## 4 Experiments
Further, for the conducted experiments, several measures were used to evaluate the classification performance. Namely, the accuracy, recall, precision, and the F1-measure were calculated based on the confusion matrix shown in Table 3, where the row corresponds to actual values, and the column reports the predicted values. In particular, TP (True Positive) represents the number of VAT under-reporting cases which the model classified correctly. On the other hand, TN (True Negative) reports the number of correctly predicted actual reporting cases, while FP (False Positive) and FN (False Negative) refer to the number of misclassified cases for both classes. Accordingly, the accuracy is defined as the ratio of correctly categorized instances. It is obtained using:  
\[Accuracy=\frac{TP+TN}{TP+TN+FP+FN} \tag{4}\]  
In addition, the recall represents the ratio of correctly classified under-reporting declarations over all records from this class. It is calculated as follows:  
\[Recall=\frac{TP}{TP+FN} \tag{5}\] \begin{table}
\begin{tabular}{l c} \hline \hline Size & 51,919 \\ \hline Audited returns & 100\% \\ \hline Positive cases & 32.84\% \\ \hline Negative cases & 67.16\% \\ \hline Business categories of taxpayers & 26 \\ \hline Business size of taxpayers & 5 \\ \hline Number of features & 44 \\ \hline \end{tabular}
\end{table} 
Table 2: Data summary. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & \multicolumn{2}{c}{Predicted Class} \\ \cline{3-4}  & & Under-Report & Actual \\ \cline{2-4}  & Under-Report & TN & FP \\ \cline{2-4}  & Actual & FN & TP \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Confusion matrix. Similarly, the precision reports the ratio of correctly categorized declarations over all instances assigned to the under-reporting class. It is obtained as follows:  
\[Precision=\frac{TP}{TP+FP} \tag{6}\]  
Finally, the F1-measure is obtained as a combination for precision and recall using:  
\[F1-measure=\frac{2*Recall*Precision}{Recall+Precision} \tag{7}\]  
To assess the regression performance, appropriate metrics such as the Mean Square Error (MSE), the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE) were used in this research experiments. Specifically, the _MSE_ is defined as an absolute measure of the model's fit goodness. It is calculated using:  
\[MSE=\frac{1}{N}{\sum_{i=1}^{N}}(h(x_{i})-y_{i})^{2} \tag{8}\]  
where \(N\) represents the number of instances in the dataset, while \(y_{i}\) and \(h(x_{i})\) and correspond to the predicted value for the input \(x\) and the actual value, respectively. Additionally, the RMSE measures the performance of the proposed model as a square root of the _MSE_ value:  
\[RMSE=\sqrt{\frac{1}{N}{\sum_{i=1}^{N}}(h(x_{i})-y_{i})^{2}} \tag{9}\]  
Finally, the _MAE_ is calculated as the sum of the error absolute values:  
\[MAE=\frac{1}{N}{\sum_{i=1}^{N}}|h(x_{i})-y_{i}| \tag{10}\]  
Since the proposed model contains two output layers, we have set weights for the loss of each output layer. In other words, the alpha value \((\beta)\) is set as the weight of the regression layer loss and \((1-\beta)\) as the weight of the classification layer loss. Therefore, different values were assigned to \(\beta\) in order to adjust the model and get the best performance for the proposed model. Table 4 proves that the proposed model achieved the best performance using the dataset without resampling when \(\beta\) was set to 0.4. On the other hand, when associating the considered dataset after applying SMOTE and hybrid SMOTE with random under-sampling (RU), the proposed model achieved the best performance for \(\beta\) equal to 0.3. Table 5 shows that the proposed model using the dataset without resampling achieved the lowest performance using a batch size of 512 and a learning rate of 1 \(\times\) 10\({}^{-4}\), while the model, using the dataset after applying SMOTE, achieved better performance with respect to Precision, Recall, and F1-score. Moreover, it yielded a lower regression error