Gaussian Process Regression With Interquartile Range Selection and Stacking Ensemble for Engineering Design

Abstract This study proposes a selection and stacking ensemble based method to facilitate the determination of covariance function type for Gaussian process modeling. The proposed method operates at the model ensemble level, employing multiple Gaussian process models with different types of covariance functions as base learners in a stacking ensemble with a final Gaussian process model as the meta-learner. First, the Pearson correlation coefficients between the leave-one-out predicted responses from each candidate base learner and the actual responses are computed and sorted in ascending order, after which the interquartile range (IQR) is calculated and the candidate base learners that fall below the lower 1.5×IQR are removed. Then, the adjacent gaps between the Pearson correlation coefficients corresponding to the remaining candidate base learners are calculated and sorted in ascending order, and some of the remaining candidate base learners are further removed according to the gaps that lie above the upper 1.5×IQR. Finally, a newly constructed Gaussian process model with Linear covariance function is employed as the meta-learner for final predictions. To validate the effectiveness of the proposed method, six analytical test functions, three engineering datasets, and one simulation case are used for performance study along with three representative approaches. The results demonstrate that the proposed method achieves competitive accuracy and generalization capability. Furthermore, its performance is evaluated across four widely used open-source toolkits for Gaussian process modeling, confirming the robustness of the method.