Development of a Wilks feature importance method with improved variable rankings for supporting hydrological inference and modelling

Abstract. Feature importance has been a popular approach for machine learning models to investigate the relative significance of model predictors. In this study, we developed a Wilks feature importance (WFI) method for hydrological inference. Compared with conventional feature importance methods such as permutation feature importance (PFI) and mean decrease impurity (MDI), the proposed WFI aims to provide more reliable variable rankings for hydrological inference. To achieve this, WFI measures the importance scores based on Wilks Λ (a test statistic that can be used to distinguish the differences between two or more groups of variables) throughout an inference tree. Compared with PFI and MDI methods, WFI does not rely on any performance measures to evaluate variable rankings, which can thus result in less biased criteria selection during the tree deduction process. The proposed WFI was tested by simulating monthly streamflows for 673 basins in the United States and applied to three interconnected irrigated watersheds located in the Yellow River basin, China, through concrete simulations for their daily streamflows. Our results indicated that the WFI could generate stable variable rankings in response to the reduction of irrelevant predictors. In addition, the WFI-selected predictors helped random forest (RF) achieve its optimum predictive accuracy, which indicates that the proposed WFI could identify more informative predictors than other feature importance measures.