## 2 Materials and Methods
### Hybrid AI Models and Evaluation Metrics
#### 2.5.2 Integral Feature Selection  
In [30], the authors introduced a novel method within the Integral Variable Selection (IVS) framework. This method identifies the optimal combinations of predictor variables for modeling, prediction, and forecasting tasks. It systematically evaluates all possible combinations of input variables to select the most efficient and effective set. Moreover, it aims to maximize the prediction accuracy of the output variable (objective function). The number of possible input combinations is determined using the \"n chooses k\" formula, represented by the binomial coefficient Equation (1) or simply using (2\({}^{\text{n}}\)-1):  
\[\text{Comb}\ =\ \sum_{\text{k}\ =\ 1}^{\text{n}}\text{C}_{\text{n}}^{\text{k}}\ =\ \sum_{\text{k}\ =\ 1}^{\text{n}}\frac{\text{n!}}{(\text{n}-\text{k})!\text{k!}} \tag{1}\]  
where n represents the total number of input variables, and k represents the number of variables to be selected in each combination.  
The proposed method comprises several steps, as illustrated in Figure 3. The algorithm is initiated, and input and output data are imported. The data are then split into training and testing-validating sets (70/30 split) and pre-processed using normalization and autonomous anomaly detection techniques. The total number of possible input combinations is computed using Equation (1). The method then enters the first loop based on the size of the data, K1. Within this loop, the number of combinations is computed for each  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Model** & **Description** & **Key Hyperparameters and Settings** & **Historical Background/Key** \\ \hline \multirow{4}{*}{9} & \multirow{4}{*}{Gaussian Process Regression (GPR)} & Non-parametric, probabilistic model treating outputs as random variables following a multivariate Gaussian distribution. & Kernel function: Rational quadratic. Sigma: auto. Basis function: constant. Fit method: Exact Gaussian process. & \\ \hline \multirow{4}{*}{10} & \multirow{4}{*}{Linear Regression (LR)} & \multicolumn{2}{c}{Predicts continuous outcomes assuming a linear relationship between input features and output. A foundational and widely applied model.} & Intercept: Included. Regularization: None. & Dates back to early 19 th century [26]. \\ \hline \multirow{4}{*}{11} & \multirow{4}{*}{\begin{tabular}{c} Linear Regression (LR) \\ \end{tabular} } & \multicolumn{2}{c}{Methods GLM by allowing non-linear, additive relationships between predictors and response variables.} & Spline order: 3. Number of spline terms per predictor: 5. Link function: Identity. & \multirow{4}{*}{Introduced in [27].} \\ \hline \multirow{4}{*}{12} & \multirow{4}{*}{\
\begin{tabular}{c} Kernelized Ridge \\ Regression Model \\ (KRRM) \\ \end{tabular} } & \multicolumn{2}{c}{Combines ridge regression with the kernel trick for modeling non-linear relationships between predictors and response variables.} & Kernel: RBF. Lambda: 0.1–1.0. Sigma (RBF scale): auto. & \multirow{4}{*}{Presented in [28].} \\ \hline \multirow{4}{*}{13} & \multirow{4}{*}{
\begin{tabular}{c} Linear Ridge \\ Regression (LRR) \\ \end{tabular} } & \multicolumn{2}{c}{Linear regression method adding a regularization term to reduce overfitting. Provides a closed-form solution for coefficient estimation.} & Regularization \\ \hline \hline \end{tabular}
\end{table}
Table 4: _Cont._ith considered size, and a second loop is initiated for each value of K2. The combnk (V, K) function generates a matrix with K columns. The ML model is loaded, and the data are processed to predict the corresponding output parameter for each combination. The predicted values are then saved, and the algorithm moves on to the next iteration. After computing the predicted values for all possible combinations, a second algorithm performs statistical analysis to identify the best input combinations that give the best accuracy prediction. Finally, the algorithm concludes after determining the optimal combinations of the predictor variables.