Logical and algorithmic properties of stable conditional independence

International Journal of Approximate Reasoning

Volumn 51, Issue 5, 2010, Pages 531-543

  Niepert, Mathias ^a   Gucht, Dirk Van ^b   Gyssens, Marc ^c  

^a UNIVERSITY OF MANNHEIM   (Germany)

^b INDIANA UNIVERSITY   (United States)

^c HASSELT UNIVERSITY   (Belgium)

Author keywords

Computational complexity; Concise representation; Conditional independence; Graphical models; Stable conditional independence

Indexed keywords

ALGORITHMIC PROPERTIES; BOOLEAN SATISFIABILITY; COMPLETE AXIOMATIZATIONS; CONCISE REPRESENTATIONS; CONDITIONAL INDEPENDENCES; CONJUNCTIVE NORMAL FORMS; GRAPHICAL MODEL; IMPLICATION PROBLEM; MARKOV NETWORKS; PERFECT MODEL; PROBABILITY MEASURES; PROPOSITIONAL FORMULAS; REDUNDANT REPRESENTATION; STABLE CONDITIONAL INDEPENDENCE; STRUCTURAL REPRESENTATION;

BOOLEAN FUNCTIONS; GRAPHIC METHODS; RANDOM VARIABLES;

COMPUTATIONAL COMPLEXITY;

EID: 77955229312     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2010.01.011     Document Type: Conference Paper

References (22)

1. J. Pearl Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference 1988 Morgan Kaufmann Publishers Inc.
2. M. Studený Probabilistic Conditional Independence Structures 2005 Springer-Verlag
3. R.R. Bouckaert, and M. Studený Racing algorithms for conditional independence inference Int. J. Approx. Reason. 45 2 2007 386 401
4. P.R. de Waal, L.C. van der Gaag, Stable independence and complexity of representation, in: Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence, 2004, pp. 112-119.
5. P.R. de Waal, L.C. van der Gaag, Stable independence in perfect maps, in: Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence, 2005, pp. 161-168.
6. F. Matú, Ascending and descending conditional independence relations, in: Transactions of the 11th Prague Conference on Information Theory, 1992, pp. 189-200.
7. D. Geiger, and J. Pearl Logical and algorithmic properties of conditional independence and graphical models Ann. Statist. 21 4 1993 2001 2021
8. M. Baioletti, G. Busanello, and B. Vantaggi Conditional independence structure and its closure: inferential rules and algorithms Int. J. Approx. Reason. 50 7 2009 1097 1114
9. M. Niepert, D.V. Gucht, M. Gyssens, On the conditional independence implication problem: a lattice-theoretic approach, in: Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence, 2008, pp. 435-443.
10. J. Pearl, A. Paz, Graphoids: graph-based logic for reasoning about relevance relations or when would x tell you more about y if you already know z?, in: Advances in Artificial Intelligence II, Seventh European Conference on Artificial Intelligence, 1986, pp. 357-363.
11. M. Studený Multiinformation and the problem of characterization of conditional independence relations Probl. Contr. Inform. Theory 18 1 1989 3 16
12. C.H. Papadimitriou Computational Complexity 2003 Birkhäuser
13. J. Peña, R. Nilsson, J. Björkegren, J. Tegnér, Reading dependencies from the minimal undirected independence map of a graphoid that satisfies weak transitivity, in: Proceedings of the European Workshop on Probabilistic Graphical Models, 2006, pp. 247-254.
14. P. Šimeek, A short note on discrete representability of independence models, in: Proceedings of the European Workshop on Probabilistic Graphical Models, 2006, pp. 287-292.
15. M. Sipser Introduction to the Theory of Computation 2006 Thomson Learning Inc.
16. G. Grätzer General Lattice Theory 1994 Addison Wesley
17. B. Sayrafi, D.V. Gucht, Differential constraints, in: Proceedings of the ACM Symposium on Principles of Database Systems, 2005, pp. 348-357.
18. M. Studený, Conditional independence statements have no complete characterization, in: Proceedings of the 11th Prague Conference on Information Theory, 1993, pp. 377-396.
19. J. Gu, P.W. Purdom, J. Franco, B.W. Wah, Algorithms for the satisfiability (sat) problem: a survey, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, 1997.
20. P. Liberatore Redundancy in logic i: Cnf propositional formulae Artif. Intell. 163 2 2005 203 232
21. P. Gandhi, F. Bromberg, D. Margaritis, Learning markov network structure using few independence tests, in: SIAM International Conference on Data Mining, 2008, pp. 680-691.
22. M. Niepert, Logical inference algorithms and matrix representations for probabilistic conditional independence, in: Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, 2009.