# Generative Modeling for Imbalanced Credit Card Fraud Transaction Detection
## 5 Results and Discussion
Overall, these findings highlight the superior effectiveness of VAE and ADASYN in enhancing sensitivity, while GAN and AE-GAN are comparatively less impactful. Table 11 presents the \(p\)-values obtained from the Wilcoxon Rank-Sum test for precision comparisons among different oversampling techniques. The results indicate that VAE significantly outperforms GAN, AE-GAN, and AE in terms of precision, with \(p\)-values of 0.0061, 0.0076, and 0.0229, respectively, highlighting its effectiveness in improving precision. Similarly, ADASYN demonstrates notable improvements over GAN, AE-GAN, and AE, with \(p\)-values of 0.0012, 0.0007, and 0.0017, respectively, confirming its strong performance. However, there is no significant difference between VAE and ADASYN, as indicated by a \(p\)-value of 0.0134, suggesting comparable performance between these two techniques. SMOTE also shows better precision than GAN and AE, with \(p\)-values of 0.4801 and 0.0012, respectively, but does not significantly differ from VAE or ADASYN, as seen in its \(p\)-values of 0.0134 and 0.4801. In contrast, GAN and AE-GAN exhibit higher \(p\)-values compared to VAE and ADASYN, indicating less substantial improvements in precision. Overall, these \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Techniques** & **GAN** & **AE-GAN** & **AE** & **VAE** & **SMOTE** & **ADASYN** \\ \hline
**GAN** & - & 0.0837 & 0.0022 & 0.6848 & 0.0034 & 0.0012 \\
**AE-GAN** & - & - & 0.0076 & 0.9593 & 0.0007 & 0.0022 \\
**AE** & - & - & - & 0.2549 & 0.0004 & 0.0002 \\
**VAE** & - & - & - & - & 0.0017 & 0.0022 \\
**SMOTE** & - & - & - & - & - & 0.1542 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Wilcoxon test \(p\)-values for sensitivity comparison between different oversampling techniques. findings underscore the superior precision performance of VAE and ADASYN, while GAN and AE-GAN perform relatively worse in this metric. Table 12 presents the \(p\)-values from the Wilcoxon Rank-Sum test for F-measure comparisons across different oversampling techniques. The results show that VAE significantly enhances the F-measure compared to GAN, AE-GAN, and AE, with \(p\)-values of 0.0327, 0.0186, and 0.0843, respectively, reinforcing its effectiveness. ADASYN also demonstrates a significant improvement over GAN, AE-GAN, and AE, with \(p\)-values of 0.0061, 0.0080, and 0.0170, respectively, further validating its strong performance. Additionally, AE-GAN outperforms AE with a \(p\)-value of 0.0262. However, the comparison between VAE and ADASYN does not indicate a significant difference, as shown by a \(p\)-value of 0.0573, suggesting comparable performance in improving F-measure. Conversely, SMOTE does not show a significant advantage over VAE or ADASYN, with \(p\)-values of 0.0942 and 0.4327, respectively, positioning it as less effective in enhancing the F-measure. Nonetheless, SMOTE performs better than GAN and AE-GAN, with \(p\)-values of 0.0061 and 0.0061, respectively. Overall, these findings confirm VAE and ADASYN as the most effective techniques for optimizing the F-measure, while GAN and AE-GAN show comparatively lower performance. Table 13 presents the \(p\)-values from the Wilcoxon Rank-Sum test for G-mean comparisons between different oversampling techniques. The results indicate that VAE significantly enhances the G-mean compared to GAN, AE-GAN, and AE, with \(p\)-values of 0.8925, 0.9374, and 0.2393, respectively, reinforcing VAE's effectiveness in improving the G-mean metric. Similarly, ADASYN demonstrates a substantial improvement over GAN, AE-GAN, and AE, with \(p\)-values of 0.0012, 0.0004, and 0.0002, respectively, highlighting its superior performance. However, there is no significant difference between VAE and ADASYN, as indicated by a \(p\)-value of 0.0002, suggesting comparable G-mean performance between these two techniques. On the other hand, SMOTE does not show a significant improvement over VAE or ADASYN, with \(p\)-values of 0.0012 and 0.9374, respectively, indicating its relatively lower effectiveness in optimizing the G-mean.