Taylor Genetic Programming for Symbolic Regression

TL;DR

This paper introduces TaylorGP, a novel genetic programming approach for symbolic regression that uses Taylor polynomial techniques to improve accuracy and speed by leveraging dataset characteristics.

Contribution

The paper presents TaylorGP, which integrates Taylor polynomial approximations into GP to guide the search process, enhancing stability and efficiency in symbolic regression.

Findings

Higher accuracy than nine baseline methods

Faster convergence to stable results

Effective across classical, machine learning, and physics benchmarks

Abstract

Genetic programming (GP) is a commonly used approach to solve symbolic regression (SR) problems. Compared with the machine learning or deep learning methods that depend on the pre-defined model and the training dataset for solving SR problems, GP is more focused on finding the solution in a search space. Although GP has good performance on large-scale benchmarks, it randomly transforms individuals to search results without taking advantage of the characteristics of the dataset. So, the search process of GP is usually slow, and the final results could be unstable.To guide GP by these characteristics, we propose a new method for SR, called Taylor genetic programming (TaylorGP) (Code and appendix at https://kgae-cup.github.io/TaylorGP/). TaylorGP leverages a Taylor polynomial to approximate the symbolic equation that fits the dataset. It also utilizes the Taylor polynomial to extract the features of the symbolic equation: low order polynomial discrimination, variable separability, boundary, monotonic, and parity. GP is enhanced by these Taylor polynomial techniques. Experiments are conducted on three kinds of benchmarks: classical SR, machine learning, and physics. The experimental results show that TaylorGP not only has higher accuracy than the nine baseline methods, but also is faster in finding stable results.