# Advancing Real-Estate Forecasting: A Novel Approach Using Kolmogorov-Arnold Networks
## 5 Discussion
However, on smaller datasets like California Housing, with fewer rows and limited input variables, ensemble-based methods such as XGBoost and LightGBM might be better suited due to their inherent ability to optimize simpler feature interactions and adapt efficiently to constrained datasets. While KAN's improvements over XGBoost (1.10%) and LightGBM (2.40%) are not statistically significant (\(p\)-values of 0.6875 and 0.502, respectively), it remains competitive with these ensemble methods, which are well regarded for their efficiency and performance on such small datasets. These findings highlight both the strengths and the challenges of KANs in regression problems. KAN addresses critical challenges in predictive modeling by capturing intricate nonlinear relationships and providing a theoretically grounded framework for feature decomposition. While LSTM models are effective for sequential data, their temporal focus is not suitable for static datasets like those used in this study. Similarly, boosting methods such as XGBoost and LightGBM rely on hierarchical tree-based splits, which may fail to capture complex nonlinear interactions present in high-dimensional data. KAN offers a distinct advantage by leveraging its spline-based architecture to learn univariate functions that are composable, scalable, and interpretable. Unlike regression models, which are constrained by linear assumptions, KAN provides a flexible framework for modeling nonlinear dependencies with theoretical rigor and empirical robustness. The proposed KAN model excels in scenarios with high-dimensional, nonlinear data, as evidenced by its superior performance. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model Compared** & \(p\)**-Value** &
\begin{tabular}{c} **Performance** \\ **Improvement** \\ \end{tabular} \\ \hline CatBoost & 0.03 (Significant) & 9.19\% \\ GRU-LSTM & 0.003 (Significant) & 3.28\% \\ LGB & 0.502 & 2.40\% \\ Linear regression & 0.005 (Significant) & 27.98\% \\ MLP & 0.003 (Significant) & 9.31\% \\ Random forest & 0.0312 (Significant) & 15.62\% \\ XGBoost & 0.6875 & 1.10\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical significance results. In general, KANs have demonstrated exceptional capabilities in scenarios that demand complex function approximation. This makes such models particularly transformative for datasets characterized by extensive variables and intricate high-dimensional relationships, such as those found in marketing, financial modeling, etc. By modeling nonlinear interactions and identify subtle patterns within data, KANs can often surpass conventional regression techniques in terms of accuracy and insight generation. On the other hand, several limitations warrant discussion and present opportunities for future research. A primary challenge lies in KAN's performance on small or low-dimensional datasets, where simpler models can achieve superior results with a significantly lower computational overhead. Moreover, KANs, due to their architecture and the nature of their computations, can be computationally intensive. This complexity may lead to longer training times and increased resource requirements, particularly when scaling to larger datasets or more intricate models. To address these challenges, several optimization methods can be applied. Regularization techniques, such as L2 regularization or dropout, can help to prevent overfitting by penalizing excessive complexity. Data augmentation or synthetic data generation can enhance the dataset, helping KANs generalize better. Moreover, simplifying the model architecture or combining KANs with simpler learning methods, like decision trees for final predictions, could reduce computational costs and improve performance on small datasets. These adjustments can enhance the adaptability of KANs, making them more effective in predictive regression tasks.