## 3 Modeling and Results
### Development and Assessment of PSVE Model
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **DT** & **RF** & **KNN** & **MLP** \\
**and Results** & & & & & \\ \hline Parameter 1 & Max\_depth\({}^{1}\): [8; 10; 12, 14, 16] & Max\_depth\({}^{1}\): [8; 10; 12, 14, 16] & N\_neighbors \({}^{5}\): [13; 14, 16] & Activate \({}^{7}\): [”relu’, ’ \\ Parameter 2 & Min\_samples\_leaf\({}^{2}\): [4, 16, 12] & Min\_samples\_leaf\({}^{2}\): [3, 16, 17] & Rush\({}^{6}\): [’uniform’, \\  & 6, 8, 10, 12] & 4, 5, 6, 7] & ‘**distance’**] & Hidden layer sizes \({}^{8}\): \\ Parameter 3 & Min\_sample\_split\({}^{3}\): [4, 16, 12] & Min\_sample split \({}^{3}\): [4, 16, 12] & / & [’constant’, ‘**in**scaling’, \\  & 5, 6, 7, 8] & 5, 6, 7, 8] & & ‘adaptive’] \\ Parameter 4 & / & N\_estimators \({}^{4}\): [58; 60, 12] & / & Max iter \({}^{10}\): (500, 2000, \\ Mean deviation & 0.010 & 0.10 & 0.013 & 0.019 \\ Standard deviation & 0.011 & 0.011 & 0.011 & 0.014 \\ \hline \hline \end{tabular}  
* Max_depth: the maximum depth of the tree; \({}^{2}\) max\_samples\_leaf: the minimum number of samples that the final node must contain; \({}^{3}\) min\_sample\_split: the minimum number of samples divided between internal nodes; \({}^{4}\) N\_estimators: the number of trees in a random forest; \({}^{5}\) N\_neighbors: the number of neighbors to be considered for classification; \({}^{6}\) weights: neighbor weight during voting; \({}^{7}\) activate: introduce nonlinearity to the neural network; \({}^{8}\) hidden layer sizes: hidden layer sizes; \({}^{9}\) learning rates: invscaling indicates that the learning rate decreases with time; \({}^{10}\) max\_iter: maximum number of iterations of the optimizer.  
\end{table} 
Table 2: Parameter configuration and final selection. Figure 6: The performance of the model improved after hyperparameter tuning; the black box line represents the improved part. The training score of the DT is consistently higher than the validation score, which may indicate demonic overfitting. RF had a small gap in training and validation, showing excellent generalization, while KNN had a slightly larger gap; low volatility indicated that adding data did not significantly improve this, with it most likely reaching its performance bottleneck. The initial performance of MLP was low, but with the increase in training data, the performance improved significantly, indicating that the model performance required a larger amount of data. Furthermore, the training time of MLP during the training process was about ten times that of other models. In conclusion, our evaluation highlights the superior generalization capabilities of the RandomForestClassifier, which consistently achieves high accuracy on both the training and validation datasets. Therefore, we have chosen RandomForestClassifier as the most suitable modeling algorithm for PSVE. RandomForestClassifier is an ensemble learning method that combines multiple decision trees, each trained on different subsets and aggregated for final predictions. It performs well on high-dimensional and large-scale datasets while being less prone to overfitting. Our analysis has recommended the following hyperparameters for model training: 60 trees, a minimum sample leaf of 5, minimum sample split of 7, and maximum depth of 12.