Theta-regularized Kriging: Modelling and Algorithms

TL;DR

This paper introduces Theta-regularized Kriging, a penalized Gaussian process model with novel optimization and tuning algorithms, improving prediction accuracy and stability over existing methods.

Contribution

It develops a new regularized Kriging model with specific penalty methods and optimization algorithms, enhancing model accuracy and stability.

Findings

The proposed model outperforms existing penalized Kriging models in accuracy.

It demonstrates improved stability across multiple numerical and engineering tests.

The model effectively incorporates Lasso, Ridge, and Elastic-net penalties.

Abstract

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.