TY - JOUR
T1 - Quantifying Uncertainties of Residuals in Symbolic Regression via Kriging
AU - Yang, Kaifeng
AU - Affenzeller, Michael
N1 - Publisher Copyright:
© 2022 The Authors. Published by Elsevier B.V.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Gaussian Processes
KW - Genetic Programming
KW - Kriging
KW - Residuals
KW - Uncertainties
KW - White-box modelling
UR - http://www.scopus.com/inward/record.url?scp=85127756883&partnerID=8YFLogxK
U2 - 10.1016/j.procs.2022.01.293
DO - 10.1016/j.procs.2022.01.293
M3 - Conference article
AN - SCOPUS:85127756883
VL - 200
SP - 954
EP - 961
JO - Procedia Computer Science
JF - Procedia Computer Science
T2 - 3rd International Conference on Industry 4.0 and Smart Manufacturing, ISM 2021
Y2 - 19 November 2021 through 21 November 2021
ER -