Chain Graphs for Learning

TL;DR

This paper introduces a simplified mathematical framework for chain graphs, combining Bayesian and Markov networks, and extends their representation with plates for data analysis, discussing implications for learning.

Contribution

It provides a new simplified definition of chain graphs and extends their notation with plates for better data modeling and analysis.

Findings

Chain graphs unify directed and undirected models.

Plate notation enables representation of samples and data analysis.

Implications for learning algorithms are discussed.

Abstract

Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and Markov (undirected) networks. Examples of a chain graph are multivariate feed-forward networks, clustering with conditional interaction between variables, and forms of Bayes classifiers. Chain graphs are then extended using the notation of plates so that samples and data analysis problems can be represented in a graphical model as well. Implications for learning are discussed in the conclusion.