# Explainable Machine Learning for Mapping Rainfall-Induced Landslide Thresholds in Italy
## 3 Results
### SHAP Value Analysis  
SHAP analysis was applied to the trained XGBoost model on the test set to systematically investigate feature importance in landslide prediction, quantifying each variable's contribution to the predictive process. As shown in Figure 5a, total rainfall emerges as the primary driver of model predictions, with a mean SHAP value of approximately 5.0--far surpassing the contributions of other variables. Rainfall intensity ranked second (mean SHAP value \(\approx\) 0.3), followed by soil moisture (mean SHAP value \(\approx\) 0.15), highlighting the crucial role of hydrological factors in the predictive model. In comparison, topographic and environmental variables--including elevation, distance to river, plan curvature, soil type, profile curvature, distance to road, lithology, land use, slope, and aspect--all exhibited relatively low importance (mean SHAP values < 0.1), reflecting their limited contribution to rainfall threshold modeling within this modeling framework, though they still play a role to a certain extent in the modeling process. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **AUC** & **Sensitivity** & **Specificity** & **F1 Score** & **Precision** & **Optimized Hyperparameter** \\ \hline XGBoost & 0.917 \(\pm\) 0.026 & 0.792 \(\pm\) 0.075 & 0.812 \(\pm\) 0.033 & 0.731 \(\pm\) 0.037 & 0.681 \(\pm\) 0.032 & \begin{tabular}{c} n\_estimators = 200, \\ max\_depth = 40, \\ learning\_rate = 0.01, \\ subsample = 0.8, \\ \end{tabular} \\ \hline Random Forest & 0.916 \(\pm\) 0.026 & 0.696 \(\pm\) 0.134 & 0.906 \(\pm\) 0.043 & 0.736 \(\pm\) 0.063 & 0.795 \(\pm\) 0.059 & \begin{tabular}{c} n\_estimators = 200, \\ max\_depth = 40, \\ min\_samples\_split = 5, \\ min\_samples\_leaf = 2, \\ max\_features = ‘sqrt’ \\ \end{tabular} \\ \hline LightGBM & 0.917 \(\pm\) 0.026 & 0.670 \(\pm\) 0.111 & 0.930 \(\pm\) 0.035 & 0.739 \(\pm\) 0.074 & 0.831 \(\pm\) 0.060 & \
\begin{tabular}{c} n\_estimators = 300, \\ max\_depth = 20, \\ learning\_rate = 0.01, \\ subsample = 0.8, \\ subsample\_bytree = 0.8 \\ \end{tabular} \\ \hline Logistic Regression & 0.813 \(\pm\) 0.016 & 0.699 \(\pm\) 0.085 & 0.747 \(\pm\) 0.137 & 0.637 \(\pm\) 0.032 & 0.597 \(\pm\) 0.099 &
\begin{tabular}{c} C = 0.1, penalty = ‘elasticnet’, \\ solver = ‘saga’, \\ max\_iter = 500 \\ \end{tabular} \\ \hline E-D curve & 0.903 \(\pm\) 0.032 & 1.000 \(\pm\) 0.000 & 0.219 \(\pm\) 0.034 & 0.565 \(\pm\) 0.012 & 0.394 \(\pm\) 0.012 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Model performance and hyperparameter configurations of machine learning models. Figure 5b reveals complex relationships between feature values and landslide prediction, exhibiting distinct patterns in how different variables influence model outputs. Total rainfall exerted the strongest influence, with higher values (red points) consistently generating SHAP contributions ranging from 2 to 6, while lower values (blue points) yielded contributions around \(-8\). This pattern indicated a clear threshold effect, where the amount of rainfall critically determines the landslide risk. Rainfall intensity and soil moisture followed similar trends, with elevated values increasing the landslide probability through enhanced SHAP contributions. Conversely, high elevation values correlated with reduced SHAP contributions, whereas the distance to river exhibits the reverse pattern. Figure 5: (a) SHAP feature importance ranking and (b) SHAP summary plot for numerical features. Topographic features such as slope presented more nuanced behavior, displaying both positive and negative SHAP values across different ranges, suggesting that terrain factors exert varying effects depending on specific environmental conditions. This analysis encompassed only numerical features, as categorical variables were excluded due to their encoded representations lacking meaningful interpretation within the SHAP analytical framework.