Abstract
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.
Highlights
Machine learning (ML) has been used for hydrological forecasting and examining modelling processes underpinned by statistical and physical relationships
All the feature importance methods will be evaluated through recursive feature elimination (RFE) (Guyon et al, 2002) as follows: (1) train stepwise clustered ensemble (SCE) and random forest (RF) models with all predictors; (2) calculate the importance scores using the three interpretation methods embedded in their corresponding models; (3) exclude the three least relevant predictors for each set of the importance scores obtained in step 2; (4) retrain the models using the remaining predictors in step 3; and (5) repeat step 2 to 4 until the number of predictors is less than or equal to a threshold
Our results indicate that the proposed Wilks feature importance (WFI) can provide more robust variable rankings than well-known permutation feature importance (PFI) and mean decrease impurity (MDI) methods
Summary
Machine learning (ML) has been used for hydrological forecasting and examining modelling processes underpinned by statistical and physical relationships. Due to the rapid progress in data science, increased computational power, and recent advances in ML, the predictive accuracy of hydrological processes has been greatly improved (Reichstein et al, 2019; Shortridge et al, 2016). Even though obtaining exact mappings from data input to prediction is technically infeasible for ML models, previous research has shown opportunities to understand the model decisions through either post hoc explanations or statistical summaries of model parameters (Murdoch et al, 2019). Quality interpretable information from ML models is much desired for evolving our understanding of nature’s laws (Reichstein et al, 2019)
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