Abstract
A chain graph (CG) is a graph admitting both directed and undirected edges with forbidden directed cycles. It generalizes both the concept of undirected graph (UG) and the concept of directed acyclic graph (DAG). CGs can be used efficiently to store graphoids, that is, independency knowledge of the form “X is independent of Y given Z” obeying a set of five properties (axioms).
Two equivalent criteria for reading independencies from a CG are formulated, namely the moralization criterion and the separation criterion. These criteria give exactly the graphoid closure of the input list for the CG. Moreover, a construction of a CG from a graphoid (through an input list), which produces a minimal I-map of that graphoid, is given.
This work was partially supported by the grants: GA AVČR no. 275105 and CEC no. CIPA3511CT930053.
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References
R. Bouckaert and M. Studený: Chain graphs: semantics and expressiveness — Extended version. Res. rep. Institute of Information Theory and Automation, Prague 1995 (in preparation).
M. Frydenberg: The chain graph Markov property. Scand. J. Statist. 17 (1990), 333–353.
D. Geiger, T. Verma, J. Pearl: Identifying independence in Bayesian networks. Networks 20 (1990), 507–534.
D. Geiger, J. Pearl: On the logic of causal models. In Uncertainty in Artificial Intelligence 4 (R. D. Shachter, T. S. Lewitt, L. N. Kanal, J. F. Lemmer eds.), North-Holland 1990, 3–14.
D. Geiger, J. Pearl: Logical and algorithmic properties of conditional independence and graphical models. Ann. Statist. 21 (1993), 2001–2021.
H. Kiiveri, T. P. Speed, J. B. Carlin: Recursive causal models. J. Aust. Math. Soc. A 36 (1984), 30–52.
S. L. Lauritzen, N. Wermuth: Mixed interaction models. Res. rep. R-84-8, Inst. Elec. Sys., University of Aalborg 1984 (the report was later changed and published as an journal paper here referenced as [8]).
S. L. Lauritzen, N. Wermuth: Graphical models for associations between variables, some of which are qualitative and some quantitative. Ann. Statist. 17 (1989), 31–57.
S. L. Lauritzen: Mixed graphical association models. Scand. J. Statist. 16 (1989), 273–306.
S. L. Lauritzen, A. P. Dawid, B. N. Larsen, H.-G. Leimer: Independence properties of directed Markov fields. Networks 20 (1990), 491–505.
J. Pearl: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, CA 1988.
M. Studený: Formal properties of conditional independence in different calculi if AI. In Symbolic and Quantitative Approaches to Reasoning and Uncetainty (M. Clarke, R. Kruse, S. Moral eds.), Springer-Verlag, Berlin Heidelberg 1993, 341–348.
T. Verma, J. Pearl: Causal netwoks: semantics and expressiveness. In Uncertainty in Artificial Intelligence 4 (R. D. Shachter, T. S. Lewitt, L. N. Kanal, J. F. Lemmer eds.), North-Holland 1990, 69–76.
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Bouckaert, R.R., Studený, M. (1995). Chain graphs: Semantics and expressiveness. In: Froidevaux, C., Kohlas, J. (eds) Symbolic and Quantitative Approaches to Reasoning and Uncertainty. ECSQARU 1995. Lecture Notes in Computer Science, vol 946. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60112-0_9
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DOI: https://doi.org/10.1007/3-540-60112-0_9
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