Fast Symbolic Regression Benchmarking

TL;DR

This paper introduces improved benchmarking methods for symbolic regression that use curated acceptable expressions and early stopping, leading to higher rediscovery rates and reduced computational costs for SR algorithms.

Contribution

It proposes new benchmarking techniques with curated expression lists and early termination, enhancing evaluation accuracy and efficiency for symbolic regression algorithms.

Findings

SymbolicRegression.jl rediscovery rate increased from 26.7% to 44.7%.

Benchmarking reduces computational expense by 41.2%.

TiSR achieves a 69.4% rediscovery rate with 63% less time.

Abstract

Symbolic regression (SR) uncovers mathematical models from data. Several benchmarks have been proposed to compare the performance of SR algorithms. However, existing ground-truth rediscovery benchmarks overemphasize the recovery of "the one" expression form or rely solely on computer algebra systems (such as SymPy) to assess success. Furthermore, existing benchmarks continue the expression search even after its discovery. We improve upon these issues by introducing curated lists of acceptable expressions, and a callback mechanism for early termination. As a starting point, we use the symbolic regression for scientific discovery (SRSD) benchmark problems proposed by Yoshitomo et al., and benchmark the two SR packages SymbolicRegression.jl and TiSR. The new benchmarking method increases the rediscovery rate of SymbolicRegression.jl from 26.7%, as reported by Yoshitomo et at., to 44.7%. Performing the benchmark takes 41.2% less computational expense. TiSR's rediscovery rate is 69.4%, while performing the benchmark saves 63% time.