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Reducing the Structure Space of Bayesian Classifiers Using Some General Algorithms

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Journal of Mathematical Modelling and Algorithms in Operations Research

Abstract

The use of Bayesian Networks (BNs) as classifiers in different application fields has recently witnessed a noticeable growth. Yet, using the Naïve Bayes application, and even the augmented Naïve Bayes, to classifier-structure learning, has been vulnerable to some extent, which accounts for the resort of experts to other more sophisticated types of algorithms. Consequently, the use of such algorithms has paved the way for raising the problem of super-exponential increase in computational complexity of the Bayesian classifier learning structure, with the increasing number of descriptive variables. In this context, the main objective of our present work lies in trying to conceive further solutions to solve the problem of the intricate algorithmic complexity imposed during the learning of Bayesian classifiers structure through the use of sophisticated algorithms. Our results revealed that the newly suggested approach allows us to considerably reduce the execution time of the Bayesian classifier structure learning without any information loss.

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References

  1. Langley, P., Sage, S.: Induction of selective Bayesian classifiers In: Proceedings of the 10th conference on uncertainty in artificial intelligence, pp. 399–406 (1994)

  2. Friedman, N., Geiger, D., Goldszmid, M.: Bayesian network classifiers. Mach. Des., 131–163 (1997)

  3. Pernkopf, F.: Bayesian network classifiers versus selective k-NN classifier. Pattern Recogn., 1–10 (2005)

  4. Stuart, M., Yulan, H., Kecheng, L.: Choosing the best Bayesian classifier : An empirical study. IAENG Int. J. Comput. Sci., 1–10 (2009)

  5. Madden, M.G.: A new Bayesian network structure for classification tasks In: Proceedings of 13th Irish conference on artificial intelligence & cognitive science, pp. 203–208 (2002)

  6. Lerner, B., Malka, R.: Investigation of the K2 algorithm in learning Bayesian network classifiers. Appl. Artif. Intell., 74–96 (2011)

  7. Witten, H.I., Eibe, F.: Data mining: Practical machine learning tools and techniques with java implementations. Morgan Kaufmann, San Mateo (1999)

  8. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science, 671–681 (1983)

  9. Domingos, P., Pazzani, M.: On the optimality of the simple Bayesian classifier under zero-one loss. Mach. Learn., 103–130 (1997)

  10. Cooper, G., Hersovits, E.: A Bayesian method for the induction of probabilistic networks from data. Mach. Learn. 9, 309–347 (1992)

    MATH  Google Scholar 

  11. Spirtes, P., Glymour, C., Scheines, R.: Causation, prediction, and search, 2nd ed. The MIT Press, Cambridge (2000)

    Google Scholar 

  12. Judea, P., Tom, V.: A theory of inferred causation. In: Allen, J., Fikes, R., Sandewall, E. (eds.) Principles of knowledge representation and reasoning, KR’ 91, pp. 441–452 (1991)

  13. Robinson, R.W.: Counting unlabeled acyclic digraphs. Comb. Math. 622, 28–43 (1977)

    Google Scholar 

  14. Tufféry, S.: Data mining et statistique décisionnelle: l’intelligence des données. Editions TECHNIP (2010)

  15. Jain, A.K.: Data clustering: 50 years beyond K-means. Pattern Recogn. Lett. 31, 651–666 (2010)

    Article  Google Scholar 

  16. Chavent, M., Kuentz, V., Liquet, B., Saracco, J.: ClustOfVar: an R package for the clustering of variables The R user conference, p 44. University of Warwick Coventry UK (2011)

  17. Chavent, M., Kuentz, V., Saracco, J.: A partitioning method for the clustering of categorical variables. In: Locarek-Junge, H., Weihs, C. (eds.) Proceedings of the IFCS in classification as a tool for research. Springer, Berlin Heidelberg New York (2009)

  18. Lerman, I.C.: Likelihood linkage analysis (LLA) classification method :An example treated by hand. Biochimie 75(5), 379–397 (1993)

    Article  Google Scholar 

  19. Green, P., Kreiger, A.: A generalized rand-index method for consensus clustering of separate partitions of the same data base. J. Classif., 63–89 (1999)

  20. Chow, C., Liu, C.: Approximating discrete probability distributions with dependence trees. IEEE Trans. Inf. Theory 14(3), 462–467 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  21. Francois, O., Leray, P.: Evaluation d’algorithmes d’apprentissage de structure pour les réseaux bayésiens In: Proceedings of 14ème congrès francophone reconnaissance des formes et intelligence artificielle, pp. 1453–1460 (2004)

  22. Murphy, K.: The BayesNet toolbox for matlab In: Proceedings of Interface on computing science and statistics, p 33 (2001). http://www.ai.mit.edu/~murphyk/Software/BNT/bnt.html

  23. Sprinthall, R.C.: Basic statistical analysis, 7th ed. (2003)

  24. Ezawa, K., Singh, M., Norton, S.: Learning goal oriented Bayesian networks for telecommunications risk management In: Proceedings of the 13th international conference on machine learning, pp. 139–147 (1996)

  25. Porwal, A., Carranza, E., Hale, M.: Bayesian network classifiers for mineral potential mapping. Comput. Geosci. 32, 1–16 (2006)

    Article  Google Scholar 

  26. Malka, R., Lerner, B.: Classification of fluorescence in situ hybridization images using belief networks. Pattern Recogn. Lett. 25, 1777–1785 (2004)

    Article  Google Scholar 

  27. Estevam, R., Hruschka, J., Ebecken, N.: Towards efficient variables ordering for Bayesian networks classifier. Data Knowl. Eng. 63, 258–269 (2007)

    Article  Google Scholar 

  28. Carta, J.A., Velázquez, S., Matías, J.M.: Use of Bayesian networks classifiers for long-term mean wind turbine energy output estimation at a potential wind energy conversion site. Energy Convers. Manag. 52, 1137–1149 (2011)

    Article  Google Scholar 

  29. Kelner, R., Lerner, B.: Learning Bayesian network classifiers by risk minimization. Int. J. Approx. Reason. 53, 248–272 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  30. Chickering, D., Geiger, D., Heckerman, D.: Learning bayesian net-works: Search methods and experimental results In: Proceedings of 5th conference on artificial intelligence and statistics, pp. 112–128 (1995)

  31. Cheng, J., Greiner, R., Kelly, J., Bell, D., Liu, W.: Learning Bayesian networks from data: An information-theory based approach. Artif. Intell. 137(1–2), 43–90 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  32. Chickering, D.M.: Optimal structure identification with greedy search. J. Mach. Learn. Res. 3, 507–554 (2002)

    MathSciNet  Google Scholar 

  33. Lauritzen, S., Speigelhalter, D.: Local computations with probabilities on graphical structures and their application to expert systems. R. Stat. Soc. B 50, 157–224 (1988)

    MATH  Google Scholar 

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Correspondence to Heni Bouhamed.

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Bouhamed, H., Masmoudi, A., Lecroq, T. et al. Reducing the Structure Space of Bayesian Classifiers Using Some General Algorithms. J Math Model Algor 14, 197–237 (2015). https://doi.org/10.1007/s10852-014-9266-8

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  • DOI: https://doi.org/10.1007/s10852-014-9266-8

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