## 5 Comprehensive Analysis of Model Robustness, Generalizability, and Interpretability  
### Model Generalization and Statistical Validation  
To evaluate the model's generalization ability under small-sample conditions and mitigate the risk of overfitting, this study adopted a more robust 6-fold cross-validation method (\(k\) = 6). In each fold, seven samples were selected as the test set, with the remaining 35 samples used as the training set, thereby comprehensively assessing the model \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **XGBoost** & **PCA-XGBoost** & **WOA-XGBoost** & **PCA-IWOA-XGBoost** \\ \hline \(R^{2}\) & 0.936 & 0.966 & 0.984 & 0.997 \\ \(RMSE\) & 34.719 & 25.578 & 15.847 & 8.751 \\ \(RPD\) & 6.155 & 8.354 & 13.486 & 24.422 \\ \(MAE\) & 20.466 & 15.133 & 9.791 & 5.366 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comprehensive model evaluation. performance across different subset combinations. This strategy is particularly suitable for earthquake fatality prediction tasks with limited sample sizes (\(n=42\)) and potential heterogeneity in data distribution. In the implementation, the 42 samples were divided into six groups, each containing seven samples, which alternately served as the test set. For example, in the first fold, samples 1-7 were used as the test set, and samples 8-42 as the training set; in the second fold, samples 8-14 were used as the test set, with the remainder as the training set; and so forth, up to the sixth fold (samples 36-42 as the test set). For each fold of cross-validation, the PCA-IWOA-XGBoost model was trained using the same procedure, and its primary performance metrics on the test set, including R\({}^{2}\), RMSE, MAE, and RPD, were calculated. The aggregated results of the 6-fold validation are presented in Table 11, reflecting the model's stability and generalization ability across multiple data splits. The cross-validation experimental results demonstrated that the PCA-IWOA-XGBoost model exhibited extremely high stability and predictive accuracy across the 6-fold cross-validation. The \(R^{2}\) values for each fold were close to 0.99, with minimal fluctuations in _RMSE_ and _MAE_, and an average _RPD_ of 23.80, indicating consistent model performance across the different sample splits. To further mitigate potential biases introduced by sample partitioning, this study also employed Leave-One-Out Cross-Validation (LOOCV) for supplementary validation. In each iteration, one sample was selected as the test set, with the remaining 41 samples used for training, repeated 42 times. The overall performance metrics were \(R^{2}=0.99\), \(RMSE=8.18\), \(MAE=5.02\), and \(RPD=24.11\). The combined results of the 6-fold cross-validation and LOOCV confirmed that the PCA-IWOA-XGBoost model exhibited excellent generalization ability and structural robustness in small-sample scenarios, providing reliable support for high-precision prediction of earthquake fatalities  
To further verify whether the performance differences of the various models in the earthquake fatality prediction task were statistically significant, this study employed the Friedman nonparametric test method for significance analysis based on 6-fold cross-validation. The Friedman test is a robust method suitable for comparing multiple models. The test used the root mean square error (_RMSE_) of each model in the 6-fold cross-validation as the performance metric. For each fold, the _RMSE_ values of the four models (XGBoost, PCA-XGBoost, IWOA-XGBoost, and PCA-IWOA-XGBoost) were recorded and ranked by magnitude, with the smallest _RMSE_ value ranked as 1 and the largest as 4. Ultimately, six sets of ranking data were formed as the input for the Friedman test. The _RMSE_ values and ranking results of each model under the 6-fold cross-validation are summarized in Table 12.