## 6 Summary and Discussion  
Based on the constraints and research gaps identified in the current literature, the improvements introduced by this study are presented in Table 8.  
Previous research has primarily utilised basic ensembles or single-model techniques, achieving accuracy levels ranging from 0.6465 to 0.9887. However, this investigation incorporated ten distinct models, including advanced neural networks and stacked techniques, providing a more comprehensive analysis and improved forecast reliability. Unlike other studies concentrated on simple feature sets and one-dimensional reduction methods, this work leveraged various feature sets through a more sophisticated feature engineering process. The robustness of the approach is evident in the consistent performance observed across various sets. The R\({}^{2}\) scores of the 10 ML models used in this study to forecast Munich rental values ranged from 0.8903 to 0.9187 for feature set 1 and from 0.8717 to 0.9071 for feature set 2. These scores underscore the consistent accuracy achieved by integrating the PyTorch framework with ML methods. In addition, the superiority of PyTorch-based models was further validated through a comparison between FNNs and PNNs. With \(p\)-values of 8.29 \(\times\) 10\({}^{-5}\) for R\({}^{2}\) and 2.08 \(\times\) 10\({}^{-7}\) for RMSE, the statistical significance test confirms that the PNN performed more accurately than other methods on both R\({}^{2}\) and RMSE, proving these enhancements are not due to random variation. The stacked strategy consistently exhibited improved performance, aligning with previous research that supported the integrated D-stacking model for its higher accuracy compared to single-model methods. The objective of this study was to improve ML model precision in predictive tasks by leveraging the PyTorch framework, which has not been thoroughly explored in the existing literature. While previous research focused on individual model performance, this study proposed that exploring the use of PyTorch alongside ML models yields substantial benefits, offering a novel contribution to the field. The increased precision across both feature sets further highlights the advantages of this technique, suggesting a transition in home value estimation towards a more sophisticated, data-centric approach. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Reference** & **Dataset** & **Methods Used** & **Preferred Model** & **Result** & **Limitations** & **Improvement from Proposed Study** \\ \hline
[10] & Taiwan & CNN, BPNN & CNN & R\({}^{2}\) \(>\) 0.945 & & \\ \hline
[11] & Tialchung, Taiwan & LSSVR, CART, & & & & \\  & & GRNN, BPNN & LSSVR & MAPE = 0.228 & & \\ \hline
[12] & Chengdu, China & RF, XGBosot, LightGBM & XGBoset & Accuracy \(\simeq\) 0.85 & & \\  & & & & & MSE = 0.04 & \\ \hline
[13] & Shenzhen, China & SVM & SVM & R\({}^{2}\) \(=\) 1 & & \\ \hline
[15] & Boston, the US & LR, RF, SVM, & ANN & R\({}^{2}\) \(=\) 0.876 & & \\  & & AN, XGBosot, & & & \\ \hline
[14] & Boston, the US & LR, Ridge, Lasso, RF & & & & \\  & & SVM with RBF & SVM with RBF & Score = 0.799 & & \\  & & Polynomial Regression & & & \\ \hline
[19] & Bangalore, India & LR, Lasso, Ridge, DT, RF, & & & & \\  & & XGBoset, XGRoset & XGRoset & Accuracy \(\simeq\) 0.6465 & & \\ \hline
[16] & Ames, the US & Compare models with & & & & \\  & & and without priors & & & \\  & & RF, NB, LR, MLP, KNN, & & & & \\  & & RF/Three & & & \\ \hline
[17] & Ames, the US & Ridge, Lasso, XGBoset, & & & & \\  & & LightGBM, & FSO-XGBoset & R\({}^{2}\) \(=\) 0.9887 & & \\  & & PSO-XGBoset & R\({}^{2}\) \(=\) 0.1015 & & & \\  & & & & & \\ \hline
[18] & CS House & KNN, SVM, RF, GSDT, & Stacking & RMSE = 0.869 & & One stacking strategy, integrated with multiple models was used to predict the price. It’s challenging to assess the effectiveness of this method without making comparisons with alternative approaches. \\  & US House & XGBoset, BPNet & Stacking & RMSE = 1.029 & & \\  & & & & & \\ \hline \hline \end{tabular}
\end{table}