# Advancing Real-Estate Forecasting: A Novel Approach Using Kolmogorov-Arnold Networks
## 3 Materials and Methods
### Research Methodology  
The research methodology consists of the following phases (Figure 2):  
1. Literature Review  
First, a thorough literature review was made to identify state-of-the-art models and available datasets. This step was crucial for deciding which models will be implemented and comparing the proposed KAN-based model with them in the corresponding datasets. 2. Data Collection and Preprocessing  
After that, data collection, preprocessing, and cleaning were performed to ensure the quality and consistency of the data for subsequent analysis. To mitigate the impact of extreme values on model performance, outlier detection was implemented using a quantile-based approach. Specifically, observations where the price feature fell outside the 5 th and 95 th percentiles were excluded from the datasets. Additionally, feature engineering incorporated standardization techniques, including Min-Max scaling and standard scaling, to normalize the input features and enhance model performance. The next section provides all the necessary details. Figure 2: Research methodology. Model Development and Validation  
State-of-the-art models found in the literature were developed and validated, specifically tailored for regression and house price prediction tasks. In detail, the following deep learning neural network models were examined, implemented, and compared with KAN: MLP  
The MLP is a type of feedforward neural network comprising an input layer, one or more hidden layers, and an output layer. Each layer is fully connected to the subsequent layer, and neurons use an activation function to introduce nonlinearity. The mathematical representation for a neuron in a hidden layer is given by the following:  
\[h=f(Wx+b) \tag{6}\]  
where  
* \(h\) is the output of the neuron. * \(W\) is the weight matrix. * \(x\) is the input vector. * \(b\) is the bias vector. * \(f\) is the activation function (e.g., ReLU and sigmoid). MLPs are general-purpose neural networks that approximate complex functions through multiple layers. However, their black-box nature and reliance on global optimization make them less interpretable than KAN, which provides a transparent decomposition of feature interactions. LSTM  
The Long Short-Term Memory (LSTM) network enhances the RNN by incorporating memory cells and three gating mechanisms: input, forget, and output gates [21]. These gates enable the model to retain long-term dependencies. The mathematical operations are provided below:  
\[\text{Forget Gate}:\ f_{t}=\sigma\Big{(}W_{f}\cdot\Big{[}h_{\{t-1\}},\ x_{t} \Big{]}+b_{f}\Big{)} \tag{7}\]  
\[\text{Input Gate}:\ i_{t}=\sigma\Big{(}W_{i}\cdot\Big{[}h_{\{t-1\}},\ x_{t} \Big{]}+b_{i}\Big{)} \tag{8}\]  
\[\text{Candidate Cell State}:\ \stackrel{{\sim}}{{C}}_{t}=tanh \big{(}W_{c}\cdot[h_{t-1},x_{t}]+b_{c}\big{)} \tag{9}\]  
\[\text{Cell State Update}:\ C_{t}=f_{t}\odot C_{t-1}+i_{t}\odot \stackrel{{\sim}}{{C}}_{t} \tag{10}\]  
\[\text{Output Gate}:\ o_{t}=\sigma(W_{o}*[h_{t-1},\ x_{t}]+b_{o}) \tag{11}\]  
\[\text{Hidden State}:\ h_{t}=o_{t}\odot tanh(C_{t}) \tag{12}\]  
LSTM networks are designed for sequential data, leveraging memory cells to retain temporal dependencies. While effective for time-series tasks, their sequential nature makes them less suited for static datasets like house price prediction, where feature interactions are more critical than temporal patterns. In contrast, KAN focuses on capturing nonlinear dependencies across static features. GRU  
The Gated Recurrent Unit (GRU) is a variant of the recurrent neural network (RNN) that addresses the vanishing gradient problem through gating mechanisms [21]. GRUs utilize reset and update gates to control the flow of information.