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.

中文翻译：

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Theta 正则化克里金法：建模和算法


为了获得更准确的模型参数并提高预测精度，我们提出了一种对高斯随机过程中的超参数 theta 进行惩罚的正则化克里金模型，称为 Theta 正则化克里金法。我们从最大似然的角度推导了该模型的优化问题。此外，我们还提出了迭代过程的具体实现细节，包括正则化优化算法和几何搜索交叉验证调整算法。我们仔细考虑了三种不同的惩罚方法：Lasso、Ridge 和 Elastic-net 正则化。同时，所提出的 Theta 正则化克里金模型在九个常见数值函数和两个实际工程实例上进行了测试。结果表明，与其他惩罚克里金模型相比，该模型在准确性和稳定性方面表现更好。