## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{4}{c}{**Validation Results**} & \multicolumn{4}{c}{**Optimized Hyperparameters**} \\  & _RMSE_ & \(R^{2}\) & _MSE_ & _MAE_ & **Ensemble** & **Minimum** & **No of Learers** & **No. of Predictors** \\  & & & & & **Method** & **Leaf Size** & & **Preditors** \\ \hline OMC & 3.64 & 0.76 & 13.23 & 2.68 & Bag & 1 & 475 & 7 \\ MDD & 145.60 & 0.59 & 21,201 & 110.06 & Bag & 1 & 264 & 5 \\ UCS-EM\({}^{+}\) & 649.73 & 0.69 & 422,149 & 472.33 & Bag & 4 & 148 & 7 \\ UCS-EM\({}^{-}\) & 833.41 & 0.49 & 694,752 & 622.98 & Bag & 2 & 38 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical performance measurement of the developed models on unseen data and the optimized hyperparameters. Figure 2: Regression plot and validation R-square scores of: (**a**) OMC-EM, (**b**) MDD-EM, (**c**) UCS-EM\({}^{+}\) and (**d**) UCS-EM\({}^{-}\). To compare the performance of the developed four ensemble models, four other models employing ANN algorithms are developed. These models are OMC-ANN, MDD-ANN, UCS-ANN\({}^{+}\), and UCS-ANN\({}^{-}\). All the ANN models have three layers: an input, a hidden, and an output layer. The number of the input neurons for each model corresponds to the number of the predictors, which is seven neurons for OMC-ANN, MDD-ANN, and UCS-ANN\({}^{-}\) and nine neurons for UCS-ANN\({}^{+}\). The number of neurons utilized in the hidden layer was ten, which was determined based on the generalization error after performing several trainings. The number of neurons at the output layer is one for all models, which is the feature going to be predicted. The data were also randomly divided into three clusters: training, validation, and test datasets, which hold 70%, 15%, and 15% of the dataset, respectively. Once the datasets are ready, the network was trained using a Levenberg-Marquardt algorithm. The difference between the actual and the predicted OMC, MDD, and UCSs by the developed four ANN models are calculated, and their distributions are visualized with a boxplot in Figure 3. The median of the errors is designated by a red line within the blue box, embracing the middle 50% (25 th-75 th percentiles) of the errors. It can be seen from Figure 3 that the medians of errors of all the models are closer to either the first or the third quartile. For instance, the medians of the errors of OMC-ANN and UCS-ANN\({}^{+}\) models are closer to the first quartile. This means that the distributions of the errors are slightly skewed to the right. The whiskers stretch from the ends of the box to the smallest and largest error values. Errors greater than 1.5 box lengths above the whiskers are outliers and characterized by a red plus sign. It can be observed that there are a significant number of outliers in all models. Statistical performance indicators (\(MSE\) and \(R^{2}\)) of all the ensemble and ANN models are given in Table 5. The lower the \(MSE\) and the higher the \(R^{2}\) are, the more superior the model. It can be observed from Table 5 that the \(MSE\) errors of all models which employed ensemble of regression trees are lower than the corresponding models based on ANN. For instance, the \(MSE\) of the OMC-EM compared to OMC-ANN is lower by 34%. The \(R^{2}\) of all the ensemble models is higher than ANN models. For example, the \(R^{2}\) of OMC-EM is higher than OMC-ANN by 31%. All these confirm that the ensemble methods outperformed the ANN models on the utilized dataset. The developed ensemble models are a promising approach to evaluate the performance of compaction and strength properties of stabilized soils. Housing blocks based on stabilized soils have been already gaining recognition in many emerging countries, especially in the global south as the weather condition favors their wide application. Indeed, the stabilizers type varies depending on their availability. For instance, a recent research work by [PERSON].