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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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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