Advertisement

Automated Discovery of Polynomials by Inductive Genetic Programming

  • Nikolay Nikolaev
  • Hitoshi Iba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1704)

Abstract

This paper presents an approach to automated discovery of high-order multivariate polynomials by inductive Genetic Programming (iGP). Evolutionary search is used for learning polynomials represented as non-linear multivariate trees. Optimal search performance is pursued with balancing the statistical bias and the variance of iGP. We reduce the bias by extending the set of basis polynomials for better agreement with the examples. Possible overfitting due to the reduced bias is conteracted by a variance component, implemented as a regularizing factor of the error in an MDL fitness function. Experimental results demonstrate that regularized iGP discovers accurate, parsimonious, and predictive polynomials when trained on practical data mining tasks.

Keywords

Genetic Program Statistical Bias Basis Polynomial Automate Discovery Data Mining Task 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Barron, A.R., Xiao, X.: Discussion on MARS. Annals of Statistics 19, 67–82 (1991)CrossRefGoogle Scholar
  2. 2.
    Freitas, A.A.: A Genetic Programming Framework for two Data Mining Tasks: Classification and Generalized Rule Regression. In: Genetic Programming 1997: Proc. of the Second Annual Conference, pp. 96–101. Morgan Kaufmann, San Francisco (1997)Google Scholar
  3. 3.
    Gama, J.: Oblique Linear Tree. In: Liu, X., Cohen, P., Berthold, M. (eds.) Advances in Intelligent Data Analysis IDA 1997, pp. 187–198. Springer, Berlin (1997)Google Scholar
  4. 4.
    Geman, S., Bienenstock, E., Doursat, R.: Neural Networks and the Bias/Variance Dilemma. Neural Computation 4(1), 1–58 (1992)CrossRefGoogle Scholar
  5. 5.
    Iba, H., de Garis, H.: Extending Genetic Programming with Recombinative Guidance. In: Advances in Genetic Programming 2, pp. 69–88. The MIT Press, Cambridge (1996)Google Scholar
  6. 6.
    Ivakhnenko, A.G.: Polynomial Theory of Complex Systems. IEEE Trans. on Systems, Man, and Cybernetics 1(4), 364–378 (1971)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. The MIT Press, Cambridge (1992)zbMATHGoogle Scholar
  8. 8.
    Merz, C.J., Murphy, P.M.: UCI Repository of machine learning databases, Irvine, CA: University of California, Dept. of Inf. and Computer Science (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html
  9. 9.
    Nikolaev, N., Slavov, V.: Concepts of Inductive Genetic Programming. In: Banzhaf, W., Poli, R., Schoenauer, M., Fogarty, T.C. (eds.) EuroGP 1998. LNCS, vol. 1391, pp. 49–59. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  10. 10.
    Quinlan, R.: C4.5: Programs for Machine Learning. Morgan Kaufmann, San Mateo (1993)Google Scholar
  11. 11.
    Zhang, B.-T., Mühlenbein, H.: Balancing Accuracy and Parsimony in Genetic Programming. Evolutionary Computation 3(1), 17–38 (1995)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Nikolay Nikolaev
    • 1
  • Hitoshi Iba
    • 2
  1. 1.Department of Computer ScienceAmerican University in BulgariaBlagoevgradBulgaria
  2. 2.Department of Information and Communication Engineering, School of EngineeringThe University of TokyoTokyoJapan

Personalised recommendations