A review on distinct methods and approaches to perform triangulation for Bayesian networks

Studies in Fuzziness and Soft Computing

Volumn 213, Issue , 2007, Pages 127-152

  Flores, M Julia ^a   Gámez, José A ^a  

^a UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34250372497     PISSN: 14349922     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-68996-6_6     Document Type: Review

References (50)

1. Amir, E. (2001) Efficient approximation for triangulation of minimum treewidth. In: Proceedings of the 17th Conference on Uncertainty in Artificial Intelligene (UAI-01), 7-15
2. Becker A. and Geiger D. (1996) A sufficiently fast algorithm for finding close to optimal junction trees. In: Proceedings of the 12h Annual Conference on Uncertainty in Artificial Intelligence (UAI-96), 81-89
3. Berry A., Blair J.R.S. and Heggernes P. (2002) Maximum Cardinality Search for Computing Minimal Triangulations. WG '02: Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science. In: Lecture Notes in Computer Science, 2573, 1-12, Springer Verlag
4. Berry A., Blair J.R.S., Heggernes P. and Peyton B.W. (2004) Maximum Cardinality Search for Computing Minimal Triangulations of Graphs. Algorithmica 39(4): 287-298
5. Berry A., Bordat J-P., Heggernes P., Simonet G. and Villanger Y. A wide-range algorithm for minimal triangulation from an arbitrary ordering. To appear in Journal of Algorithms
6. Blair J.R.S, Heggernes P. and Telle J.A. (2001) A practical algorithm for making filled graphs minimal. Theoretical Computer Science 205(1-2):125-141
7. Bodlaender H.L., Koster A.M. et al (2001) Pre-processing for triangulation of probabilistic networks. In: Proceedings of the 17th Conference on Uncertainty in Artificial Intelligene (UAI-01), 32-39
8. Cano A. and Moral S. (1994) Heuristic algorithms for the triangulation of graphs. In: Proceedings of the 5th International Conference on Information Processing and Management of Uncertainty in Knowledge Based Systems (IPMU), 1, 166-171, Paris (France)
9. Cano A., Moral S. and Salmerón A. (2000) Penniless propagation. International Journal of Intelligent Systems, 15:1027-1059
10. Cano A., Moral S. and Salmern A. (2002) Lazy evaluation in Penniless propagation over join trees. Networks, 39:175-185
11. Darwiche A. and Hopkins M. (2001) Using Recursive Decomposition to Construct Elimination Orders, Jointrees, and Dtrees. Lecture Notes in Computer Science, 2143, 180-190, Springer Verlag.
12. Dechter R. (2003) Constraint Processing. Morgan Kaufmann, 2003
13. Dorigo M. and Gambardella L. (1997) Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem. IEEE Transactions on Evolutionary Computation, 1:53-66
14. Dorigo M. and Stützle T. Ant colony optimization. MIT Press, 2004.
15. Even S. and Tarjan R.E. (1975) Network flow and testing graph connectivity. SIAM Journal on Computing, 4:507-518
16. Flores M.J. and Gámez J.A. (2003) Triangulation of Bayesian networks by retriangulation. International Journal of Intelligent Systems 18(2):153-164
17. Flores M.J., Gámez J.A. and Olesen K.G. (2003) Incremental Compilation of Bayesian networks. In: Proceedings of the 19th Annual Conference on Uncertainty in Artificial Intelligence (UAI-03), Morgan Kaufmann, 233-240
18. Flores M.J. (2005) Bayesian networks inference: Advanced algorithms for triangulation and partial abduction. PhD thesis, Departamento de Sistemas Informaticos (Computing Systems Department), University of Castilla - La Mancha UCLM, Spain
19. de Campos L.M., Gámez J.A., and Moral S. (2002) On the problem of performing exact partial abductive inference in Bayesian belief networks using junction trees. In: B. Bouchon-Meunier, J. Gutierrez, L. Magdalena, and R.R. Yager, editors, Technologies for Constructing Intelligent Systems 2: Tools, 289-302 Springer Verlag
20. Gámez J.A. and Puerta J.M. (2002) Searching for the best elimination sequence in Bayesian networks by using ant colony optimization. Pattern Recognition Letters., 23:261-277
21. Gogate V. and Dechter R. (2004) A Complete Anytime Algorithm for Treewidth. In: Proceedings of the Twentieth Annual Conference on Uncertainty in Artificial Intelligence (UAI-04), pp. 201-208, AUAI Press
22. Goldberg D.E. (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley
23. Heggernes P. and Villanger Y. (2002) Efficient Implementation of a Minimal Triangulation Algorithm. In: ESA '02: Proceedings of the 10th Annual European Symposium on Algorithms. Lecture Notes in Computer Science, 2461, 550-561, Springer Verlag
24. Hernández L.D. (1995) Diseño y validación de nuevos algoritmos para el tratamiento de grafos de dependencias (Validation and design of new algorithms to dependency graph processing.) Doctoral thesis, Dpto. de Ciencias de la Computación e I.A. Universidad de Granada, Spain
25. HUGIN Expert A/S. API manual for the Hugin Decision Engine V6.3. http://developer.hugin.com/documentation/API_Manuals/
26. Jensen F.V., Lauritzen S.L. and Olesen K.G. (1990) Bayesian updating in causal probabilistic networks by local computation. Computational Statistics Quarterly, 4:269-282
27. Jensen F.V. and Jensen F. (1994) Optimal junction trees. In: Proceedings of the Tenth Annual Conference on Uncertainty in Artificial Intelligence (UAI-94), 360-366, Morgan-Kaufmann
28. Kjærulff U. (1990) Triangulation of graphs - algorithms giving small total space. Technical Report R 90-09, Department of Mathematics and Computer Science. Institute of Electronic Systems. Aalborg University
29. Kjærulff U. (1992) Optimal decomposition of probabilistic networks by simulated annealing. Statistics and Computing, 2:7-17
30. Larrañaga P., Kuijpers C.M., Poza M. and Murga R.H. (1997) Decomposing Bayesian networks: Triangulation of the moral graph with genetic algorithms. Statistics and Computing, 7:19-34
31. Lauritzen S.L., Speed T.P. and Vijayan K. (1984) Decomposable graphs and hypergraphs. Journal of the Australian Mathematical Society Series A 36: 12-29
32. Lauritzen S.L. and Spiegelhalter D.J. (1988) Local computations with probabilities on graphical structures and their application to expert systems. J.R. Statistics Society. Series B, 50(2):157-224
33. Leimer H.G. (1993) Optimal decomposition by clique separators. Discrete Mathematics, 113:99-123
34. Madsen A.L. and Jensen F.V. (1999) Lazy Propagation: A Junction Tree Inference Algorithm based on Lazy Evaluation. Artificial Intelligence 113(1-2):203-245, Elsevier Science Publishers, North-Holland
35. Michalewicz Z. (1996) Genectic Algorithms + Data Structures = Evolution Programs. Springer-Verlag
36. Olesen K.G. and Madsen A.L. (2002) Maximal prime subgraph decomposition of bayesian networks. IEEE Transactions on Systems, Man and Cybernetics, Part B:(32), 21-31
37. Park J.D. and Darwiche A. (2003): Solving MAP Exactly using Systematic Search. In: Proceedings of the 19th Annual Conference on Uncertainty in Artificial Intelligence (UAI-03), Morgan Kaufmann, 459-468
38. Pearl, J. (1988) Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo
39. Peyton B.W. (2001) Minimal Orderings Revisited. SIAM Journal on Matrix Analysis and Applications, 23(1):271-294
40. Rose D., Tarjan R.E. and Lueker G.S. (1976) Algorithmic aspects of vertex elimination graphs. SIAM Journal on Computing, 5 266-283
41. Selvakkumaran N. and Karypis G. Multi-Objective Hypergraph Partitioning Algorithms for Cut and Maximum Subdomain Degree Minimization IEEE Transactions on Computer Aided Design (in press)
42. Rose D. (1972) A graph theoretic study of the numerical solution of sparse positive definite systems of linear equations. In: R. Reed ed. Graph Theory and Computing, 183-217, Academic Press, New York
43. Shafer G.R. and Shenoy P.P. (1990) Axioms for probability and belief-function propagation. In: R.D. Shachter, T.S. Levitt, L.N. Kanal and J.F. Lemmer (eds.), Uncertainty in Artificial Intelligence, 4, 169-198, Elsevier Science Publishers B.V. (North-Holland)
44. Shoikhet K. and Geiger D. (1997) Practical algorithm for finding optimal triangulations. In: Proceedings of the National Conference on Artificial Intelligence, AAAI, USA, 185-190
45. Tarjan R.E. and Yannakakis M. (1984) Simple linear-time algorithms to test chordality of graps, text acyclicity of hypergraphs and selectively reduce acyclic hypergraphs. SIAM Journal on Computing, 13 566-579
46. Tarjan R.E. (1985) Decomposition by clique separators. Discrete Mathematics, 55:221-232
47. Villanger Y. (2004) LEX M versus MCS-M. Technical Report Reports in Informatics 261, University of Bergen, Norway
48. Wen, W. X. (1990) Decomposing belief networks by simulated annealing. In: (C. P. Tsang, ed.) Proceedings of the Australian Joint Conference on Artificial Intelligence, 103-118
49. Wen, W.X. (1991) Optimal decomposition of belief networks. In: P.P. Bonissone, M. Henrion, L.N. Kanal and J.F. Lemmer (eds.), Uncertainty in Artificial Intelligence, 6, 209-224 North-Holland
50. Kirkpatrick S., Gelatt C.D. and Vecchi M.P. (1983) Optimization by simulated annealing. Science, 220:671-680