## 4 Results and Discussion  
In this section, the performance of the developed OMC, MDD, and UCS models is presented. Examining the generalization performance, how well the models can make predictions for data that was not observed during training, is very essential compared to how well they fit the training set. The coefficient of determination, \(R^{2}\), is one of the statistical measures applied to examine the generalization performance of all the models. The \(R^{2}\) score indicates how well the developed OMC, MDD, and UCS models explain and predict future outcomes. It yields a score between 0 and 1. The training performance of all models is illustrated in Figure 2. Regression plot for predicted vs. measured OMC, MDD, and UCSs with their corresponding validation R-square scores, showing the true versus the predicted response. It can be perceived from Figure 2 that the score of OMC-EM, MDD-EM, and UCS-EM\({}^{+}\) models exceed 0.50. Observably, OMC-EM performs best (\(R^{2}\)= 0.76), followed by UCS-EM\({}^{+}\) (\(R^{2}\) = 0.69), and MDD-EM (\(R^{2}\) = 0.59). This validates that these models reasonably track their corresponding target features during the training stage. Among all, UCS-EM\({}^{-}\) perform least with (\(R^{2}\) = 0.49). This model entails all features under the category of amended soils (soil, cement, and lime), Afterberg (LL, PL, and PI), and soil classification, but does not entail features that describe the compaction properties (OMC and MDD). Hence, the weak performance of UCS-EM\({}^{-}\) model corroborates that the features OMC and MDD have significant importance in predicting UCS. It can be noticed that all the models exhibit a slight tendency to underestimate or overestimate their corresponding target variables in which the number of observations is very limited. For example, measurements of OMC > 25% and UCS > 3500 kN/m\({}^{2}\) represent only about 12% and 13% of the total observation, respectively. This insufficient number of observations in the data might be the cause for the underestimation in those ranges. This is a normal phenomenon as the algorithm did not obtain adequate observations to learn and generalize. Incorporating more observations could enhance the performance of the models. Scores of other statistical performance indicators (\(RMSE\), \(MSE\), and \(MAE\)) on the test dataset for all the developed models are given in Table 4. Indeed, it is impossible to compare one model with another by considering these indicators, except UCS-EM\({}^{+}\) and UCS-EM\({}^{-}\). This is because they are predicting different variables. The lower the statistical errors are the superior the performance of the model. The \(RMSE\), \(MSE\), and \(MAE\) of UCS-EM\({}^{+}\) model are considerably lower than the UCS-EM\({}^{-}\), confirming its superiority. It can also be noticed from \(MAE\) results that the average prediction errors of OMC-EM, MDD-EM, UCS-EM\({}^{+}\), and UCS-EM\({}^{-}\) are 2.68%, 110.06 kg/m\({}^{3}\), 472.33 kN/m\({}^{2}\), and 622.97 kN/m\({}^{2}\), respectively. This confirms that the three ensemble models (OMC-EM, MDD-EM, and UCS-EM\({}^{+}\)) performed rationally well on previously unseen data, considering the fact that their corresponding median values are 11.30%, 1820 kg/m\({}^{3}\), and 2260 kN/m\({}^{2}\). All the results are valid only for the employed dataset. The performance of each model could be enhanced if more data are utilized. The optimized hyperparameters are also presented in the Table 4. As presented in Section 3.2.2, five hyperparameters were considered to optimize the performance of the models. Bagged regression trees yielded optimal performance for all models. The minimum leaf size, number of learners, and number of predictors for the samples of each model are mostly different.