Contemporary Symbolic Regression Methods and their Relative Performance
Paper in proceeding, 2021

Many promising approaches to symbolic regression have been presented in recent years, yet progress in the field continues to suffer from a lack of uniform, robust, and transparent benchmarking standards. We address this shortcoming by introducing an open-source, reproducible benchmarking platform for symbolic regression. We assess 14 symbolic regression methods and 7 machine learning methods on a set of 252 diverse regression problems. Our assessment includes both real-world datasets with no known model form as well as ground-truth benchmark problems. For the real-world datasets, we benchmark the ability of each method to learn models with low error and low complexity relative to state-of-the-art machine learning methods. For the synthetic problems, we assess each method’s ability to find exact solutions in the presence of varying levels of noise. Under these controlled experiments, we conclude that the best performing methods for real-world regression combine genetic algorithms with parameter estimation and/or semantic search drivers. When tasked with recovering exact equations in the presence of noise, we find that several approaches perform similarly. We provide a detailed guide to reproducing this experiment and contributing new methods, and encourage other researchers to collaborate with us on a common and living symbolic regression benchmark.

Author

William La Cava

University of Pennsylvania

Harvard Medical School

Patryk Orzechowski

AGH University of Science and Technology

University of Pennsylvania

Bogdan Burlacu

University of Applied Sciences Upper Austria

Fabrício Olivetti de França

Analysis and Learning Laboratory

Universidade Federal do ABC

Marco Virgolin

Stichting Centrum voor Wiskunde & Informatica (CWI)

Chalmers, Mechanics and Maritime Sciences (M2), Vehicle Engineering and Autonomous Systems

Ying Jin

Stanford University

Michael Kommenda

University of Applied Sciences Upper Austria

Jason H. Moore

University of Pennsylvania

Advances in Neural Information Processing Systems

10495258 (ISSN)

Vol. 2021

35th Conference on Neural Information Processing Systems - Track on Datasets and Benchmarks, NeurIPS Datasets and Benchmarks 2021
Virtual, Online, ,

Subject Categories (SSIF 2025)

Computer Sciences

More information

Latest update

4/2/2025 9