Genetic Programming and Evolvable Machines

, Volume 5, Issue 3, pp 259–269

Scaled Symbolic Regression

Authors

  • Maarten Keijzer
Article

DOI: 10.1023/B:GENP.0000030195.77571.f9

Cite this article as:
Keijzer, M. Genet Program Evolvable Mach (2004) 5: 259. doi:10.1023/B:GENP.0000030195.77571.f9

Abstract

Performing a linear regression on the outputs of arbitrary symbolic expressions has empirically been found to provide great benefits. Here some basic theoretical results of linear regression are reviewed on their applicability for use in symbolic regression. It will be proven that the use of a scaled error measure, in which the error is calculated after scaling, is expected to perform better than its unscaled counterpart on all possible symbolic regression problems. As the method (i) does not introduce additional parameters to a symbolic regression run, (ii) is guaranteed to improve results on most symbolic regression problems (and is not worse on any other problem), and (iii) has a well-defined upper bound on the error, scaled squared error is an ideal candidate to become the standard error measure for practical applications of symbolic regression.

genetic programminglinear regressionsymbolic regression

Copyright information

© Kluwer Academic Publishers 2004