A recovery algorithm for chain graphs

Abstract

The class of chain graphs ( CGs) involving both undirected graphs (=Markov networks) and directed acyclic graphs (=Bayesian networks) was introduced in middle eighties for description of probabilistic conditional independence structures. Every class of Markov equivalent CGs (that is, CGs describing the same conditional independence structure) has a natural representative, which is called the largest CG. The paper presents a recovery algorithm, which on the basis of the conditional independence structure given by a CG (in the form of a dependency model) finds the largest CG representing the corresponding class of Markov equivalent CGs. As a byproduct a graphical characterization of graphs which are the largest CGs (for a class of Markov equivalent CGs) is obtained and a simple algorithm changing every CG into the largest CG of the corresponding equivalence class is given.