On Separation Criterion and Recovery Algorithm for Chain Graphs
This work provides a theoretical framework for modeling conditional independence in chain graphs, which unifies Markov and Bayesian networks, but is incremental in nature.
The paper introduces c-separation, a graphical separation criterion for chain graphs that generalizes d-separation for Bayesian networks, and presents a recovery algorithm to find the largest chain graph from dependency data.
Chain graphs 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 chain graphs, called c-separation, which generalizes the d-separation criterion for Bayesian networks is introduced (recalled). It is equivalent to the classic moralization criterion for chain graphs and complete in sense that for every chain graph there exists a probability distribution satisfying exactly conditional independencies derivable from the chain graph by the c-separation criterion. Every class of Markov equivalent chain graphs can be uniquely described by a natural representative, called the largest chain graph. A recovery algorithm, which on basis of the (conditional) dependency model induced by an unknown chain graph finds the corresponding largest chain graph, is presented.