## 2 Materials and Methods
### The Optimal Model Selection
#### 2.3.1 GridSearchCV  
GridSearchCV, representing \"Grid Search and Cross Validation\", embodies a meticulous approach for scanning an extensive array of parameter configurations while concurrently conducting cross-validation to identify the most efficacious model settings [54]. This comprehensive methodology is instrumental in harnessing the aggregate predictive capability of the ensemble model, thereby attaining pinnacle levels of accuracy and reliability. Concurrently, a fivefold cross-validation was executed for each permutation of hyperparameters within every pipeline. Table 2 enumerates the hyperparameters necessitated for consideration in each pipeline. Following the delineated procedure, a total of 33,210 models were trained in the scope of this study. The substantial volume of model outcomes generated is pivotal in facilitating the identification of the superl  
Figure 3: Flowchart depicting the process, including GridSearchCV, evaluation criteria, and machine learning algorithm, for selecting the optimal model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pipeline** & **Method** & **Hyperparameter** & **Range of Values** \\ \hline \multirow{6}{*}{PS-XGB} & PCA & n\_components & 2/4/6 \\ \cline{2-3}  & & learning\_rate & 0.01/0.1/0.5 \\  & & n\_estimators & 50/100/200 \\ \multirow{2}{*}{PS-XGB} & XGBoost & max\_depth & 1/2/3 \\  & & min\_child\_weight & 1/3/5 \\  & & booster & “gbtree”/“gblinear” \\ \hline \multirow{6}{*}{PS-RF} & PCA & n\_components & 2/4/6 \\ \cline{2-3}  & PCA & n\_estimators & 400/500/600 \\ \multirow{2}{*}{PS-RF} & Random Forest & max\_depth & 2/6/10 \\  & & min\_samples\_split & 10/15/20 \\ \multirow{6}{*}{PS-RF} & Random Forest & min\_samples\_leaf & 4/6/8 \\  & & max\_features & “auto”/\"sqrt\" \\ \cline{2-3}  & & bootstrap & True/False \\ \hline \multirow{6}{*}{PS-NN} & PCA & n\_components & 2/4/6 \\ \cline{2-3}  & PCA & hidden\_layer\_sizes & (50), (100), (200), (100, 50), (200, 100), \\ \cline{2-3}  & Neural network & activation function & “tanh”, “relu”, “logistic” \\ \cline{2-3}  & & alpha & 0.0001/0.001/0.01/0.1 \\ \cline{2-3}  & & max\_iter & 3000/5000/7000 \\ \hline \multirow{6}{*}{PFS-XGB} & PolynomialFeatures & poly\_degree & 2/3/4 \\ \cline{2-3}  & & learning\_rate & 0.01/0.1/0.5 \\ \multirow{2}{*}{PS-XGB} & XGBoost & n\_estimators & 50/100/200 \\ \multirow{2}{*}{PS-RF} & XGBoost & max\_depth & 1/2/3 \\  & & min\_child\_weight & 1/3/5 \\  & & booster & “gbtree”/“gblinear” \\ \hline \multirow{6}{*}{PFS-NF} & PolynomialFeatures & poly\_degree & 2/3/4 \\ \cline{2-3}  & & n\_estimators & 400/500/600 \\ \cline{2-3}  & & max\_depth & 2/6/10 \\ \cline{1-1} \cline{2-3}  & Random Forest & min\_samples\_split & 10/15/20 \\ \cline{1-1}  & & min\_samples\_leaf & 4/6/8 \\ \cline{1-1}  & & max\_features & “auto”/\"sqrt\" \\ \cline{1-1}  & & bootstrap & True/False \\ \hline \multirow{6}{*}{PFS-NN} & PolynomialFeatures & poly\_degree & 2/3/4 \\ \cline{2-3}  & & hidden\_layer\_sizes & (50), (100), (200), (100, 50), (200, 100), \\ \cline{1-1}  & & hidden\_layer\_sizes & (300, 200, 100), (400, 300, 200, 100) \\ \cline{1-1}  & Neural network & activation function & “tanh”, “relu”, “logistic” \\ \cline{1-1}  & & alpha & 0.0001/0.001/0.01/0.1 \\ \cline{1-1}  & & max\_iter & 3000/5000/7000 \\ \hline \multirow{6}{*}{PR-XGB} & PCA & n\_components & 2/4/6 \\ \cline{2-3}  & & learning\_rate & 0.01/0.1/0.5 \\ \cline{1-1}  & & n\_estimators & 50/100/200 \\ \multirow{2}{*}{PR-XGB} & XGBoost & max\_depth & 1/2/3 \\ \cline{1-1}  & & min\_child\_weight & 1/3/5 \\ \cline{1-1}  & & booster & “gbtree”/“gblinear” \\ \hline \multirow{6}{*}{PR-RF} & PCA & n\_components & 2/4/6 \\ \cline{2-3}  & & n\_estimators & 400/500/600 \\ \cline{1-1}  & & max\_depth & 2/6/10 \\ \cline{1-1}  & & min\_samples\_split & 10/15/20 \\ \cline{1-1}  & Random Forest & min\_samples\_leaf & 4/6/8 \\ \cline{1-1}  & & max\_features & “auto”/\"sqrt\" \\ \cline{1-1}  & & bootstrap & True/False \\ \hline \end{tabular}
\end{table}
Table 2: Hyperparameter tuning combination list.