# Generative Modeling for Imbalanced Credit Card Fraud Transaction Detection
## 5 Results and Discussion
Simpler models such as Logistic Regression (LR) and Naive Bayes (NB) underperformed despite having high sensitivity (0.955882 for LR and 0.911765 for NB), with low precision (0.016447 and 0.035048, respectively) and corresponding low F-measures (0.032338 and 0.067501). GB and AB also showed weak performance in precision (0.044720 and 0.025422) and F-measure (0.085442 and 0.049476), highlighting their difficulty in effectively handling the oversampled data. Overall, ensemble-based models--particularly RF, XGB, and ANN--demonstrated the best performance under ADASYN, achieving a strong balance between sensitivity and precision. In contrast, simpler models like LR, NB, and boosting algorithms struggled to maintain high precision, limiting their effectiveness in this context. The bar plots Figure 12 highlight the performance of various classifiers with ADASYN in fraud detection. RF is the top performer, excelling in accuracy, specificity, sensitivity, and F-measure. XGB and ANN also show strong results, particularly in sensitivity and F-measure. LR struggles with precision and F-measure, while GB and AB underperform in these metrics. NB has moderate performance but is weaker in fraud detection. KNN, LGBM, and RNN show consistent sensitivity but need improvement in precision and F-measure. Overall, RF and XGB lead in performance, while LR and AB require further optimization. To assess the effectiveness of the proposed methods, we employed a Wilcoxon Rank-Sum test at a 95% confidence level. This non-parametric test is used to determine whether  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Accuracy** & **Specificity** & **Sensitivity** & **Precision** & **F-Measure** & **G-Mean** \\ \hline LR & 0.908945 & 0.908870 & 0.955882 & 0.016447 & 0.032338 & 0.932080 \\ DT & 0.998022 & 0.998359 & 0.786765 & 0.433198 & 0.558747 & 0.886269 \\ RF & 0.999544 &  
there are significant differences between two independent samples. After resampling the dataset, the resampled datasets were used to train six different classifiers. The classifiers' performances were evaluated using various metrics. To compare the resampling techniques, the average performance metrics were calculated. The null hypothesis \(H_{0}\) and alternative hypothesis \(H_{1}\) for the Wilcoxon Rank-Sum test in this case can be formulated as follows:  
* **Null Hypothesis \(H_{0}\)** : There is no significant difference between the performance metrics of the two oversampling methods when applied to the resampled datasets. * **Alternative Hypothesis \(H_{1}\)**: There is a significant difference between the performance metrics of the two oversampling methods when applied to the resampled datasets. The results of the statistical significance tests are presented in Tables 10-13, which show the \(p\)-values for comparisons of sensitivity, precision, F-measure, and G-mean, respectively. These tables display the \(p\)-values obtained from the Wilcoxon test for comparisons between pairs of resampling techniques for sensitivity, precision, F-measure, and G-mean metrics. Table 10 presents the \(p\)-values from the Wilcoxon Rank-Sum test for sensitivity comparisons among various oversampling techniques. The results indicate that VAE significantly improves sensitivity compared to GAN, AE-GAN, and AE, with \(p\)-values of 0.6848, 0.9593, and 0.2549, respectively, suggesting its effectiveness. Similarly, ADASYN demonstrates notable improvements over GAN, AE-GAN, and AE, with \(p\)-values of 0.0012, 0.0022, and 0.0002, respectively, confirming its strong performance. However, the difference between VAE and ADASYN is not statistically significant, as indicated by a \(p\)-value of 0.0022. SMOTE also exhibits better sensitivity than GAN and AE, with \(p\)-values of 0.0034 and 0.0004, respectively, but does not significantly outperform VAE or ADASYN, as seen in its \(p\)-values of 0.0017 and 0.1542. In contrast, GAN and AE-GAN show relatively higher \(p\)-values compared to VAE and ADASYN, indicating less substantial improvements in sensitivity.