# Ordering-Based Causal Structure Learning in the Presence of Latent Variables

arXiv: https://arxiv.org/abs/1910.09014 · HTML: https://mlsanity.com/paper/1910.09014/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2019.

## Built on by (most cited first, 26 of 26)

- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Ordering-Based Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/2105.06631/) (2021)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [Computably Continuous Reinforcement-Learning Objectives are PAC-learnable](https://mlsanity.com/paper/2303.05518/) (2023)
- [Recursive Causal Discovery](https://mlsanity.com/paper/2403.09300/) (2024)
- [Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variables](https://mlsanity.com/paper/2208.06935/) (2022)
- [Constraint-Free Structure Learning with Smooth Acyclic Orientations](https://mlsanity.com/paper/2309.08406/) (2023)
- [Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding](https://mlsanity.com/paper/2103.15106/) (2021)
- [Expert-Aided Causal Discovery of Ancestral Graphs](https://mlsanity.com/paper/2309.12032/) (2023)
- [Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)](https://mlsanity.com/paper/2406.10537/) (2024)
- [The Impact of Variable Ordering on Bayesian Network Structure Learning](https://mlsanity.com/paper/2206.08952/) (2022)
- [Causal Homotopy](https://mlsanity.com/paper/2112.01847/) (2021)
- [Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variables](https://mlsanity.com/paper/2107.07087/) (2021)
- [CMVAE: Causal Meta VAE for Unsupervised Meta-Learning](https://mlsanity.com/paper/2302.09731/) (2023)
- [s-ID: Causal Effect Identification in a Sub-Population](https://mlsanity.com/paper/2309.02281/) (2023)
- [Score-Based Causal Discovery of Latent Variable Causal Models](https://mlsanity.com/paper/2605.20396/) (2026)
- [Score-informed Neural Operator for Enhancing Ordering-based Causal Discovery](https://mlsanity.com/paper/2508.12650/) (2025)
- [DAG DECORation: Continuous Optimization for Structure Learning under Hidden Confounding](https://mlsanity.com/paper/2510.02117/) (2025)
- [Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Models](https://mlsanity.com/paper/2510.04378/) (2025)
- [Improving Accuracy of Permutation DAG Search using Best Order Score Search](https://mlsanity.com/paper/2108.10141/) (2021)
- [A Review and Roadmap of Deep Causal Model from Different Causal Structures and Representations](https://mlsanity.com/paper/2311.00923/) (2023)
- [QWO: Speeding Up Permutation-Based Causal Discovery in LiGAMs](https://mlsanity.com/paper/2410.23155/) (2024)
- [Identification of Latent Variables From Graphical Model Residuals](https://mlsanity.com/paper/2101.02332/) (2021)
- [Reinforcement Causal Structure Learning on Order Graph](https://mlsanity.com/paper/2211.12151/) (2022)
- [Machine Learning and Data Analysis Using Posets: A Survey](https://mlsanity.com/paper/2404.03082/) (2024)

## Abstract (arXiv)

We consider the task of learning a causal graph in the presence of latent confounders given i.i.d.~samples from the model. While current algorithms for causal structure discovery in the presence of latent confounders are constraint-based, we here propose a score-based approach. We prove that under assumptions weaker than faithfulness, any sparsest independence map (IMAP) of the distribution belongs to the Markov equivalence class of the true model. This motivates the Sparsest Poset formulation - that posets can be mapped to minimal IMAPs of the true model such that the sparsest of these IMAPs is Markov equivalent to the true model. Motivated by this result, we propose a greedy algorithm over the space of posets for causal structure discovery in the presence of latent confounders and compare its performance to the current state-of-the-art algorithms FCI and FCI+ on synthetic data.