Abstract
The representation problem of independence models is studied by focusing on acyclic directed graph (DAG). We present the algorithm PC* in order to look for a perfect map. However, when a perfect map does not exist, so that PC* fails, it is interesting to find a minimal I–map, which represents as many triples as possible in J *. Therefore we describe an algorithm which finds such a map by means of a backtracking procedure.
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Baioletti, M., Busanello, G., Vantaggi, B.: Algorithms for the closure of graphoid structures. In: Proc. of 12th Inter. Conf. IPMU 2008, Malaga, pp. 930–937 (2008)
Baioletti, M., Busanello, G., Vantaggi, B.: Conditional independence structure and its closure: Inferential rules and algorithms. Int. J. Approx. Reasoning 50, 1097–1114 (2009)
Baioletti, M., Busanello, G., Vantaggi, B.: Acyclic directed graphs to represent conditional independence models. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS, vol. 5590, pp. 530–541. Springer, Heidelberg (2009)
Baioletti, M., Busanello, G., Vantaggi, B.: An algorithm to find a perfect map for graphoid structures Proc. of 13th Inter. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. Communications in Computer and Information Science, vol. 80, pp. 1–10. Springer, Heidelberg (2010)
Baioletti, M., Busanello, G., Vantaggi, B.: Acyclic directed graphs representing independence models. Int. J. Approx. Reasoning 52, 2–18 (2011)
Bouckaert, R.R., Studený, M.: Racing algorithms for conditional independence inference. Int. J. Approx. Reasoning 45, 386–401 (2007)
Cowell, R.G., Dawid, A.P., Lauritzen, S.L., Spiegelhalter, D.J.: Probabilistic Networks and Expert Systems. Springer, New York (1999)
Jensen, F.V., Lauritzen, S.L.: Probabilistic networks Handbook of Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic Publishers, Netherlands (2000)
Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press, Cambridge (2009)
Lauritzen, S.L.: Graphical models. Clarendon Press, Oxford (1996)
Meek, C.: Causal inference and causal exploration with background knowledge. In: 11th Conf. in Uncertainty in Artificial Intelligence, UAI 1995, pp. 403–410 (1995)
Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, Los Altos (1988)
Pearl, J.: Causality. Cambridge University Press, Cambridge (2000)
Pearl, J., Verma, T.: An Algorithm for Deciding if a Set of Observed Independencies Has a Causal Explanation. In: 8th Conf. in Uncertainty in Artificial Intelligence, UAI 1992, pp. 323–330 (1992)
Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search. MIT Press, Cambridge (2001)
Studený, M.: Semigraphoids and structures of probabilistic conditional independence. Ann. Math. Artif. Intell. 21, 71–98 (1997)
Studený, M.: Probabilistic Conditional Independence Structures. Springer, London (2005)
Tsamardinos, I., Brown, L.E., Aliferis, C.F.: The max–min hill–climbing Bayesian network structure learning algorithm. Machine Learning 65, 31–78 (2006)
Wong, S.K.M., Butz, C.J., Wu, D.: On the Implication Problem for Probabilistic Conditional Independency. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans 30(6), 785–805 (2000)
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Baioletti, M., Busanello, G., Vantaggi, B. (2011). Finding P–Maps and I–Maps to Represent Conditional Independencies. In: Liu, W. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2011. Lecture Notes in Computer Science(), vol 6717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22152-1_21
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DOI: https://doi.org/10.1007/978-3-642-22152-1_21
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