Abstract
We consider approximate bayesian networks, which almost keep the information entropy of data and encode knowledge about approximate dependencies between features. We develop the rough set based framework for extraction of such networks from empirical data, by relating the notion of an approximiate rough membership decision reduct and the notion of an approximate Markov boundary.
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References
Bouckaert R.R.: Properties of Bayesian Belief Network Learning Algorithms. In: Proc. of UAI’94, Morgan Kaufmann, U.S., 1994, 102–109.
Buntine W.: A guide to the literature on learning probabilistic networks from data. IEEE Transactions on Knowledge and Data Engineering, 1996.
Chickering D.M., Geiger D., Heckerman D.E.: Learning Bayesian Networks is NP-Hard. Microsoft Research Technical Report MSR-TR-94–17, 1994.
Duentsch I., Gediga G.: Uncertainty measures of rough set prediction. Artificial Intelligence 106, 1998, 77–107.
Gallager R.G.: Information Theory and Reliable Communication. Wiley, 1968.
Pawlak Z.: Rough sets — Theoretical aspects of reasoning about data. Kluwer, 1991.
Pawlak Z., Skowron A.: Rough membership functions. In: Advances in the Dempster Shafer Theory of Evidence. Wiley, 1994, 251–271.
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, 1988.
Polkowski L., Skowron A. (eds.): Rough Sets in Knowledge Discovery. PhysicaVerlag, 1998, parts 1, 2.
Rissanen J.: Minimum-description-length principle. In: S. Kotz, N.L. Johnson (eds.), Encyclopedia of Statistical Sciences. Wiley, 1985, 523–527.
Skowron A., Rauszer C.: The discernibility matrices and functions in information systems. In: R. Slowirński (ed.): Intelligent Decision Support. Handbook of Applications and Advances of the Rough Set Theory. Kluwer, 1992, 311–362.
Ślęzak D.: Approximate reducts in decision tables. In: Proc. of IPMU’96. Spain, 1996, 1159–1164.
Ślęzak D.: Foundations of Entropy-Based Bayesian Networks. In: Proc. of IPMU’00. Spain, 2000, 248–255.
SŚlęzak D.: Data Models based on Approximate Bayesian Networks. In: Proc. of JSAI RSTGC’2001. Japan, 2001, 89–92.
Ślęzak D.: Approximate decision reducts (In Polish). Ph.D. thesis, Institute of Mathematics, Warsaw University, 2001.
Slęzak D.: Approximate Bayesian networks. In: B. Bouchon-Meunier, J. Gutierrez-Rios, L. Magdalena, R.R. Yager (eds.), Technologies for Contructing Intelligent Systems 2: Tools. Springer-Verlag, 2002, 313–326.
Ślęzak D., Wróblewski J.: Order-based genetic algorithms for extraction of approximate bayesian networks from data. In: Proc. of IPMU’02. France, 2002.
Ślęzak D., Wróblewski J.: Approximate bayesian network classifiers. In: Proc. of RSCTC’02. U.S., 2002.
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Ślęzak, D. (2003). Approximate Markov Boundaries and Bayesian Networks: Rough Set Approach. In: Inuiguchi, M., Hirano, S., Tsumoto, S. (eds) Rough Set Theory and Granular Computing. Studies in Fuzziness and Soft Computing, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36473-3_11
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DOI: https://doi.org/10.1007/978-3-540-36473-3_11
Publisher Name: Springer, Berlin, Heidelberg
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