Advertisement

Adaptation, Performance and Vapnik-Chervonenkis Dimension of Straight Line Programs

  • José L. Montaña
  • César L. Alonso
  • Cruz E. Borges
  • José L. Crespo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5481)

Abstract

We discuss here empirical comparation between model selection methods based on Linear Genetic Programming. Two statistical methods are compared: model selection based on Empirical Risk Minimization (ERM) and model selection based on Structural Risk Minimization (SRM). For this purpose we have identified the main components which determine the capacity of some linear structures as classifiers showing an upper bound for the Vapnik-Chervonenkis (VC) dimension of classes of programs representing linear code defined by arithmetic computations and sign tests. This upper bound is used to define a fitness based on VC regularization that performs significantly better than the fitness based on empirical risk.

Keywords

Genetic Programming Linear Genetic Programming Vapnik-Chervonenkis dimension 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Giusti, M., Heintz, J., Morais, J.E., Pardo, L.M.: Straight line programs in Geometric elimination Theory. Journal of Pure and Applied Algebra 124, 121–146 (1997)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Alonso, C.L., Montaña, J.L., Puente, J.: Straight line programs: a new Linear Genetic Programming Approach. In: Proc. 20th IEEE International Conference on Tools with Artificial Intelligence, ICTAI, pp. 517–524 (2008)Google Scholar
  3. 3.
    Brameier, M., Banzhaf, W.: Linear Genetic Programming. Springer, Heidelberg (2007)zbMATHGoogle Scholar
  4. 4.
    Aldaz, M., Heintz, J., Matera, G., Montaña, J.L., Pardo, L.: Time-space tradeoffs in algebraic complexity theory. Journal of Complexity 16, 2–49 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Teytaud, O., Gelly, S., Bredeche, N., Schoenauer, M.A.: Statistical Learning Theory Approach of Bloat. In: Proceedings of the 2005 conference on Genetic and Evolutionary Computation, pp. 1784–1785 (2005)Google Scholar
  6. 6.
    Vapnik, V., Chervonenkis, A.: Ordered risk minimization. Automation and Remote Control 34, 1226–1235 (1974)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Vapnik, V.: Statistical learning theory. John Wiley & Sons, Chichester (1998)zbMATHGoogle Scholar
  8. 8.
    Vapnik, V., Chervonenkis, A.: On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and its Applications 16, 264–280 (1971)CrossRefzbMATHGoogle Scholar
  9. 9.
    Lugosi, G.: Pattern classification and learning theory. In: Principles of Nonparametric Learning, pp. 5–62. Springer, Heidelberg (2002)Google Scholar
  10. 10.
    Karpinski, M., Macintyre, A.: Polynomial bounds for VC dimension of sigmoidal and general Pffafian neural networks. J. Comp. Sys. Sci. 54, 169–176 (1997)CrossRefzbMATHGoogle Scholar
  11. 11.
    Milnor, J.: On the Betti Numbers of Real Varieties. Proc. Amer. Math. Soc. 15, 275–280 (1964)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Cherkassky, V., Yunkian, M.: Comparison of Model Selection for Regression. Neural Computation 15, 1691–1714 (2003)CrossRefzbMATHGoogle Scholar
  13. 13.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. The MIT Press, Cambridge (1992)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • José L. Montaña
    • 1
  • César L. Alonso
    • 2
  • Cruz E. Borges
    • 1
  • José L. Crespo
    • 3
  1. 1.Departamento de Matemáticas, Estadística y ComputaciónUniversidad de CantabriaSantanderSpain
  2. 2.Centro de Inteligencia ArtificialUniversidad de OviedoGijónSpain
  3. 3.Departamento de Matemática Aplicada, Estadística y Ciencias de la ComputaciónUniversidad de CantabriaSantanderSpain

Personalised recommendations