Robust Kriging models in computer experiments
针对克里金模型在存在异常值时预测误差大的问题，提出用L1和ε不敏感损失函数替代L2准则来稳健估计模型参数，并通过加工实验数据验证了方法的有效性。
In the Gaussian Kriging model, errors are assumed to follow a Gaussian process. This is reasonable in many cases, but such an assumption is not appropriate for the situations when outliers are present. Large prediction errors may occur in those cases and more robust estimation is critical. In this article, we propose a robust estimation of Kriging parameters by utilizing other loss functions rather than classical L2. In the Gaussian Kriging model, regression parameters are estimated by generalized least squares, which are also referred to as L2 criterion. To make these estimators more robust to outliers, the L1 and the ɛ-insensitive loss functions are introduced in place of L2 in this article. Mathematical programming formulations are developed upon the idea of support vector machine. A machining experiment data are analysed to verify usefulness of the proposed method.