Conditional independence structure and its closure: Inferential rules and algorithms

International Journal of Approximate Reasoning

Volumn 50, Issue 7, 2009, Pages 1097-1114

  Baioletti, Marco ^a   Busanello, Giuseppe ^b   Vantaggi, Barbara ^b  

^a UNIVERSITY OF PERUGIA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Closure; Conditional independence models; Generalized inclusion; Graphoid properties; Inferential rules

Indexed keywords

CLOSURE; CONDITIONAL INDEPENDENCE MODELS; GENERALIZED INCLUSION; GRAPHOID PROPERTIES; INFERENTIAL RULES;

EID: 67449128192     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2009.05.002     Document Type: Article

References (37)

1. Amor B.N., and Benferhat S. Graphoid properties of qualitative possibilistic independence relations. International Journal of Uncertainty Fuzziness Knowledge-Based Systems 13 1 (2005) 59-96
2. M. Baioletti, G. Busanello, B. Vantaggi, Algorithms for the closure of graphoid structures, in: Proceedings of 12th International Conference IPMU 2008, 2008, Malaga, pp. 899-906.
3. G. Busanello, Probabilistic conditional independence models: closure and construction of acyclic directed graphs, Ph.D. Thesis, 2008.
4. Coletti G., and Scozzafava R. Zero probabilities in stochastical independence. In: Bouchon- Meunier B., Yager R.R., and Zadeh L.A. (Eds). Information, Uncertainty, Fusion (2000), Kluwer Academic Publishers, Dordrecht 185-196
5. Coletti G., and Scozzafava R. The role of coherence in eliciting and handling imprecise probabilities and its application to medical diagnosis. Information Science 130 (2000) 41-65
6. G. Coletti, R. Scozzafava, Probabilistic Logic in a Coherent Setting, Kluwer, Dordrecht/Boston/London, 2002 (Trends in logic n.15).
7. Coletti G., and Vantaggi B. Possibility theory: conditional independence. Fuzzy Sets and Systems 157 (2006) 1491-1513
8. Couso I., Moral S., and Walley P. A survey of concepts of independence for imprecise probabilities. Risk, Decision and Policy 5 (2000) 165-181
9. Cobb B.R., and Shenoy P.P. Operations for inference in continuous Bayesian networks with linear deterministic variables. International Journal of Approximate Reasoning Volume 42 (2006) 21-36
10. Cowell R.G., Dawid A.P., Lauritzen S.L., and Spiegelhalter D.J. Probabilistic Networks and Expert Systems (1999), Springer-Verlag, New York
11. F.G. Cozman, T. Seidenfeld, Independence for full conditional measures, graphoids and Bayesian networks, Boletim BT/PMR/0711 Escola Politecnica da Universidade de Sao Paulo, Sao Paulo, Brazil, 2007, (To appear at Benedikt Lwe, Eric Pacuit, Jan-Willem Romeijn (Eds.), Foundations of the Formal Sciences VI - Reasoning about Probabilities and Probabilistic Reasoning.).
12. Cozman F.G., and Walley P. Graphoid properties of epistemic irrelevance and independence. Annals of Mathematics and Artificial Intelligence 45 (2005) 173-195
13. Cox D.R., and Wermuth N. Multivariate Dependencies - Models, Analysis, and Interpretation (1996), Chapman and Hall
14. Dawid A.P. Conditional independence in statistical theory. Journal of the Royal Statistical Society B 41 (1979) 15-31
15. Dawid A.P. Separoids: a mathematical framework for conditional independence and irrelevance. Representations of uncertainty. Annals of Mathematics and Artificial Intelligence 32 (2001) 335-372
16. de Campos L.M., and Castellano J.G. Bayesian network learning algorithms using structural restrictions International. Journal of Approximate Reasoning Volume 45 (2007) 233-254
17. de Campos L.M., and Huete J.F. Independence concepts in possibility theory. I. Fuzzy Sets and Systems 103 (1999) 127-152
18. L. de Campos, S. Moral, Independence concepts for convex sets of probabilities, in: Proceedings of the XI Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann, San Francisco, CA, 1995, pp. 108-115.
19. B. de Finetti, Sull'impostazione Assiomatica del Calcolo Delle Probabilità(Ch. 5 in Probability, Induction, Statistics, Wiley, London), Annali Univ. Trieste 19, 1949, pp. 3-55.
20. Feelders A., and van der Gaag L.C. Learning Bayesian network parameters under order constraints. International Journal of Approximate Reasoning Volume 42 (2006) 37-53
21. Hill J.R. Comment on graphical models. Statistical Science 8 (1993) 258-261
22. Lauritzen S.L. Graphical Models (1996), Clarendon Press, Oxford
23. Moral S., and Cano A. Strong conditional independence for credal sets. Annals of Mathematics and Artificial Intelligence 35 (2002) 295-321
24. Pearl J. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (1988), Morgan Kaufmann, Los Altos CA
25. San Marti{dotless}̀n E., Mouchart M., and Rolin J. Ignorable common information, null sets and Basu's first theorem. Sankhya 67 (2005) 674-698
26. Shenoy P.P. Conditional independence in valuation-based systems. International Journal of Approximate Reasoning 10 (1994) 203-234
27. Studený M. Semigraphoids and structures of probabilistic conditional independence. Annals of Mathematics and Artificial Intelligence 21 (1997) 71-98
28. M. Studený, Complexity of structural models, in: Proceedings of the Prague Stochastics'98, Prague, 1998, pp. 521-528.
29. Studený M., and Bouckaert R.R. On chain graph models for description of conditional independence structures. Annals of Statistics 26 4 (1998) 1434-1495
30. Vantaggi B. Conditional independence in a coherent setting. Annals of Mathematics and Artificial Intelligence 32 (2001) 287-313
31. Vantaggi B. The L-separation criterion for description of cs-independence models. International Journal of Approximate Reasoning 29 3 (2002) 291-316
32. Vantaggi B. Conditional independence structures and graphical models. International Journal of Uncertainity Fuzziness Knowledge-Based Systems 11 5 (2003) 545-571
33. Vantaggi B. Qualitative Bayesian Networks with Logical Constraints. Lecture Notes in Computer Sciences vol. 2711 (2003), Springer, New York
34. Vantaggi B. The Role of Coherence for Handling Probabilistic Evaluations and Independence. Soft Computing vol. 69(8) (2005), Springer, Berlin/Heidelberg pp. 617-628
35. Veinarova J. Conditional independence relations in possibility theory. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems 8 3 (2000) 253-269
36. Witthaker J. Graphical Models in Applied Multivariate Statistic (1990), Wiley, New York
37. Wong S.K.M., Butz C.J., and Wu D. On the implication problem for probabilistic conditional independency. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans 30 6 (2000) 785-805