• Corpus ID: 7650573

# Segregated Graphs and Marginals of Chain Graph Models

@inproceedings{Shpitser2015SegregatedGA,
title={Segregated Graphs and Marginals of Chain Graph Models},
author={Ilya Shpitser},
booktitle={NIPS},
year={2015}
}
• I. Shpitser
• Published in NIPS 7 December 2015
• Computer Science
Bayesian networks are a popular representation of asymmetric (for example causal) relationships between random variables. Markov random fields (MRFs) are a complementary model of symmetric relationships used in computer vision, spatial modeling, and social and gene expression networks. A chain graph model under the Lauritzen-Wermuth-Frydenberg interpretation (hereafter a chain graph model) generalizes both Bayesian networks and MRFs, and can represent asymmetric and symmetric relationships…

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## References

SHOWING 1-10 OF 27 REFERENCES

### Bayesian Networks from the Point of View of Chain Graphs

The paper gives a few arguments in favour of use of chain graphs for description of probabilistic conditional independence structures and a separation criterion for reading independences from a chain graph is formulated.

### Discrete chain graph models

The statistical literature discusses different types of Markov properties for chain graphs that lead to four possible classes of chain graph Markov models. The different models are rather well

### INTRODUCTION TO NESTED MARKOV MODELS

• Computer Science
• 2014
A natural extension of the ordinary Markov approach is described, whereby both conditional independences and generalized constraints are used to define a nested Markov model, and most structural features of hidden variable DAGs can be recovered exactly when a single generalized independence constraint holds under the distribution of the observed variables.

### A characterization of Markov equivalence classes for acyclic digraphs

• Mathematics
• 1997
Undirected graphs and acyclic digraphs (ADGs), as well as their mutual extension to chain graphs, are widely used to describe dependencies among variables in multivariate distributions. In

### PROBABILITY DISTRIBUTIONS WITH SUMMARY GRAPH STRUCTURE

A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes

### Chain graph models and their causal interpretations

• Mathematics
• 2002
Chain graphs are a natural generalization of directed acyclic graphs and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence

### Markovian acyclic directed mixed graphs for discrete data

• Mathematics
• 2014
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.

### Markov properties for mixed graphs

• Mathematics
• 2014
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence

### Ancestral graph Markov models

• Mathematics, Computer Science
• 2002
A class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models, called maximal ancestral graphs, which lead to a simple parametrization of the corresponding set of distributions in the Gaussian case.

### Marginalizing and conditioning in graphical models

A class of graphs is introduced which is closed under marginalizing and conditioning. It is shown that these operations can be executed by performing in arbitrary order a sequence of simple, strictly