## 4 Results and Discussion  
### ML Regression  
Table 4 indicates the statistical measures of performance of the ML regression algorithms used for prediction of intrinsic compressibility index of the soils. The TVS method was used for training, testing, and subsequent validation of the datasets. An indication of good performance is usually depicted by high values of coefficient of determination (R\({}^{2}\)) with corresponding low mean error values given as the mean absolute error (MAE) \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Stand-Alone Algorithms**} \\ \hline REG & \multicolumn{2}{c}{Parameter} & Option/value \\ Regularisation wt. (L\({}_{2}\)) & 0.001 & \\ Method & \multicolumn{2}{c}{Ordinary least squares (OLS)} \\  & Optimisation tolerance & \(1\times 10^{-7}\) \\ LR & Regularisation wt. (L\({}_{1}\) \& L\({}_{2}\)) & 1.00 \\ BLR & \multicolumn{2}{c}{Regularisation wt. (L\({}_{2}\))} & 1.00 \\ Normaliser & \multicolumn{2}{c}{min-max} \\  & No. of hidden nodes & 100.00 \\ ANN & No. of iterative learning & 100.00 \\  & Hidden layer spec. & Full connection \\ \hline  & \multicolumn{2}{c}{Tree-ensembles} \\ \hline  & \multicolumn{2}{c}{Parameter} & Option/value \\  & \multicolumn{2}{c}{Constructed trees} & 100.00 \\ Boosted decision tree (BDT) & Tree-forming training instances & 10.00 \\  & Leaves/tree (max.) & 20.00 \\  & Tree depth (max.) & 32.00 \\  & \multicolumn{2}{c}{Constructed trees} & 8.00 \\ Random decision forest (RDF) & \multicolumn{2}{c}{Method of resampling} & Bagging \\  & \multicolumn{2}{c}{Samples/leaf node (min.)} & 1.00 \\  & \multicolumn{2}{c}{Randomised splits/node} & 128.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Models’ optimised parameter settings. and the root mean square error (RMSE). Among the traditional regression models, the tree ensembles (RDF and BDT) seem to outperform the stand-alone models (REG, ANN and BLR) as could be observed in Table 4. With regards the stand-alone algorithms, BLR does clearly produce the least accuracy when compared to REG and ANN. The outcome of REG and BLR on a non-linear problem such as that presented by this study may not be entirely surprising given the models' underlying assumptions of linearity thus, being unable to implicitly detect all the possible combinations or interactions between explanatory and predictor variables. Notwithstanding, the relatively less accuracy of prediction given by ANN is quite remarkable. Though, depending on a given regression problem, opinions are quite divided as to the behaviour of ANN as a result of its inherent structure comprising of 'black boxes' which may tend to either cause an over-estimation or not being able to explicitly learn several unobserved causal relationships during data training. ANN has a criterion that is not well-established to enable an interpretation of the weights and biases that exist in a connection matrix. In ANN's backpropagation method of instinctive search and optimisation of its weight matrix, successive upgrades or updates tend to all converge to local minimum error spaces rather than one that is more global. Among the tree-based algorithms, RDF does appear to outperform (R\({}^{2}\) of 0.86 and RMSE of 0.48) though slightly, the BDT with an R\({}^{2}\) of approximately 0.82 and RMSE of about 0.53 both of which have incorporated the technique of 'bagging' or 'bootstrapping' in order to improve their performances. This method of boosting in addition to their innate architecture does improve the tree-ensembles' capacity to learn and predict the complexities of non-linear interactions between the input features especially when compared to the aforementioned stand-alone models. Nonetheless, tree-ensembles are also known to be ridden with some setbacks of their own.