## 3 Results
### Classification Performance  
This section presents the classification results provided by linear (LASSO and SVM) and nonlinear (DT and KNN) classifiers using SMOTEN, TVAE, and CTGAN and considering different resampling strategies. In Figure 5, we show the mean and std of sensitivity and AUC values on 5 test subset partitions, considering different classifiers (LASSO, SVM, DT and KNN) and oversampling strategies. It can be seen that there is a direct relationship between the IR and the model performance in terms of sensitivity and AUC, indicating that the higher the number of synthetic samples generated, the better the performance of the ML models. By analyzing Figure 5a,c,e, it can be observed that the sensitivity values present high variability for the DT model and all oversampling methods. On the contrary, the linear models LASSO and SVM present lower variability (low std), being the most robust classifiers. For small IR values (0.4), the AUC is approximately 0.6 for all models (see Figure 5b,d,f), achieving better performance when the IR increases. The highest AUC values are obtained when CTGAN linear models are considered (see Figure 5f). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **KLD** & **HD** & **MAEP** & **RSVR** & **PCD** & **LCM** \\ \hline SMOTEN & 0.092 \(\pm\) 0.004 & 0.168 \(\pm\) 0.006 & 0.298 \(\pm\) 0.014 & 0.609 \(\pm\) 0.011 & 0.005 \(\pm\) 0.001 & \(\mathbf{-8.116\pm 0.407}\) \\ TVAE & 0.299 \(\pm\) 0.022 & 0.313 \(\pm\) 0.013 & 0.590 \(\pm\) 0.032 & 0.177 \(\pm\) 0.020 & 0.006 \(\pm\) 0.001 & \(\mathbf{-3.926\pm 0.517}\) \\ CTGAN & \(\mathbf{0.017\pm 0.002}\) & \(\mathbf{0.061\pm 0.003}\) & \(\mathbf{0.145\pm 0.006}\) & \(\mathbf{0.001\pm 0.001}\) & \(\mathbf{0.003\pm 0.001}\) & \(\mathbf{-6.110\pm 0.235}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean \(\pm\) std (evaluated on 5 training partitions) of the data quality metrics for different oversampling techniques when considering IR = 1.0. The best values are shown in bold. Figure 5: Mean \(\pm\) std of the sensitivity (left panels) and AUC (right panels) considering 5 test subset partitions and different IR values, classifiers (LASSO, SVM, DT and KNN) and an oversampling approach with: (**a,b**) SMOTEN; (**c,d**) TVAE; and (**e,f**) CTGAN. In general, the best figures of merit are obtained when applying linear models and considering SMOTEN and CTGAN techniques. The results obtained for TVAE are slightly different, where higher values are obtained with the nonlinear KNN model than with the linear models, specifically when IR increases. We can conclude that the best performance is obtained when considering CTGAN and IR = 1.0, i.e., when the number of samples of the minority and the majority classes is the same. Next, we show in Figure 6, the sensitivity and AUC values when using different classifiers and the hybrid resampling approach. Two main insights can be drawn. Firstly, in general terms and referring to the six panels, it can be observed that the increase in the IR values (from 0.5 to 1.0), which refers to the increase in the generation of the number of samples of the minority class, does not have a positive impact on the classification measures (neither for sensitivity nor for AUC). For this approach, generating a high number of synthetic samples from the minority class and training the ML classifiers with a more substantial number of synthetic data does not imply obtaining a better predictive performance. This indicates that, after a given IR value, no matter how many additional samples are added, the performance remains unchanged. In terms of sensitivity and AUC, it is interesting to note that linear models (LASSO and SVM) using SMOTEN and CTGAN provide best performance than when using nonlinear models such as DT and KNN. Table 3 summarizes the best sensitivity and AUC values using different resampling methods and class balancing strategies.