Regression and independence based variable importance measure

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-beta, PLS-VIP, Lasso, HSIC, and permutation importance with random forest in the variable identification accuracy. (C) 2020 Elsevier Ltd. All rights reserved.