Theta-regularized Kriging: Modelling and Algorithms
For practitioners using Kriging models, this work offers a regularization approach that enhances prediction accuracy and stability, though it is an incremental improvement over existing penalized Kriging methods.
The paper introduces a Theta-regularized Kriging model that penalizes the hyperparameter theta to improve parameter estimation and prediction accuracy. Tested on nine numerical functions and two engineering examples, the model outperforms other penalized Kriging models in accuracy and stability.
To obtain more accurate model parameters and improve prediction accuracy, we proposed a regularized Kriging model that penalizes the hyperparameter theta in the Gaussian stochastic process, termed the Theta-regularized Kriging. We derived the optimization problem for this model from a maximum likelihood perspective. Additionally, we presented specific implementation details for the iterative process, including the regularized optimization algorithm and the geometric search cross-validation tuning algorithm. Three distinct penalty methods, Lasso, Ridge, and Elastic-net regularization, were meticulously considered. Meanwhile, the proposed Theta-regularized Kriging models were tested on nine common numerical functions and two practical engineering examples. The results demonstrate that, compared with other penalized Kriging models, the proposed model performs better in terms of accuracy and stability.