On Separation Criterion and Recovery Algorithm for Chain Graphs

Abstract

Chain graphs (CGs) give a natural unifying point of view on Markov and Bayesian networks and enlarge the potential of graphical models for description of conditional independence structures. In the paper a direct graphical separation criterion for CGs which generalizes the d-separation criterion for Bayesian networks is introduced (recalled). It is equivalent to the classic moralization criterion for CGs and complete in the sense that for every CG there exists a probability distribution satisfying exactly independencies derivable from the CG by the separation criterion. Every class of Markov equivalent CGs can be uniquely described by a natural representative, called the largest CG. A recovery algorithm, which on basis of the (conditional) dependency model given by a CG finds the corresponding largest CG, is presented.