Chain Graphs for Learning
This work provides a foundational framework for graphical models in machine learning, potentially impacting various applications like feed-forward networks and clustering.
The paper tackles the problem of representing complex probabilistic models by introducing a simplified definition of chain graphs that combine Bayesian and Markov networks, and extends them with plates to represent samples and data analysis problems.
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.