A robust elastic net via bootstrap method under sampling uncertainty for significance analysis of high-dimensional design problems

Abstract

Y The elastic net can analyze the significance of input variables regardless of the data type of input variables and statistical assumptions. However, the significance can alter owing to sampling uncertainty arising from the design of experiments such as the optimal Latin hypercube design which may generate different datasets at each time even if the same number of data points is sampled. This sampling uncertainty affects elastic net modeling and causes incorrect inferences. Additionally, studies on the reduction of sampling uncertainty for the elastic net are not addressed yet. Therefore, this study proposes a robust elastic net via bootstrap method (RENBOOT) to reduce sampling uncertainty. Relevance of input variables was analyzed using the statistical criterion that is based on bootstrap confidence intervals for estimated coefficients of the elastic net to accurately analyze the significance of input variables. Then, the significance of relevant input variables was analyzed using the significance measure that is based on bootstrap replications for the estimated coefficients of the elastic net. Through mathematical examples, the accuracies (balanced accuracy, F1 score, Cohen's kappa, root mean square error) of the relevance and significance of input variables using RENBOOT were verified to be highly improved compared with those of the elastic net. Furthermore, the significance of input variables for the body-in-white of a vehicle was analyzed using RENBOOT, which can give useful information for significant input variable selection. That is, we expect that design optimization can be performed efficiently by selecting significant input variables based on the significance via RENBOOT.