separation under marginalisation and conditioning and exploit this to implement a test of σ-separation on a σ-CG. This then leads us to the first causal discovery algorithm that can handle non-linear functional relations, latent confounders, cyclic causal relationships, and data from different (stochastic) perfect interventions. As a proof of concept, we show on synthetic data how well the algorithm recovers features of the causal graph of modular structural causal models.