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Correlation Versus RMSE Loss Functions in Symbolic Regression Tasks

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Genetic Programming Theory and Practice XIX

Part of the book series: Genetic and Evolutionary Computation ((GEVO))

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Abstract

The use of correlation as a fitness function is explored in symbolic regression tasks and its performance is compared against a more typical RMSE fitness function. Using correlation with an alignment step to conclude the evolution led to significant performance gains over RMSE as a fitness function. Employing correlation as a fitness function led to solutions being found in fewer generations compared to RMSE. We also found that fewer data points were needed in a training set to discover correct equations. The Feynman Symbolic Regression Benchmark as well as several other old and recent GP benchmark problems were used to evaluate performance.

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Acknowledgements

Part of this work was funded by the Koza Endowment to MSU. Computer support by MSU’s iCER high-performance computing center is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI, USA

    Nathan Haut & Bill Punch

  2. Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, USA

    Wolfgang Banzhaf

Authors
  1. Nathan Haut
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  2. Wolfgang Banzhaf
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  3. Bill Punch
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Corresponding author

Correspondence to Nathan Haut .

Editor information

Editors and Affiliations

  1. Engineering Sciences Graduate Program, Tecnológico Nacional de México/Instituto Tecnológico de Tijuana, Tijuana, Baja California, Mexico

    Leonardo Trujillo

  2. Heuristic and Evolutionary Algorithms Laboratory, University of Applied Sciences Upper Austria, Wels, Austria

    Stephan M. Winkler

  3. Department of Informatics, Faculty of Sciences, University of Lisbon, Lisbon, Portugal

    Sara Silva

  4. Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, USA

    Wolfgang Banzhaf

8 Appendix

8 Appendix

This appendix lists all 100 AI Feynman problems and their solution using correlation and RMSE as fitness functions, for 0 and 10% noise levels at 3 data points only (Tables 4 and 5). More performance results are available online at https://tinyurl.com/stackGPGPTP.

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Haut, N., Banzhaf, W., Punch, B. (2023). Correlation Versus RMSE Loss Functions in Symbolic Regression Tasks. In: Trujillo, L., Winkler, S.M., Silva, S., Banzhaf, W. (eds) Genetic Programming Theory and Practice XIX. Genetic and Evolutionary Computation. Springer, Singapore. https://doi.org/10.1007/978-981-19-8460-0_2

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  • DOI: https://doi.org/10.1007/978-981-19-8460-0_2

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-8459-4

  • Online ISBN: 978-981-19-8460-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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