On Separation Criterion and Recovery Algorithm for Chain Graphs
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.
Keywords: Chain graph, conditional independence, Markov equivalence of chain
PS Link: ftp://ftp.utia.cas.cz/pub/staff/studeny/portland.ps.Z
PDF Link: /papers/96/p509-studeny.pdf
AUTHOR = "Milan Studeny
TITLE = "On Separation Criterion and Recovery Algorithm for Chain Graphs",
BOOKTITLE = "Proceedings of the Twelfth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-96)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1996",
PAGES = "509--516"