# A factorization criterion for acyclic directed mixed graphs

arXiv: https://arxiv.org/abs/1406.6764 · HTML: https://mlsanity.com/paper/1406.6764/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2014.

## Built on by (most cited first, 8 of 8)

- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [Causal Homotopy](https://mlsanity.com/paper/2112.01847/) (2021)
- [Differentiable Cyclic Causal Discovery Under Unmeasured Confounders](https://mlsanity.com/paper/2508.08450/) (2025)
- [Testing Causal Models with Hidden Variables in Polynomial Delay via Conditional Independencies](https://mlsanity.com/paper/2409.14593/) (2024)
- [ExMAG: Learning of Maximally Ancestral Graphs](https://mlsanity.com/paper/2503.08245/) (2025)
- [Graphical Models for Decision-Making: Integrating Causality and Game Theory](https://mlsanity.com/paper/2504.13210/) (2025)
- [Graph Distance Based on Cause-Effect Estimands with Latents](https://mlsanity.com/paper/2510.25037/) (2025)

## Abstract (arXiv)

Acyclic directed mixed graphs, also known as semi-Markov models represent the conditional independence structure induced on an observed margin by a DAG model with latent variables. In this paper we present a factorization criterion for these models that is equivalent to the global Markov property given by (the natural extension of) d-separation.