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Bayesian networks have many practical applications due to their capability to represent joint probability distribution over many variables in a compact way. Though there exist many algorithms for learning Bayesian networks from data, they are not satisfactory because the learned networks usually are not suitable directly for reasoning as they need to be transformed to some other form (tree, polytree, hypertree) statically or dynamically, and this transformation is not trivial [25]. So far only a restricted class of very simple Bayesian networks: trees and poly-trees are directly applicable in reasoning. This paper defines and explores a new class of networks: the Structured Bayesian Networks. Two methods of reasoning are outlined for this type of networks. Possible methods of learning from data are indicated. Similarity to hierarchical networks is pointed at.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
105--137
Opis fizyczny
Bibliogr. 27 poz., wykr.
Twórcy
autor
- Institute of Computer Science, Polish Academy of Science, Ordona 21, 01-237 Warsaw, Poland, klopotek@ipipan.waw.pl
Bibliografia
- [1] M. Bloemeke, M. Valtorta, A hybrid algorithm to compute marginal and joint beliefs in Bayesian networks and its complexity, UAI98 pp 16-23, 1998
- [2] Cercone N., Wong S.K.M., Xiang Y.: A ’microscopic’ study of minimum entropy search in learning decomposable Markov networks. Machine Learning, 1997, vol. 26, nr 1, 65-92
- [3] Cheng J., Bell D.A. and Liu W.: Learning belief networks from data: an information theory based approach. Proceedings of the Sixth ACM Int. Conf. on Information and Knowledge Management, 1997
- [4] C.K. Chow, C.N. Liu: Approximating discrete probability distributions with dependence trees, IEEE Transactions on Information Theory, Vol. IT-14, No.3, (1968), 462-467
- [5] Cooper G. The computational complexity of probabilistic inference using Bayesian belief networks. Artif. Intell. 42,1990, 395-405
- [6] R. G. Cowell, A. P. Dawid, S. L. Lauritzen, and D. J. Spiegelhalter. Probabilistic networks and expert systems. Springer-Verlag New York, Inc., 1999.
- [7] Geiger D., Verma T., Pearl J.: D-Separation: From theorems to algorithms. M. Henrion, et.al eds., Uncertainty in Artificial Intelligence 5, Elsevier 139-148
- [8] Jensen J., An Introduction to Bayesian Networks, Springer Verlag, 1996
- [9] F. V. Jensen, F. B. Jensen Bayesian Networks and Decision Graphs (Statistics for Engineering and Information Science) Springer-Verlag, New York, 2001
- [10] Klopotek M.A.: Partial Dependency Separation - a new concept for expressing dependence/ independence relations in causal networks. Demonstratio Mathematica. Vol XXXII No 1,1999, pp. 207-226
- [11] Klopotek M.A.: On a Deficiency of the FCI Algorithm Learning Bayesian Networks from Data. Demonstratio Mathematica. Vol. XXXIII, 2000. No. 1, pp. 181-194
- [12] Klopotek M.A.: Fast Restricted Causal Inference. Demonstratio Mathematica, Vol. XXXIII, No.2, 2000. pp. 419-442
- [13] Klopotek M.A., Wierzchoń S.T.: Partial D-Sepaation for Discovery of Bayesian Networks from Data. R. Trappl, ed.: Cybernetics and Systems. Proc. EMCSR’2000, 25-28.4.2000, Vienna, Austrian Society for Cybernetics, Vol. 2, pp. 707-712
- [14] Klopotek M.A.: Inteligentne wyszukiwarki internetowe. Akademicka Oficyna Wydawnicza Exit, Warszawa 2001, ISBN 83-87674-31-1, chapter 8.9
- [15] Kłopotek M.A., Wierzchoń S.T., Michalewicz M., Bednarczyk M., Pawłowski W., Wsowski A.: Bayesian network mining system. M.A. Kłopotek, M. Michalewicz, S.T. Wierzchoń, eds. Intelligent Information Systems 2001. Physica/Springer Verlag, 2001, 180-193
- [16] Klopotek M.A., Well-Structured Program Graphs and the issue of local computations. Proc. Intelligent Inf. Systems Conf., Sopot, 3-6 June 2002. Advances in Soft Computing. Physica/Springer Verlag, Heidelberg New York 2002. ISBN-3-7908-1509-8, pp. 365-368
- [17] M.A. Kłopotek: On the Distance Hypothesis in Tree-like Bayesian Networks. ICS PAS Report 952, Warszawa, January 2003
- [18] M.A.Kłopotek: Reasoning in Structured Bayesian Networks TO APPPEAR IN Rutkowski, L., Kacprzyk, J., (Eds.) ”Neural Networks and Soft Computing” Proceedings of the Sixth International Conference on Neural Network and Soft Computing, Zakopane, Poland, June 11-15, 2002, Springer-Verlag 2003, ISBN 3-7908-0005-8
- [19] Koller D., Pfeffer A.: Object-Oriented Bayesian Networks. Proc. of the 13th Conf. on Uncertainty in Artificial Intelligence (UAI-97), 1997, 302-313
- [20] Lauritzen, S.L., and Spiegelhalter, D.J. Local computations with probabilities on graphical structures and their application to expert systems. J. R. Statist. Soc. B-50(1988)157-224
- [21] Pearl J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo CA, 1988
- [22] Shachter B.D.: Evidence absorption and propagation through evidence reversals. In M. Henrion, B.D. Shachter, L.N. Kanal, J.F. Lemmer (eds): Uncertainty in Artificial Intelligence 5, Elsevier Science Publishers B.V (1990), 173- 190
- [23] Shafer, G.: Probabilistic Expert Systems, SIAM CBMS-NSF Regional Conference Series in Applied Mathematics, Philadelphia, 1996, vol. 67
- [24] Spirtes P., Glymour C., Scheines R.: Causation, Prediction and Search, Lecture Notes in Statistics 81, Springer-Verlag, 1993
- [25] Valtorta, M., Loveland, D.W.: On the Complexity of belief network synthesis and refinement, International Journal of Approximate Reasoning, 1992:7:121-148
- [26] Wierzchoń S.T.: Methods of Representation and rocessing of Uncertauin Information in the Dempster-shafer Theory (in Polish), Publisher: Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland, 1996
- [27] Wierzchoń S.T., Kłopotek M.A.: Evidential Reasoning. An Interpretative Investigation. Wydawnictwo Akademii Podlaskiej, Siedlce, 2002 PL ISSN 0860-2719, 304 pages
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0004-0163