# Product Demand Prediction with Spatial Graph Neural Networks
## 4 Experiments
### Hyperparameter Robustness (RQ3)  
In pursuit of answering Research Question 3 (RQ3), our investigation delves into the sensitivity of the Spatial Graph Neural Network model's predictive accuracy to variations in key hyperparameters: the decay factor, batch size, and the number of SGNN layers. This exploration aims to discern the extent to which these parameters influence the model's precision in predicting product demand.  
Decay Factor: We initiate our exploration by adjusting the decay factor within our model across a spectrum from 0.1 to 0.9. The empirical findings, encapsulated in Table 3, reveal an intriguing pattern: while the overall performance remains relatively stable across a wide range of decay factor values, we observe a discernible dip in predictive accuracy at the extremities of this range. This phenomenon underscores the delicate balance required in setting the decay factor, as values that are too high or too low can adversely affect the scope of information propagation within the SGNN, thereby impacting learning efficiency.  
Batch Size: Further scrutiny is applied to the impact of batch size variations on model performance, with our analysis spanning batch sizes from 1000 to 20,000. As detailed in Table 4, the results showcase an impressive resilience in performance metrics (MAE, RMSE, and R2) against changes in batch size. Notably, the SGNN model consistently maintains a MAE above the 0.1700 threshold across almost all tested batch sizes, highlighting its robustness and stability in handling varying data volumes during training.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Avito**} \\ \cline{2-4}  & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline SGNN w/o spatial & 0.2103 & 0.2014 & 0.8976 \\ and attention & 0.1962 & 0.1897 & 0.9045 \\ \hline SGNN w/o attention & 0.1876 & 0.1721 & 0.9108 \\ \hline SGNN & 0.1685 & 0.1504 & 0.9234 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The ablation study results for our SGNN model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Decay Factor**} & \multicolumn{3}{c}{**Avito**} \\ \cline{2-4}  & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline
0.1 & 0.1958 & 0.1792 & 0.9063 \\ \hline
0.3 & 0.1731 & 0.1565 & 0.9187 \\ \hline
0.5 & 0.1685 & 0.1504 & 0.9234 \\ \hline
0.7 & 0.1786 & 0.1592 & 0.9146 \\ \hline
0.9 & 0.1901 & 0.1712 & 0.9084 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The hyperparameter robustness analysis on the decay factor.  
Layer Number: The final dimension of our hyperparameter analysis focuses on the number of SGNN layers, ranging from 1 to 5. This examination, presented in Table 5, seeks to ascertain whether a deeper SGNN architecture translates to enhanced predictive performance. The findings confirm the model's resilience to variations in layer numbers, with an optimal performance observed at a layer count of 3. Beyond this point, an increase in layers leads to a noticeable decline in performance across all metrics (MAE, RMSE, and R\({}^{2}\)), attributed to the over-smoothing issue prevalent in deeper Graph Neural Network models. This observation highlights the criticality of layer number selection in preserving the model's capacity to generate distinct and informative node representations without succumbing to the diluting effects of over-smoothing.  
This comprehensive analysis of hyperparameter sensitivity not only affirms the SGNN model's robustness across a range of configurations but also sheds light on the optimal settings conducive to maximizing predictive accuracy. The insights garnered from this exploration provide valuable guidance for fine-tuning the SGNN framework, ensuring its adaptability and effectiveness in the dynamic landscape of product demand prediction.