Quantifying Uncertainties of Residuals in Symbolic Regression via Kriging

Genetic programming (GP) based symbolic regression is a powerful technique for white-box modelling. However, the prediction uncertainties of the symbolic regression are still unknown. This paper proposes to use Kriging to model the residual of a symbolic expression. The residual model follows a normal distribution with parameters of a mean value and a standard deviation, where the mean value can be used to regulate the prediction and the standard deviation represents the uncertainties of residuals in a specific symbolic expression. The proposed algorithms are compared with a canonical GP-based symbolic regression and Kriging regression on three benchmarks in symbolic regression field. The results show that the proposed algorithm significantly outperforms the other two algorithms on the three benchmarks w.r.t. mean squared error in the test dataset with a small generation budget.