Chain Graphs for Learning

Abstract

Chain graphs combine directed and undi­ rected graphs and their underlying mathe­ matics 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, cluster­ ing with conditional interaction between vari­ ables, 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.