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Optimal estimator of hypothesis probability for data mining problems with small samples Cover

Optimal estimator of hypothesis probability for data mining problems with small samples

Open Access
|Sep 2012

References

  1. Ben-Haim, Y. (2006). Info-gap Decision Theory, Elsevier, Oxford/ Amsterdam.
  2. Burdzy, K. (2009). The Search for Certainty. On the Clash of Science and Philosophy of Probability, World Scientific, Singapore.10.1142/7312
  3. Burdzy, K. (2011a). Blog on the book The Search for Certainty. On the Clash of Science and Philosophy of Probability, http://search4certainty.blogspot.com/.
  4. Burdzy, K. (2011b). Philosophy of probability, Website, http://www.math.washington.edu/burdzy/philosophy/.
  5. Carnap, R. (1952). Logical Foundations of Probability, University Press, Chicago, IL.
  6. Cestnik, B. (1990). Estimating probabilities: A crucial task in machine learning, in L. Aiello (Ed.), ECAI’90, Pitman, London, pp. 147-149.
  7. Cestnik, B. (1991). Estimating Probabilities in Machine Learning, Ph.D. thesis, Faculty of Computer and Information Science, University of Ljubljana, Ljubljana.
  8. Chernoff, H. (1952). A measure of asymptotic efficiency for test of a hypothesis based on the sum of observations, Annals of Mathematical Statistics 23(4): 493-507.10.1214/aoms/1177729330
  9. Cichosz, P. (2000). Learning Systems, Wydawnictwa Naukowo-Techniczne, Warsaw, (in Polish).
  10. Cios, K. and Kurgan, L. (2001). SPECT heart data set, UCI Machine Learning Repository, http://archive.ics.uci.edu/ml/datasets/spect+heart.
  11. De Finetti, B. (1975). Theory of Probability: A Critical Introductory Treatment, Willey, London.
  12. Dubois, D. and Prade, H. (1988). Possibility Theory, Plenum Press, New York/NY, London.
  13. Furnkranz, J. and Flach, P.A. (2005). Roc’n’rule learning: Towards a better understanding of covering algorithms, Machine Learning 58(1): 39-77.10.1007/s10994-005-5011-x
  14. Hajek, A. (2010). Interpretations of probability, in E.N. Zalta, (Ed.), The Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/probability-interpret/.
  15. Khrennikov, A. (1999). Interpretations of Probability, Brill Academic Pub., Utrecht/ Boston, MA.
  16. Klirr, G.J. and Yuan, B. (1996). Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems. Selected Papers by Lotfi Zadeh, World Scientific, Singapore.
  17. Laplace, P.S. (1814, English edition 1951). A Philosophical Essay on Probabilities, Dover Publication, New York/NY.
  18. Larose, D.T. (2010). Discovering Statistics, W.H. Freeman and Company, New York, NY.
  19. Piegat, A. (2011a). Uncertainty of probability, in K.T. Atanassov, M. Baczy´nski, J. Drewniak, J. Kacprzyk, M. Krawczak, E. Schmidt, M. Wygralak and S. Zadro˙zny (Eds.) Recent Advances in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, Vol. I: Foundations, IBS PAN, Warsaw, pp. 159-173.
  20. Piegat, A. (2011b). Basic lecture on completeness interpretation of probability, Website, http://kmsiims.wi.zut.edu.pl/pobierz-pliki/cat view/47-publikacje.
  21. Polkowski, L. (2002). Rough Sets, Physica-Verlag, Heidelberg/New York, NY.10.1007/978-3-7908-1776-8
  22. Popper, K.R. (1957). The propensity interpretation of the calculus of probability and the quantum theory, in S. Korner (Ed.), Observation and Interpretation: A Symposium of Philosophers and Physicists, Butterworth Scientific Publications, London, pp. 65-70.
  23. Rocchi, P. (2003). The Structural Theory of Probability: New Ideas from Computer Science on the Ancient Problem of Probability Interpretation, Kluwer Academic/Plenum Publishers, New York, NY.10.1007/978-1-4615-0109-1_6
  24. Rokach, L. and Maimon, O. (2008). Data Mining with Decision Trees: Theory and Applications, Machine Perception and Artificial Intelligence, Vol. 69, World Scientific Publishing, Singapore.
  25. Shafer, G. (1976). A Mathematical Theory of Evidence, Princetown University Press, Princetown, NJ .10.1515/9780691214696
  26. Siegler, R.S. (1976). Three aspects of cognitive development, Cognitive Psychology 8(4): 481-520.10.1016/0010-0285(76)90016-5
  27. Siegler, R.S. (1994). Balance scale weight & distance database, UCI Machine Learning Repository, http://archive.ics.uci.edu/ml/datasets/balance+scale.
  28. Sulzmann, J.N. and Furnkranz, J. (2009). An empirical comparison of probability estimation techniques for probabilistic rules, in J. Gama, J. Santos Costa, A.M. Jorge and P. Brazdil (Eds.), Proceedings of the 12th International Conference on Discovery Science (DS-09), Springer-Verlag, Heidelberg/New York, NY, pp. 317-331.10.1007/978-3-642-04747-3_25
  29. Sulzmann, J.N. and Furnkranz, J. (2010). Probability estimation and aggregation for rule learning, Technical Report TUDKE-201-03, Knowledge Engineering Group, TU Darmstadt, Darmstadt.
  30. von Mises, R. (1957). Probability, Statistics and the Truth, Macmillan, Dover/New York, NY.
  31. Witten, I.H. and Frank, E. (2005). Data Mining, Elsevier, Amsterdam.
  32. Zadeh, L.A. (1965). Fuzzy sets, Information and Control 8(3): 338-353.10.1016/S0019-9958(65)90241-X
  33. Ziarko, W. (1999). Decision making with probabilistic decision tables, in N. Zhong (Ed.), New Directions in Rough Sets, Data Mining, and Granular-Soft Computing, Proceedings of the 7th International Workshop, RSFDGrC99, Yamaguchi, Japan, Springer-Verlag, Berlin/Heidelberg, New York, NY, pp. 463-471.10.1007/978-3-540-48061-7_57
DOI: https://doi.org/10.2478/v10006-012-0048-z | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 629 - 645
Published on: Sep 28, 2012
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2012 Andrzej Piegat, Marek Landowski, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.