# Markovian acyclic directed mixed graphs for discrete data

arXiv: https://arxiv.org/abs/1301.6624 · HTML: https://mlsanity.com/paper/1301.6624/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2013.

## Built on by (most cited first, 10 of 10)

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- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [Incorporating Causal Graphical Prior Knowledge into Predictive Modeling via Simple Data Augmentation](https://mlsanity.com/paper/2103.00136/) (2021)
- [On Testability of the Front-Door Model via Verma Constraints](https://mlsanity.com/paper/2203.00161/) (2022)
- [CURE: Simulation-Augmented Auto-Tuning in Robotics](https://mlsanity.com/paper/2402.05399/) (2024)
- [Causal Razors](https://mlsanity.com/paper/2302.10331/) (2023)
- [Zero Inflation as a Missing Data Problem: a Proxy-based Approach](https://mlsanity.com/paper/2406.00549/) (2024)

## Abstract (arXiv)

Acyclic directed mixed graphs (ADMGs) are graphs that contain directed (rightarrow) and bidirected (leftrightarrow) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the conditional independence structure induced by a DAG model containing hidden variables on its observed margin. The Markovian model associated with an ADMG is simply the set of distributions obeying the global Markov property, given via a simple path criterion (m-separation). We first present a factorization criterion characterizing the Markovian model that generalizes the well-known recursive factorization for DAGs. For the case of finite discrete random variables, we also provide a parameterization of the model in terms of simple conditional probabilities, and characterize its variation dependence. We show that the induced models are smooth. Consequently, Markovian ADMG models for discrete variables are curved exponential families of distributions.