# Generative Modeling for Imbalanced Credit Card Fraud Transaction Detection
## 5 Results and Discussion
Overall, the findings confirm that VAE and ADASYN are the most effective techniques for enhancing the G-mean, whereas GAN, AE-GAN, and AE exhibit comparatively weaker performance in this regard. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Techniques** & **GAN** & **AE-GAN** & **AE** & **VAE** & **SMOTE** & **ADASYN** \\ \hline
**GAN** & - & 0.5829 & 0.4801 & 0.0061 & 0.0012 & 0.0012 \\
**AE-GAN** & - & - & 0.2860 & 0.0076 & 0.0004 & 0.0007 \\
**AE** & - & - & - & 0.0229 & 0.0012 & 0.0017 \\
**VAE** & - & - & - & - & 0.0134 & 0.0134 \\
**SMOTE** & - & - & - & - & - & 0.4801 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Wilcoxon test \(p\)-values for precision comparison between different oversampling techniques. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Techniques** & **GAN** & **AE-GAN** & **AE** & **VAE** & **SMOTE** & **ADASYN** \\ \hline
**GAN** & - & 0.1360 & 0.0060 & 0.0327 & 0.0061 & 0.0061 \\
**AE-GAN** & - & - & 0.0262 & 0.0186 & 0.0061 & 0.0080 \\
**AE** & - & - & - & 0.0843 & 0.0170 & 0.0170 \\
**VAE** & - & - & - & - & 0.0942 & 0.0573 \\
**SMOTE** & - & - & - & - & - & 0.4327 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Wilcoxon test \(p\)-values for f-measure comparison between different oversampling techniques. Table 14 presents the Balanced F-Measure (BFDS) scores for various models across different oversampling techniques, highlighting their effectiveness in handling class imbalance. Among the oversampling techniques evaluated, AE-GAN consistently provides the highest BFDS scores for most models, indicating its superior ability to enhance classifier performance in detecting fraudulent transactions. Specifically, RF, with a BFDS of 0.697, and XGB, with a BFDS of 0.691, achieve the highest scores, showcasing their robustness and precision. These models, combined with AE-GAN, demonstrate the best performance, effectively balancing sensitivity and precision. In comparison, traditional oversampling techniques like SMOTE and ADASYN perform slightly lower, with RF scoring 0.685 and 0.671, respectively, under these methods. While these techniques are still effective, AE-GAN's innovative approach seems to offer a more nuanced enhancement, particularly for ensemble methods like RF and XGB. Deep learning models, such as ANN, also benefit significantly from AE-GAN, achieving a BFDS of 0.692, indicating strong potential for these models in fraud detection tasks. Conversely, simpler models like NB and RNN exhibit poor performance across all oversampling techniques, with notably low BFDS scores, underscoring their limited utility in this context. Overall, the combination of AE-GAN with advanced ensemble methods like RF and XGB emerges as the most effective strategy for fraudulent transaction detection. This combination not only maximizes the BFDS but also ensures a balanced approach to handling class imbalance, making it a superior choice for optimizing model performance in this challenging domain. The Wilcoxon test \(p\)-values for BFDS comparison across various oversampling techniques are presented in Table 15. This table provides a comprehensive statistical analysis of performance differences among the tested methods. The results indicate that VAE exhibits significant improvements over multiple techniques, particularly compared to GAN (\(p\)-value = 0.0024), AE-GAN (\(p\)-value = 0.0002), and AE (\(p\)-value = 0.0075). Similarly, ADASYN demonstrates statistically significant differences when compared to GAN \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Techniques** & **GAN** & **AE-GAN** & **AE** & **VAE** & **SMOTE** & **ADASYN** \\ \hline
**GAN** & - & 0.0843 & 0.0022 & 0.8925 & 0.0034 & 0.0012 \\
**AE-GAN** & - & - & 0.0076 & 0.9374 & 0.0007 & 0.0004 \\
**AE** & - & - & - & 0.2393 & 0.0004 & 0.0002 \\
**VAE** & - & - & - & - & 0.0012 & 0.0002 \\
**SMOTE** & - & - & - & - & - & 0.9374 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Wilcoxon test \(p\)-values for G-mean comparison between different oversampling techniques.