Application of uncertainty measures on credal sets on the naive Bayesian classifier

International Journal of General Systems

Volumn 35, Issue 6, 2006, Pages 675-686

  Abellán, Joaquín ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

Classification; Imprecise Dirichlet model; Imprecise probabilities; Maximum entropy; Naive Bayesian classifier; Uncertainty measures

Indexed keywords

DATA REDUCTION; DATABASE SYSTEMS; MATHEMATICAL MODELS; PROBABILITY;

IMPRECISE DIRICHLET MODEL; IMPRECISE PROBABILITIES; MAXIMUM ENTROPY; UNCERTAINTY MEASURES;

SET THEORY;

EID: 33750897026     PISSN: 03081079     EISSN: 15635104     Source Type: Journal    
DOI: 10.1080/03081070600867039     Document Type: Article

References (32)

1. J. Abellán, "Uncertainty measures on probability intervals from imprecise Dirichlet model", To appear in Int. J. Gen. Syst., 35(3), 2006.
2. J. Abellán and S. Moral, "A non-specificity measure for convex sets of probability distributions", Int. J. Unc. Fuzz. Knawl. Based Syst., 8, pp. 357-367, 2000.
3. J. Abellán and S. Moral, "Maximum of entropy for credal sets", Int. J. Unc. Fuzz. Knowl. Based Syst., 11 (5), pp. 587-597, 2003.
4. J. Abellán and S. Moral, "Maximum difference of entropies as a non-speciflcty measure for credal sets", Int. J. Gen. Syst., 34(3), pp. 201 -214, 2005a.
5. J. Abellán and S. Moral, "Upper entropy of credal sets. Applications to credal classification", Int. J. Approx. Reasoning, 39, pp. 235-255, 2005b.
6. J. Abellán and S. Moral, "An algorithm that computes the upper entropy for order-2 capacities", Int. J. Unc. Fuzz,. Knowl. Based Syst., 14(2), pp. 141-154, 2006.
7. J. Abellán, G.J. Klir and S. Moral, "Disaggregated total uncertainty measure for credal sets", Int. J. Gen. Syst., 35(1), pp. 29-44, 2006a.
8. J. Abellán, S. Moral, M. Gómez and A. Masegosa, "Varying parameter in classification based on imprecise probabilities" Accepted in Third international conference on Soft Methods in Probability and Statistics 2006, 2006b.
9. J.M. Bernard, "An introduction to the imprecise Dirichlet model for multinomial data", Int. J. Appmx. Reasoning, 39, pp. 123-150, 2005.
10. L.M. Campos, J.F de Huete and S. Moral, "Probability intervals: a tool for uncertainty reasoning", Int. J. Unc. Fuzz. Knowl. Based Syst., 1, pp. 167-196, 1994.
11. A.P. Dempster, "Upper and lower probabilities induced by a multivaluated mapping", Ann. Math. Statist., 38, pp. 325-339, 1967.
12. R.O. Duda and P.E. Hart, Pattern Classification And Scene Analysis, New York: John Wiley and Sons. 1973.
13. N. Friedman, D. Geiger and M. Goldszmidt, "Bayesian networks classifiers", Mach. Learn., 29, pp. 131-163, 1997.
14. K. Huang, I. King and M. Lyu, "Learning maximum likelihood semi-naive Bayesian network classifier". Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, Hammamet, Tunisia, Vol. 3. 2002.
15. E.J. Keogh and M.J. Pazzani, "Learning augmented Bayesian classifiers: a comparizon of distribution-based and classification-based approaches", Proc. Int. Workshop on Artificial Intelligence and Statistics, 1999, pp. 225-230.
16. J. Kittler, "Feature selection and extraction", in Handbook of Pattern Recognition and Image Processing, T.Y. Young and K.S. Fu, Eds., New York: Academic Press, 1986.
17. G.J. Klir, Uncertainty and Information: Foundations of Generalize Information theory, Hoboken, NJ: John Wiley, 2006.
18. G.J. Klir and R.M. Smith, "On measuring uncertainty and uncertainty-based information: recent developments", Ann. Math. An. Intell., 32, pp. 5-33, 2001.
19. G.J. Klir and M.J. Wierman, Uncertainty-Based Information, Heidelberg, Germany: Phisica-Verlag, 1998.
20. I. Kononenko. "Semi-naive Bayesian classifier", Proceedings of the 6th European Working Session on Machine Learning, Berlin: Springer-Verlag, 1991, pp. 206-219.
21. I. Kononenko and B. Zupan, "Attribute mining: evaluation, discretization, subset selection and constructive induction", Proceedings of the ICML-99 Workshop on From Machine Learning to Knowledge Discovery in Databases, Bled, Slovenia, 1999, pp. 1-15.
22. P. Langley and S. Sage, "Induction of selective Bayesian classifiers", Proceedings of the Tenth Conference Uncertainty in Artificial Intelligence, San Francisco: Morgan Kaufmann, 1994, pp. 399-406.
23. M.J. Pazzani, "Constructive induction of Cartesian product attribute", Inform. Stat. Induction Sci., pp. 66-77, 1996.
24. J.R. Quinlan, "Induction of decision trees", Mach. Learn., 1, pp. 81-106, 1986.
25. J.R. Quinlan, Programs for Machine Learning, San Francisco: Morgan Kaufmann, 1993, series in Machine Learning.
26. G. Sharer, A Mathematical Theory of Evidence, Princeton: Princeton University Press, 1976.
27. C.E. Shannon, "A mathematical theory of communication", Bell Syst. Tech. J., 27, pp. 379-423, 623-656 1948.
28. P. Walley, Statistical Reasoning with Imprecise Probabilities, New York: Chapman and Hall, 1991.
29. P. Walley, "Inferences from multinomial data; learning about a bag of marbles", J. Roy, Statist. Soc. B, 58, pp. 3-57, 1996.
30. G.I. Webb, J. Boughton and Z. Wang, "Not so naive Bayes: aggregating one-dependence estimators", Mach. Learn., 58, pp. 5-24, 2005.
31. Z. Zheng and G.I. Webb, "Lazy learning of Bayesian rules", Mach. Learn., 41, pp. 53-84, 2000.
32. Z. Zheng and G.I. Webb, "A comparative study of semi-naive Bayes methods in classification learning", Proc. Fourth Australasian Conference on Knowledge Discovery and Data Mining, 2005. pp. 141-156.