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.
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References
Barron, A.R., Xiao, X.: Discussion on MARS. Annals of Statistics 19, 67–82 (1991)
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)
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)
Geman, S., Bienenstock, E., Doursat, R.: Neural Networks and the Bias/Variance Dilemma. Neural Computation 4(1), 1–58 (1992)
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)
Ivakhnenko, A.G.: Polynomial Theory of Complex Systems. IEEE Trans. on Systems, Man, and Cybernetics 1(4), 364–378 (1971)
Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. The MIT Press, Cambridge (1992)
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
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)
Quinlan, R.: C4.5: Programs for Machine Learning. Morgan Kaufmann, San Mateo (1993)
Zhang, B.-T., Mühlenbein, H.: Balancing Accuracy and Parsimony in Genetic Programming. Evolutionary Computation 3(1), 17–38 (1995)
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Nikolaev, N., Iba, H. (1999). Automated Discovery of Polynomials by Inductive Genetic Programming. In: Żytkow, J.M., Rauch, J. (eds) Principles of Data Mining and Knowledge Discovery. PKDD 1999. Lecture Notes in Computer Science(), vol 1704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48247-5_58
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DOI: https://doi.org/10.1007/978-3-540-48247-5_58
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