Symbolic regression for the interpretation of quantitative structure-property relationships

Abstract

The interpretation of quantitative structure–activity or structure–property relationships is important in the field of chemoinformatics. Although multivariate linear regression models are typically interpretable, they do not generally have high predictive abilities. Symbolic regression (SR) combined with genetic programming (GP) is a well-established technique for generating the mathematical expressions that describe the relationships within a dataset. However, SR sometimes produces complicated expressions that are hard for humans to interpret. This paper proposes a method for generating simpler expressions by incorporating three filters into GP-based SR. The filters are further combined with nonlinear least-squares optimization to give filter-introduced GP (FIGP), which improves the predictive ability of SR models while retaining simple expressions. As a proof-of-concept, the quantitative estimate of drug-likeness and the synthetic accessibility score are predicted based on the chemical structures of compounds. Overall, FIGP generates less-complicated expressions than previous SR methods. In terms of predictive ability, FIGP is better than GP, but is outperformed by a support vector machine with a radial basis function kernel. Furthermore, quantitative structure–activity relationship models are constructed for three matching molecular series with biological targets. In the case of one target, the activity prediction models given by FIGP exhibit better predictive ability than multivariate linear regression and support vector regression with the radial basis function kernel, whereas for the remaining cases, FIGP is slightly less accurate than multivariate linear regression.