# Advancing Real-Estate Forecasting: A Novel Approach Using Kolmogorov-Arnold Networks
## 5 Discussion  
Starting with the first dataset, the Kolmogorov-Arnold network (KAN) model demonstrated its efficacy by achieving the lowest Mean Absolute Error (MAE) of 35,861, Root Mean Squared Error (RMSE) of 52,158, and Symmetric Mean Absolute Percentage Error (SMAPE) of 16.53%. These results highlight the model's ability to capture complex nonlinear relationships effectively, outperforming advanced architectures such as GRU-LSTM and widely used machine learning models, including CatBoost, XGBoost, and LightGBM. In contrast, on the default California Housing dataset, traditional machine learning models such as XGBoost and LightGBM emerged as the top performers. XGBoost achieved the lowest MAE (30,625), RMSE (42,477), and SMAPE (15.81%), closely followed by LightGBM. While KAN remained competitive, it recorded slightly higher metrics, with an MAE of 31,961, an RMSE of 44,191, and an SMAPE of 16.45%. These results suggest that the relatively small size and limited feature set of the California Housing dataset may constrain the full potential of neural-network-based models like KAN.  
To further explore this limitation, in the augmented version of the California Housing dataset, KAN demonstrated its ability to leverage the increased data complexity and size, outperforming XGBoost across all metrics. Specifically, KAN achieved a test MAE of 34,716, an RMSE of 53,378, and an SMAPE of 17.74%, compared to XGBoost's MAE of 36,102, RMSE of 55,533, and SMAPE of 18.31%. Notably, KAN showed an improvement of approximately 3.6% in prediction accuracy. This additional benchmarking highlights the robustness of KAN in handling augmented datasets and underscores its potential to outperform state-of-the-art methods in scenarios where data complexity and size are increased. The findings demonstrate that while traditional models may excel on simpler \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Name** & **MAE** & **RMSE** & **SMAPE (\%)** \\ \hline KAN & 34,716 & 53,378 & 17.74 \\ XGBoost & 36,102 & 55,533 & 18.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: KAN and XGBoost test results in augmented California Housing dataset. Figure 6: Comparison plot of predicted and actual values in Dataset B—KAN. datasets, KAN offers significant advantages when applied to richer, more diverse datasets, further establishing its applicability to complex predictive tasks. To assess further the performance differences between KAN and other models on the two datasets, the Wilcoxon Signed-Rank test was conducted [23]. This non-parametric test was chosen over the paired t-test to address violations of the normality assumption in the data. Additionally, the overall performance improvement of KAN was calculated as the average percentage improvement across all metrics. The results, summarized in Table 5, provide \(p\)-values indicating the statistical significance of the comparisons and the average percentage improvements for each model. The results of the statistical analysis underscore the effectiveness of the KAN model in predictive tasks, particularly in comparison to several state-of-the-art models. KAN demonstrates statistically significant improvements in performance metrics against widely used models such as CatBoost, GRU-LSTM, MLP, random forest, and linear regression, as indicated by \(p\)-values less than 0.05. Notably, the KAN model achieves a 9.19% improvement over CatBoost, a model known for its robustness, and a 27.98% improvement over linear regression, emphasizing its ability to capture complex nonlinear relationships. This difference highlights a notable aspect of KAN's behavior: its performance tends to excel with larger datasets and high-dimensional inputs, where its advanced approximation capabilities and ability to model intricate patterns shine.