Symbol Graph Genetic Programming for Symbolic Regression

Jinglu Song, Qiang Lu, Bozhou Tian, Jingwen Zhang, Jake Luo, Zhiguang Wang

Abstract: This paper tackles the challenge of symbolic regression (SR) with a vast mathematical expression space, where the primary difficulty lies in accurately identifying subspaces that are more likely to contain the correct mathematical expressions. Establishing the NP-hard nature of the SR problem, this study introduces a novel approach named Symbol Graph Genetic Programming (SGGP) (Code is available at https://github.com/SymbolGraph/sggp). SGGP begins by constructing a symbol graph to represent the mathematical expression space effectively. It then employs the generalized Pareto distribution based on semantic similarity to assess the likelihood that each edge (subspace) in this graph will yield superior individuals. Guided by these probabilistic evaluations, SGGP strategically samples new individuals in its quest to discover accurate mathematical expressions. Comparative experiments conducted across three different benchmark types demonstrate that SGGP outperforms 21 existing baseline SR methods, achieving greater accuracy and conciseness in the mathematical expressions it generates.