## 4 Uncertainty Analysis
### The Interpretability of \"Black-Box\" Models  
Some scholars argue that the high accuracy of machine learning models is not sufficient to guarantee their credibility. Therefore, it is necessary to increase their interpretability so that people can understand the reasons behind their predictions [128, 129, 130]. [PERSON] et al. [131] point out that white-box models like logistic regression and decision trees can provide insight into their prediction mechanisms through their weights or decision nodes. However, models like random forests and artificial neural networks lack this transparency, as the internal complexities hinder understanding of the decision mechanisms. Therefore, interpretable artificial intelligence represents a future research direction. [PERSON] and [PERSON] [132] introduced SHAP (Shapley additive explanations), a method designed to explain the predictions of various models to non-users, particularly when the reasons behind the predictions in black-box models are difficult to understand. SHAP quantifies the contribution of each evaluation factor in the model and explains the model's predictions as the sum of the Shapley values of each input feature, as follows:  
\[\text{g}\big{(}\text{x}^{\prime}\big{)}=\varphi_{0}+\sum_{\text{j}=1}^{\text{M }}\varphi_{\text{j}}\text{x}^{\prime}\]  
In the equation, \(\text{g}(\text{x}^{\prime})\) represents the model's predicted value; \(\text{x}^{\prime}\in\{0,1\}^{\text{M}}\), where \(\text{x}^{\prime}=1\) if the sample contains factor j, otherwise \(\text{x}^{\prime}=0\); \(\varphi_{0}\) is the constant for explaining the model (i.e., the mean prediction of all training samples); \(\varphi_{\text{j}}\) is the estimated value (Shapley value) for each feature. The SHAP interpretability analysis process is shown in Figure 8. The SHAP method can calculate the Shapley value of each feature in an individual sample for local explanations, demonstrating the contribution of each feature to the predicted value [133]. Additionally, it can combine individual local explanations for global explanations, ensuring a high level of consistency between local and global explanations [134]. [PERSON] [135] utilized SHAP models to provide explanations at both global and local levels for landslide susceptibility in the study area, using summary plots, dependency plots, and waterfall plots. The results indicated that factors such as the water dynamic index, rainfall conditions, and elevation were the primary influencers of landslides, which finding was consistent with the findings from field surveys. [PERSON] et al. [136] utilized the SHAP algorithm to explain the landslide event on the Shangshan Highway in Baitaping, Hechuan District. They found that factors such as slope, terrain ruggedness, the NDVI (normalized difference vegetation index), and POI (point of interest) density promoted landslide occurrences, while factors such as lithology and elevation inhibited them. This effectively explained the intrinsic causal mechanisms of individual landslides, providing reference for future research into landslide susceptibility. [PERSON] et al. [129] proposed a comprehensive explanation framework based on the SHAP-XGBoost model, which quantifies the importance and contribution of factors at both global and local levels. This framework provides a reference for research on machine learning interpretability. In addition, landslide evaluation factors can also be ranked through ROC-AUC analysis. [PERSON] et al. [136] excluded one factor at a time from the random forest analysis and calculated the relative difference in AUC between the model that excluded the factor and the model that included all factors. The difference in importance is expected to be related to larger differences. The random forest model can utilize the out-of-bag (OOB) sorting function to assess the importance of each factor in landslide events (Figure 9). The principle behind this is that the more important the evaluation factor, the faster the OOB accuracy decreaseswhen adding random noise to the specified evaluation factor.