## 5 Investigation Assessment  
PyTorch is an ML framework built upon the Torch library and is used for multiple applications, including computer vision and NLP. According to the findings, PyTorch framework, when used with standalone ML models, can also be applied to different scenarios for predicting rental values in the real estate industry. In feature set 1, it is worth noting that while RF and GBR exhibited greater performance compared to the stacked models, their performance decreased when the features were altered. This highlights the limitations of relying solely on individual models. In set 2, the tree-based models exhibited poor performance, whereas these algorithms performed well in set 1. The variation in performance across distinct feature sets may be attributed to the use of various feature selection techniques. CatBoost demonstrated robust predictive capabilities and greater accuracy across various datasets. This discrepancy can be attributed to the ways in which each approach processes the data. Changes in predicted accuracy may result from PSO performance variability, especially if the original feature set is insufficient. Figure 5: Comparison of model performance across feature set 2. While PSO can fine-tune feature weights, it may struggle with generalisation if the features chosen fail to capture the whole spectrum of significant variables. On the other hand, the ensemble technique of CatBoost improves its ability to generalize to untested data by combining several weak learners. Moreover, the feature relevance rankings of CatBoost provide insights into which factors influence predictions, crucial for those in the real estate industry to comprehend the primary attributes affecting rental rates. As opposed to this, the feature significance of PSO is less apparent, as it depends on the weighted combination of specific characteristics rather than an evaluation of individual features contributions to the model. As a result, while CatBoost and PSO both provide useful techniques for predictive modelling, the distinctions between these methods in feature selection and performance underscore the importance of choosing the right algorithm for certain tasks. PSO may need thorough evaluation of initial feature sets and optimisation procedures; however, the strong handling of categorical data of CatBoost and ensemble learning capabilities often lead to better outcomes, especially for complex datasets. Comprehending these variations not only aids in selecting suitable models but also amplifies the overall efficacy of predictive analyses in real estate. This study utilised a stacking strategy, integrating a PyTorch-based neural network with various other ML models. A variety of ML methods, such as LR, XGB, GBR, and RFR, were employed as base models, with a PNN implemented as the meta-model. The base models generated predictions, which were then used as input features for the meta-model. This stacking approach consistently enhanced the performance of single models. For instance, the R\({}^{2}\) score of XGB rose from 0.8903 to 0.9097 in feature set 1 and from 0.8717 to 0.9022 in feature set 2. Stacked models performed consistently across various feature sets, indicating increased resilience and generalisation. By optimally integrating predictions from multiple models, stacking helps overcome the shortcomings of a single model. In predicting rental prices in the Munich real estate market, this technique shows the potential for combining conventional ML models with neural networks via PyTorch to improve forecast accuracy and reliability. Previous research primarily utilised standalone models such as CNNs, BPNNs, and SVMs for predicting tasks. This study explored the benefits of integrated techniques to improve model performance and reliability, which can be applied to various scenarios, such as investigating the housing market in other regions. Further research could explore further applications of PyTorch for more sophisticated methodologies within this field.