# Towards Complete Causal Explanation with Expert Knowledge

arXiv: https://arxiv.org/abs/2407.07338 · HTML: https://mlsanity.com/paper/2407.07338/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2024.

## Built on by (most cited first, 7 of 7)

- [When Selection Meets Intervention: Additional Complexities in Causal Discovery](https://mlsanity.com/paper/2503.07302/) (2025)
- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Constraint-based causal discovery with tiered background knowledge and latent variables in single or overlapping datasets](https://mlsanity.com/paper/2503.21526/) (2025)
- [New Rules for Causal Identification with Background Knowledge](https://mlsanity.com/paper/2407.15259/) (2024)
- [Complete Causal Identification from Ancestral Graphs under Selection Bias](https://mlsanity.com/paper/2603.26301/) (2026)
- [Retrieving Classes of Causal Orders with Inconsistent Knowledge Bases](https://mlsanity.com/paper/2412.14019/) (2024)
- [Integrating Background Knowledge for Scalable Causal Discovery](https://mlsanity.com/paper/2607.10456/) (2026)

## Abstract (arXiv)

We study the problem of restricting a Markov equivalence class of maximal ancestral graphs (MAGs) to only those MAGs that contain certain edge marks, which we refer to as expert or orientation knowledge. Such a restriction of the Markov equivalence class can be uniquely represented by a restricted essential ancestral graph. Our contributions are several-fold. First, we prove certain properties for the entire Markov equivalence class including a conjecture from Ali et al. (2009). Second, we present several new sound graphical orientation rules for adding orientation knowledge to an essential ancestral graph. We also show that some orientation rules of Zhang (2008b) are not needed for restricting the Markov equivalence class with orientation knowledge. Third, we provide an algorithm for including this orientation knowledge and show that in certain settings the output of our algorithm is a restricted essential ancestral graph. Finally, outside of the specified settings, we provide an algorithm for checking whether a graph is a restricted essential graph and discuss its runtime. This work can be seen as a generalization of Meek (1995) to settings which allow for latent confounding.