# Machine-Learning-Based Path Loss Prediction
## 4 Results and Discussion
\begin{table}
\begin{tabular}{l l c c c} \hline \hline
**Prediction Type** & **Model Type** & **MAE** & **MSE** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline \multirow{8}{*}{Machine Learning} & RF & 0.0557 & 0.0059 & 0.0774 & 0.97 \\  & GB & 0.0701 & 0.0093 & 0.0964 & 0.96 \\  & ANN & 0.1080 & 0.0222 & 0.1477 & 0.91 \\  & SVR & 0.1108 & 0.0235 & 0.1533 & 0.90 \\  & AB & 0.1782 & 0.0483 & 0.2198 & 0.79 \\  & LR & 0.2299 & 0.0772 & 0.2780 & 0.68 \\ \hline \multirow{2}{*}{Empirical Model} & Log-Distance & - & 15.840 & 3.98840 & 0.92 \\  & Two-Ray & - & 100.602 & 10.0380 & 0.32 \\  & Log-Ray & - & 70.5625 & 8.4032 & 0.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance comparison of path loss prediction models (validation). Figure 7: Comparison of machine learning models for path loss prediction using performance metrics (MAE, MSE, RMSE, \(\mathbf{R^{2}}\)). When the performance comparison of the models before and after the application of the feature selection methods was examined, it was observed that each method had a different effect on the RMSE values of each model. The RMSE values for the RF and GB models remained rather constant, indicating that these models were already highly optimized regarding feature relevance and redundancy. In particular, the RMSE value of the RF model increased slightly from 0.0774 to about 0.081, and the RMSE value of the GB model increased from 0.0964 to about 0.1053. This slight increase means that feature selection had a negligible effect, which is likely because these models already demonstrated the best performance with the original feature set. The performance of the ANN and SVR models with feature selection produced different outcomes. While the ANN model experienced a marginal increase in RMSE values, PCA and MRMR contributed to an increase in RMSE from 0.1477 to 0.1488 and 0.1493, respectively. Thus, it is clear that these techniques are not successful in the performance of the ANN model. In contrast, the F-Test resulted in a notable reduction in the ANN model's RMSE to 0.1032, demonstrating the effectiveness of the F-Test in identifying the most important features and consequently improving the accuracy of the model. Nevertheless, the RMSE of the SVR model increased from 0.1533 to 0.1601 when using PCA, 0.1645 with MRMR, and 0.1585 with the F-Test. These observations suggest that the original set of features provided a greater advantage for the SVR model, and the feature selection process did not have a significant impact on improving the accuracy of the predictions. The AB model exhibited noteworthy efficacy when employing both the PCA and MRMR approaches, with a decrease in the RMSE from 0.2198 to 0.1787 and 0.1998, respectively. This led to the conclusion that PCA and MRMR successfully identified the most critical features of AB and enhanced its performance. Moreover, the F-Test caused a marginal reduction in the RMSE to 0.2156, but this improvement was not as significant as that of the PCA and MRMR. Therefore, it can be concluded that the F-Test was not as efficient as PCA and MRMR for the AB model, although helpful. Finally, the RMSE of the LR model did not exhibit significant changes with the feature selection. Minor increases from 0.2780 to 0.2793 with PCA, 0.2815 with MRMR, and 0.2832 with the F-Test show that the initial feature set was optimal for the LR model. In summary, the impact of feature selection methods on model performance can vary significantly depending on the model architecture. This highlights the necessity of model-specific feature selection to optimize prediction accuracy. The significant decrease in RMSE for the ANN model with the F-Test highlights the importance of selecting the appropriate feature selection technique for each model to optimize prediction accuracy. For the AB models, both PCA and MRMR, and for the ANN model, the F-Test proved to be highly effective, underlining the need for model-specific strategies for feature selection.