Evaluating the importance of input (predictor) variables is of interest in many applications of statistical models. However, nonlinearity and correlation among variables make it difficult to measure variable importance accurately. In this work, a novel variable importance measure, called regression and independence based variable importance (RIVI), is proposed. RIVI is designed by integrating Gaussian process regression (GPR) and Hilbert-Schmidt independence criterion (HSIC) so that it is applicable to nonlinear systems. The results of two numerical examples demonstrate that RIVI is superior to several conventional measures including the Pearson correlation coefficient, PLS-β, PLS-VIP, Lasso, HSIC, and permutation importance with random forest in the variable identification accuracy.

在许多统计模型应用中，评估输入（预测变量）变量的重要性是很重要的。但是，变量之间的非线性和相关性使得难以准确地测量变量的重要性。在这项工作中，提出了一种新的变量重要性度量，称为回归和基于独立变量的重要性（RIVI）。RIVI是通过将高斯过程回归（GPR）和希尔伯特-施密特独立性准则（HSIC）集成在一起而设计的，因此它可应用于非线性系统。两个数值例子的结果表明，RIVI优于Pearson相关系数，PLS- β，PLS-VIP，Lasso，HSIC以及在随机森林中在变量识别精度上的置换重要性等几种常规测度。