# Marginalization and Conditioning for LWF Chain Graphs

arXiv: https://arxiv.org/abs/1405.7129 · HTML: https://mlsanity.com/paper/1405.7129/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2014.

## Built on by (most cited first, 3 of 3)

- [Robustness of Algorithms for Causal Structure Learning to Hyperparameter Choice](https://mlsanity.com/paper/2310.18212/) (2023)
- [Conditions and Assumptions for Constraint-based Causal Structure Learning](https://mlsanity.com/paper/2103.13521/) (2021)
- [Network Causal Effect Estimation In Graphical Models Of Contagion And Latent Confounding](https://mlsanity.com/paper/2411.01371/) (2024)

## Abstract (arXiv)

In this paper, we deal with the problem of marginalization over and conditioning on two disjoint subsets of the node set of chain graphs (CGs) with the LWF Markov property. For this purpose, we define the class of chain mixed graphs (CMGs) with three types of edges and, for this class, provide a separation criterion under which the class of CMGs is stable under marginalization and conditioning and contains the class of LWF CGs as its subclass. We provide a method for generating such graphs after marginalization and conditioning for a given CMG or a given LWF CG. We then define and study the class of anterial graphs, which is also stable under marginalization and conditioning and contains LWF CGs, but has a simpler structure than CMGs.