Regression and independence based variable importance measure Abstract   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 HilbertSchmidt 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, PLSxcexb2, PLSVIP, Lasso, HSIC, and permutation importance with random forest in the variable identification accuracy.

Quantifying Total Influence between Variables with Information Theoretic and Machine Learning Techniques The increasingly sophisticated investigations of complex systems require more robust estimates of the correlations between the measured quantities. The traditional Pearson correlation coefficient is easy to calculate but sensitive only to linear correlations. The total influence between quantities is, therefore, often expressed in terms of the mutual information, which also takes into account the nonlinear effects but is not normalized. To compare data from different experiments, the information quality ratio is, therefore, in many cases, of easier interpretation. On the other hand, both mutual information and information quality ratio are always positive and, therefore, cannot provide information about the sign of the influence between quantities. Moreover, they require an accurate determination of the probability distribution functions of the variables involved. As the quality and amount of data available are not always sufficient to grant an accurate estimation of the probability distribution functions, it has been investigated whether neural computational tools can help and complement the aforementioned indicators. Specific encoders and autoencoders have been developed for the task of determining the total correlation between quantities related by a functional dependence, including information about the sign of their mutual influence. Both their accuracy and computational efficiencies have been addressed in detail, with extensive numerical tests using synthetic data. A careful analysis of the robustness against noise has also been performed. The neural computational tools typically outperform the traditional indicators in practically every respect.