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Contemporary Symbolic Regression Methods and their Relative Performance

Paper · 2021 · William La Cava, Patryk Orzechowski, Bogdan Burlacu et al.

Summary

Progress in symbolic regression (SR) has been hard to measure because studies rely on small, easy, or outdated test problems. They also compare against weak baselines or closed commercial tools such as Eureqa. To address this, the authors built SRBench, an open, reproducible, and revision-controlled benchmark that is open to new contributions. They also extended the Penn Machine Learning Benchmark (PMLB) with 130 datasets whose generating equations are known. In total, 14 SR methods and 7 standard ML regressors were evaluated on 252 problems. These include real-world "black-box" datasets and synthetic ground-truth tasks drawn from Feynman physics equations and Strogatz dynamical systems, with varying target noise. Methods were judged on accuracy, model simplicity, and exact recovery of the true equation. On black-box data, GP-based methods that combine evolution with parameter fitting or semantic search, led by Operon, performed best. They matched or beat gradient-boosted trees while yielding smaller models. For exact equation recovery, AIFeynman excelled only with little or no noise. The work gives the field a shared, living baseline.

Key points

  • Resources: SRBench (github.com/EpistasisLab/srbench) plus 130 new ground-truth SR datasets in PMLB, with metadata on equations and units. Contributed methods must expose a Scikit-learn-style Python API and return the final model as a sympy-compatible string.
  • Accuracy vs. simplicity: On black-box problems, the Pareto front of accuracy versus model size consists of Operon, GP-GOMEA, and DSR.
  • Noise-free recovery: On noise-free ground-truth tasks, AIFeynman recovered exact solutions in 53% of cases, about twice as often as the runner-up GP-GOMEA (27%).
  • Noisy recovery: At noise above 0.01, DSR, gplearn, AFP_FE, and AFP recovered exact solutions more often than AIFeynman. Operon, despite near-perfect test scores, seldom found exact forms.
  • Limitations: Parallel execution was not tested, and real-world data from systems with known first-principles models was not included. Both are planned for future versions.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓Stanford UniversityStanford · United States567 works · 335,190 citations🎓University of PennsylvaniaPhiladelphia · United States241 works · 66,904 citations🎓Harvard UniversityCambridge · United States137 works · 45,850 citations🔬Centrum Wiskunde & InformaticaAmsterdam · Netherlands6 works · 6,228 citations🏥Boston Children's HospitalBoston · United States7 works · 834 citations🎓University of Applied Sciences Upper AustriaWels · Austria2 works · 156 citations

Also on the byline: Universidade Federal do ABC.

 Fields, topics and concepts

📚 Shelves 3The field of science this work belongs to (OpenAlex fields).Computer Science · 19,503 worksArtificial Intelligence · 18,805 worksInformation Systems · 1,888 works

Cite

Cite as William La Cava, Patryk Orzechowski, Bogdan Burlacu, Fabrício Olivetti de França, Marco Virgolin, Ying Jin, Michael Kommenda and Jason H. Moore. 2021. Contemporary Symbolic Regression Methods and their Relative Performance. arXiv:2107.14351.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2107.14351 · arXiv 2107.14351

@misc{cava2021contemporary,
  title = {{Contemporary Symbolic Regression Methods and their Relative Performance}},
  author = {William {La Cava}, Patryk Orzechowski, Bogdan Burlacu, Fabrício Olivetti {de França}, Marco Virgolin, Ying Jin, Michael Kommenda and Jason H. Moore},
  year = {2021},
  doi = {10.48550/arxiv.2107.14351},
  eprint = {2107.14351},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2107.14351}
}

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