Abstract
We introduce the notion of an approximate Bayesian network, which almost keeps the information entropy of data and encodes knowledge about approximate dependencies between features. Presented theoretical results, as well as relationships to fundamental concepts of the rough set theory, provide a novel methodology of applying the Bayesian net models to the real life data analysis.
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References
Bouckaert, R.R.: Properties of Bayesian Belief Network Learning Algorithms. In: Proc. of UAI’94, University of Washington, Seattle, Morgan Kaufmann, San Francisco, CA (1994) pp. 102–109.
Cooper, F.G., Herskovits, E.: A Bayesian Method for the Induction of Probabilistic Networks from Data. In: Machine Learning,9, Kluwer Academic Publishers, Boston (1992) pp. 309–347.
Duentsch, I., Gediga, G.: Uncertainty measures of rough set prediction. Artificial Intelligence106 (1998) pp. 77–107.
Gallager, R.G.: Information Theory and Reliable Communication. John Wiley & Sons, New York (1968).
Kapur, J.N., Kesavan, H.K.: Entropy Optimization Principles with Applications. Academic Press (1992).
Li, M., Vitanyi, P.: An Introduction to Kolmogorov Complexity and Its Applications. Springer Verlag (1997).
Pawlak, Z.: Rough sets - Theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht (1991).
Pawlak, Z.: Decision rules, Bayes’ rule and rough sets. In: Proc. of RSFDGrC’99, Yamaguchi, Japan, LNAI 1711 (1999) pp. 1–9.
Pawlak, Z., Skowron, A.: Rough membership functions. In: Advances in the Dempster Shafer Theory of Evidence, John Wiley & Sons Inc., New York, (1994) pp. 251–271.
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann (1988).
Pearl, J., Paz, A.: Graphoids: A graph-based logic for reasoning about relevance relations. In: Advanves in Artificial Intelligence II, B. Du Boulay, D. Hogg and L. Steels (eds.), North-Holland, Amsterdam (1987) pp. 357–363.
Polkowski, L., Skowron, A. (eds.): Proc. of RSCTC’98, June 22–26, Warsaw, Poland, Springer Verlag, Berlin (1998).
Polkowski, L., Skowron, A. (eds.): Rough Sets in Knowledge Discovery. Physica Verlag, Heidelberg (1998), parts 1, 2.
Polkowski, L., Tsumoto, S., Lin, T.Y. (eds.): Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems. Physica Verlag/Springer Verlag (2000).
Rissanen, J.: Modeling by the shortest data description. Authomatica14 (1978) pp. 465–471.
Slgzak, D.: Approximate reducts in decision tables. In: Proc. of IPMU’96, July 1–5, Granada, Spain (1996)3, pp. 1159–1164.
Slgzak, D.: Normalized decision functions and measures for inconsistent decision tables analysis. Fundamenta Informaticae44/3, IOS Press (2000) pp. 291–319.
Slgzak, D.: Foundations of Entropy-Based Bayesian Networks: Theoretical Results Rough Set Based Extraction from Data. In: Proc. of IPMU’00, July 3–7, Madrid, Spain (2000)1, pp. 248–255.
Slgzak, D.: Data Models based on Approximate Bayesian Networks. In: Proc. of JSAI RSTGC’2001, May 20–22, Shimane, Japan (2001).
Slgzak, D., Wróblewski, J.: Application of Normalized Decision Measures to the New Case Classification. In: Proc. of RSCTC’00, October 16–19, Banff, Canada (2000).
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Ślęzak, D. (2002). Approximate Bayesian Networks. In: Bouchon-Meunier, B., Gutiérrez-Ríos, J., Magdalena, L., Yager, R.R. (eds) Technologies for Constructing Intelligent Systems 2. Studies in Fuzziness and Soft Computing, vol 90. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1796-6_25
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DOI: https://doi.org/10.1007/978-3-7908-1796-6_25
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2504-6
Online ISBN: 978-3-7908-1796-6
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