Abstract
In this paper we consider conditional independence models closed under graphoid properties. We investigate their representation by means of acyclic directed graphs (DAG). A new algorithm to build a DAG, given an ordering among random variables, is described and peculiarities and advantages of this approach are discussed. Finally, some properties ensuring the existence of perfect maps are provided. These conditions can be used to define a procedure able to find a perfect map for some classes of independence models.
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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. Accepted for Publication in International Journal of Approximate Reasoning (2008)
Baioletti, M., Busanello, G., Vantaggi, B.: Conditional independence structure and its closure: inferential rules and algorithms. In: Technical Report, 5/2009 of University of Perugia (2009)
Coletti, G., Scozzafava, R.: Zero probabilities in stochastical independence. In: Bouchon- Meunier, B., Yager, R.R., Zadeh, L.A. (eds.) Information, Uncertainty, Fusion, pp. 185–196. Kluwer Academic Publishers, Dordrecht (2000)
Coletti, G., Scozzafava, R.: Probabilistic logic in a coherent setting. Kluwer, Dordrecht (2002) (Trends in logic n.15)
Dawid, A.P.: Conditional independence in statistical theory. J. Roy. Stat. Soc. B 41, 15–31 (1979)
Jensen, F.V.: An Introduction to bayesian Networks. UCL Press/ Springer Verlag (1966)
Lauritzen, S.L.: Graphical models. Clarendon Press, Oxford (1996)
Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, Los Altos (1988)
Studený, M.: Semigraphoids and structures of probabilistic conditional independence. Ann. Math. Artif. Intell. 21, 71–98 (1997)
Studený, M.: Complexity of structural models. In: Proc. Prague Stochastics 1998, Prague, pp. 521–528 (1998)
Studený, M., Bouckaert, R.R.: On chain graph models for description of conditional independence structures. Ann. Statist. 26(4), 1434–1495 (1998)
Vantaggi, B.: Conditional independence in a coherent setting. Ann. Math. Artif. Intell. 32, 287–313 (2001)
Verma, T.S.: Causal networks: semantics and expressiveness. Technical Report R–65, Cognitive Systems Laboratory, University of California, Los Angeles (1986)
Witthaker, J.J.: Graphical models in applied multivariate statistic. Wiley & Sons, New York (1990)
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. (2009). Acyclic Directed Graphs to Represent Conditional Independence Models. In: Sossai, C., Chemello, G. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2009. Lecture Notes in Computer Science(), vol 5590. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02906-6_46
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DOI: https://doi.org/10.1007/978-3-642-02906-6_46
Publisher Name: Springer, Berlin, Heidelberg
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