Abstract
We provide a necessary and sufficient condition for the existence of a perfect map representing an independence model and we give an algorithm for checking this condition and drawing a perfect map, when it exists.
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Baioletti, M., Busanello, G., Vantaggi, B.: Conditional independence structure and its closure: inferential rules and algorithms. Int. J. of Approx. Reason. 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 (LNAI), vol. 5590, pp. 530–541. Springer, Heidelberg (2009)
Baioletti, M., Busanello, G., Vantaggi, B.: Closure of independencies under graphoid properties: some experimental results. In: Proc. 6th Int. Symp. on Imprecise Probability: Theories and Applications, pp. 11–19 (2009)
Baioletti, M., Busanello, G., Vantaggi, B.: Acyclic directed graphs representing independence models. Int. J. of Approx. Reason (2009) (submitted)
Baioletti, M., Busanello, G., Vantaggi, B.: Necessary and sufficient conditions for the existence of a perfect map. Tech. Rep. 01/2010. Univ. of Perugia (2010)
Coletti, G., Scozzafava, R.: Probabilistic logic in a coherent setting. Kluwer, Dordrecht (2002) (Trends in logic n.15)
Cozman, F.G., Seidenfeld, T.: Independence for full conditional measures, graphoids and Bayesian networks, Boletim BT/PMR/0711 Escola Politecnica da Universidade de Sao Paulo, Sao Paulo, Brazil (2007)
Cozman, F.G., Walley, P.: Graphoid properties of epistemic irrelevance and independence. Ann. of Math. and Art. Intell. 45, 173–195 (2005)
Dawid, A.P.: Conditional independence in statistical theory. J. Roy. Stat. Soc. B 41, 15–31 (1979)
de Waal, P.R., van der Gaag, L.C.: Stable Independence in Perfect Maps. In: Proc. 21st Conf. Uncertainty in Artificial Intelligence, UAI 2005, Edinburgh, pp. 161–168 (2005)
Jensen, F.V.: An introduction to Bayesian networks. UCL Press, Springer (1996)
Lauritzen, S.L.: Graphical models. Clarendon Press, Oxford (1996)
Moral, S., Cano, A.: Strong conditional independence for credal sets. Ann. of Math. and Art. Intell. 35, 295–321 (2002)
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. of Math. Artif. Intell. 21, 71–98 (1997)
Studený, M.: Probabilistic conditional independence structures. Springer, London (2005)
Vantaggi, B.: Conditional independence structures and graphical models. Int. J. Uncertain. Fuzziness Knowledge-Based Systems 11(5), 545–571 (2003)
Verma, T.S.: Causal networks: semantics and expressiveness. Tech. Rep. R–65, Cognitive Systems Laboratory, University of California, Los Angeles (1986)
Verma, T.S., Pearl, J.: Equivalence and synthesis of causal models. Uncertainty in Artificial Intelligence 6, 220–227 (1991)
Witthaker, J.: Graphical models in applied multivariate statistic. Wiley & Sons, New York (1990)
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Baioletti, M., Busanello, G., Vantaggi, B. (2010). An Algorithm to Find a Perfect Map for Graphoid Structures. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_1
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DOI: https://doi.org/10.1007/978-3-642-14055-6_1
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