# Advancing Real-Estate Forecasting: A Novel Approach Using Kolmogorov-Arnold Networks
## 3 Materials and Methods
### Research Methodology
The mathematical formulations are the following:\[\text{Update Gate}:\ z_{t}=\sigma\Big{(}W_{z}\cdot\Big{[}h_{\{t-1\}},\ x_{t} \Big{]}+b_{z}\Big{)} \tag{13}\] \[\text{Reset Gate}:\ r_{t}=\sigma\Big{(}W_{r}\cdot\Big{[}h_{\{t-1\}},\ x_{t}\Big{]}+b_{r}\Big{)}\] (14) \[h=f(Wx+b) \tag{6}\]0 (15) \[h=f(Wx+b) \tag{6}\]1  
GRU, like LSTM, is a recurrent neural network architecture designed for sequential data. It simplifies the LSTM architecture by combining the forget and input gates, making it computationally efficient. However, GRU's focus on temporal dependencies limits its applicability to static datasets, where KAN's spline-based decomposition excels at modeling complex, nonlinear feature interactions. Regression-Based Models  
These models are primarily focused on fitting data through regression techniques. First, linear regression was utilized. Linear regression tries to fit a straight line to minimize errors between predictions and actual values. Also, a random forest regressor was developed and tested. This algorithm combines multiple decision trees by averaging predictions for robustness. Regression models, including linear and nonlinear variants, are foundational for predictive modeling. However, their performance is often constrained by assumptions of linearity or predefined functional forms. KAN overcomes these limitations by learning univariate functions adaptively, providing a more flexible and accurate framework for nonlinear prediction. Boosting-Based Models  
These models use boosting techniques to combine weak learners (e.g., decision trees) into a strong ensemble. XGBoost, CatBoost, and LightGBM were implemented and tested [20, 21, 22]. Boosting methods combine weak learners (e.g., decision trees) to create strong predictive models, excelling in structured data tasks. However, their reliance on hierarchical splits can oversimplify complex feature interactions. KAN addresses this gap by decomposing multivariate relationships into univariate functions, enabling precise and interpretable predictions. 4. Integration and Testing--Experiments  
Comprehensive testing was conducted to evaluate the performance of the models. Two widely used datasets were utilized for conducting the experiments, namely, the Greece listings ([[https://www.kaggle.com/datasets/argyrisanastopoulos/greece-property-listings/accessed](https://www.kaggle.com/datasets/argyrisanastopoulos/greece-property-listings/accessed)]([https://www.kaggle.com/datasets/argyrisanastopoulos/greece-property-listings/accessed](https://www.kaggle.com/datasets/argyrisanastopoulos/greece-property-listings/accessed)) on 10 September 2024) and the California house pricing ([[https://www.kaggle.com/code/ahmedmahmoud16/california-housing-prices](https://www.kaggle.com/code/ahmedmahmoud16/california-housing-prices)]([https://www.kaggle.com/code/ahmedmahmoud16/california-housing-prices](https://www.kaggle.com/code/ahmedmahmoud16/california-housing-prices)) accessed on 10 September 2024). Metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), and Symmetric Mean Absolute Percentage Error (SMAPE) were used to assess model effectiveness. Based on testing outcomes, iterative refinement of the models was undertaken to enhance their performance and reliability. The next section provides detailed information about the experiments and the results.