Lasso Kriging for efficiently selecting a global trend model

Kriging has been more and more widely used as a method to construct surrogate models in a variety of areas within the engineering field. The universal Kriging is less appealing than the ordinary Kriging in the case that an informed decision could be hardly made to select the variables for capturing the global trends in responses. The Penalized Blind Kriging (PBK) systematically carries out model selection with penalizing the likelihood function, which leads to improving the predictive performance of a universal Kriging model. However, the PBK demands the execution of an iterative algorithm, which involves repeatedly solving a possibly time-consuming optimization problem to find a varying optimal solution to the correlation coefficient vector. In this paper, the Lasso Kriging (LK) is proposed to not only improve the predictive performance but avoid the iterative computation. The LK selects the important variables fundamentally by solving a Lasso problem using the LARS algorithm with CV. The one-standard error rule is employed to compensate for less penalizing the regression coefficients than the PBK does. Given the selected important variables, unknown Kriging parameters are estimated in the same manner as in the universal Kriging. A linear and a nonlinear mathematical problem and seven highly nonlinear benchmark problems are used to demonstrate the effectiveness of the LK concerning the model selection and predictive performance as well as the computational efficiency. The LK proves to be an effective approach that both improves predictive accuracy as much as the PBK does and requires a little more computational complexity than the universal Kriging.

Automated summary

Kriging is widely used in engineering fields, with Penalized Blind Kriging (PBK) improving predictive performance by systematically selecting models and penalizing likelihood functions.