Contemporary Symbolic Regression Methods and their Relative Performance

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. ∗corresponding author. Formerly Institute for Biomedical Informatics, University of Pennsylvania †Department of Automatics and Robotics, AGH University of Science and Technology, Krakow, Poland ‡Center for Mathematics, Computation and Cognition | Heuristics, Analysis and Learning Laboratory §Formerly (during preparation of this paper) at Chalmers University of Technology, Sweden 35th Conference on Neural Information Processing Systems (NeurIPS 2021) Track on Datasets and Benchmarks.