Gaining Hydrological Insights Through Wilk's Feature Importance: A Test-Statistic Interpretation method for Reliable and Robust Inference

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 Wilk's feature importance (WFI) method for hydrological inference. Compared with conventional feature importance methods such as permutation feature importance (PFI) and mean decrease in impurity (MDI), the proposed WFI aims to provide more reliable importance scores that could partially address the equifinality problem in hydrology. To achieve this, the WFI measures the importance scores based on Wilk's Ʌ (a test-statistic that can be used to distinguish the differences between two or more groups of variables) throughout a decision tree. The WFI has an advantage over PFI and MDI as it does not account for predictive accuracy so the risk of overfitting will be greatly reduced. The proposed WFI was applied to three interconnected irrigated watersheds located in the Yellow River Basin, China. By employing the recursive feature elimination approach, our results indicated that the WFI could generate more stable relative importance scores in response to the reduction of irrelevant predictors, as compared with PFI and MDI embedded in three different machine learning algorithms. In addition, the comparative study also shows that the predictors identified by WFI achieved the highest predictive accuracy on the testing dataset, which indicates the proposed WFI could identify more informative predictors among many irrelevant ones. We also extended the WFI to the local importance scores for reflecting the varying characteristics of a predictor in the hydrological processes. The related findings could help to gain insights into different hydrological behaviours.