## 3 Results
### Algorithms Analysis
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Tree** & **Naive Bayes** & **Neural Network** & **Logistic Regression** \\ \hline Tree & & 0.589 & 0.335 & 0.681 \\ Naive Bayes & 0.411 & & 0.215 & 0.475 \\ Neural Network & 0.665 & 0.785 & & 0.767 \\ Logistic Regression & 0.319 & 0.525 & 0.233 & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Logistic loss. Table 3 shows the probabilities that the score for the model in the row is higher than that of the model in the column; small numbers show that the probability of the difference is negligible. The model comparison shown in Table 3 shows that the logistic regression model once again provides the best fit. As illustrated in Table 3, the logistic regression model exhibits the highest AUC value (0.791), thereby indicating its superior overall capacity to discriminate between the various classes. The neural network exhibits a second-best AUC (0.740), yet this value is markedly inferior to that of the logistic regression model. The performance of the tree and naive Bayes models in terms of AUC indicates that they are less effective at distinguishing between the classes. Table 4 reveals that tree exhibits the highest classification accuracy (0.893), indicating that it is the most effective at correctly classifying instances. Moderate accuracies are observed for the neural network (0.561) and logistic regression (0.474). Conversely, naive Bayes has the lowest accuracy (0.107), suggesting poor performance in classifying data correctly. Table 5 reveals that the neural network has the highest F1-score (0.795), indicating an optimal balance between precision and recall. Logistic regression and tree also demonstrate satisfactory performance (0.665 and 0.520, respectively), whereas naive Bayes exhibits the lowest F1-score (0.174), suggesting suboptimal precision and recall balancing. Table 6 reveals that the neural network has the highest precision (0.741), indicating an ability to minimize false positives. Logistic regression also performs well with a precision of 0.525, while naive Bayes and tree demonstrate lower precision values, with naive Bayes exhibiting the lowest precision (0.292). Table 7 reveals that tree has the highest recall (0.893), indicating its effectiveness in identifying all relevant instances. The neural network and logistic regression also demonstrate high recall scores, although not as high as that of tree. Conversely, naive Bayes exhibits a notably low recall (0.200), suggesting a tendency to overlook relevant instances. Table 8 reveals that the neural network exhibits the highest specificity (0.767), indicating its efficacy in identifying negative instances. Both tree and logistic regression demonstrate satisfactory performance with specificity values of 0.681 and 0.319, respectively. Conversely, naive Bayes exhibits lower specificity values, suggesting its diminished capacity in identifying non-relevant instances. Finally, Table 9 reveals that the neural network and logistic regression models exhibit the lowest logistic loss values, indicating superior performance in terms of minimizing prediction error. In contrast, the tree and naive Bayes models demonstrate higher logistic loss, suggesting inferior performance in this regard. Logistic regression excels in AUC and shows competitive results in F1-score, precision, and recall, making it a strong overall model. The neural network performs well in AUC, F1-score, precision, and specificity but struggles with classification accuracy and logistic loss. Tree shows high classification accuracy and recall but is weaker in AUC, precision, and logistic loss. Naive Bayes generally performs poorly across most metrics, including AUC, classification accuracy, precision, recall, and specificity. Overall, logistic regression appears to be the most balanced model, offering strong performance across multiple metrics, while the neural network and tree have their own strengths and weaknesses. Naive Bayes is consistently the least effective across the board.