## 2 Related Work
### Justification for Model Selection and Performance Metric
The activations are calculated at every layer until they reach the output ones, while the activated score creates the predicted result [8]. FNNs can execute regression tasks and learn intricate characteristics of the supplied data, as well as fit most functions and have strong nonlinear fitting capabilities with a simple principle and feasible implementation. Thus, the task of forecasting rental value in the German housing sector could be completed by its application [43]. A model that has the capability to represent intricate connections between input and output variables. An FNN model is well suited for collecting complex patterns in the housing market data due to the capacity to learn nonlinear representations. * PNN: The neural network (NN) models based on PyTorch can be defined, trained, and inferred by applying Python language with a Tensor type of data [44]. The process is more rapid and effective when PyTorch is used. Moreover, it is achievable to optimise the efficiency of DL models while maintaining complete flexibility throughout the model development and execution procedures [45]. * Stacked models: this is a technique that involves merging the predictions of multiple models to enhance overall performance and accuracy. This study intends to combine PNN with RFR, GBR, XGB, and LR to obtain superior accuracy compared to using a standalone model. * The R\({}^{2}\) score evaluates the effectiveness of regression models by displaying the variance proportion of the dependent variable, which together establishes the independent factor [46]. The range of values for R\({}^{2}\) is 0 to 1. A score of 0 indicates that the model explains no variability around the mean of the response variable, while a score of 1 indicates that all the variability around the mean is explained by the response variable [47]. A higher R\({}^{2}\) score denotes the level of quality of the trained model [48]. * The RMSE is applied to evaluate the efficiency and performance of various prediction models by comparing the difference between predicted and actual values [47]. The model performs better at estimates when the value is smaller [49]. This methodology of the study stresses a well-balanced combination of traditional, ensemble, and neural network models, supported by extensive literature, to guarantee a thorough examination of rental price prediction techniques. In conclusion, the literature review emphasises the extensive application of AI-based techniques for forecasting housing market trends. It also underscores the crucial role of feature selection in improving model performance. Prominent predictive models, including CNNs, XGBoost, RF, and hybrid models like PSO-XGBoost, have demonstrated high accuracy in various real estate markets. These models exhibit remarkable proficiency in handling complex relationships and high-dimensional datasets, showcasing their ability to capture the nonlinear interactions essential for precise home price forecasting. In the field of feature selection, methods such as lasso filtering and PSO have shown promise in reducing dimensionality and identifying relevant factors. Research shows that combining these feature selection techniques with ML models can significantly improve prediction accuracy, particularly when dealing with high-dimensional datasets, such as those found in real estate [50]. Advanced models and feature selection algorithms work together to address issues related to overfitting, model robustness, and generalisation across various market conditions. Nonetheless, prior studies reveal significant gaps. More comprehensive research is required, as indicated by the limited attention given to ensemble and hybrid approaches as well as the inconsistent assessment of model performance across various feature sets. Additionally, concerns about the generalisability of current research results arise due to a focus on specific market scenarios or individual datasets.