# Initialize GroupKFold for cross-validation group_kfold = GroupKFold(n_splits = 5)
## 5 Results  
### Real Data Analysis  
Our initial analysis focused on the real Reddit thread data (Figure 20). Despite the limited sample size (eight unique networks, 72 observations), we identified several notable patterns in information diffusion.  
The Random Forest model performed best on real data, achieving a moderate R\({}^{2}\) of 0.512 \(\pm\) 0.222. This indicated that network structure and diffusion parameters could explain approximately half of the variance in information coverage, even with limited data.  
The cross-validation results showed considerable variability (standard deviation of 0.222 for Random Forest). This variability highlighted the challenges in making reliable predictions with limited data. Other models performed less effectively, with Gradient Boosting (R\({}^{2}\) = 0.426 \(\pm\) 0.206) and Huber Regressor (R\({}^{2}\) = 0.394 \(\pm\) 0.178) showing moderate performance, while ElasticNet and SVR showed poor performance (negative R\({}^{2}\)). The variability in real data model performance (\(\sigma\) = 0.222 for Random Forest) stemmed primarily from the limited sample size (72 observations from eight networks) and structural heterogeneity rather than from overfitting. Tree-based models performed better by capturing non-linear diffusion dynamics without requiring extensive regularization.  
Feature importance analysis (Figure 21) revealed that spread probability (p_spread) was the most influential factor (importance = 0.321), followed closely by network density (importance = 0.302) and average community size (importance = 0.178). Delay mechanism (represented by delay_type_exponential) and network diameter also showed measurable influence. The remaining features had relatively minor impacts (<0.02 importance).  
Figure 20: Model performance comparison on real data. Left panel shows R\({}^{2}\) scores (higher is better) with the best-performing Random Forest model highlighted in green. Right panel shows Mean Absolute Error (lower is better) with all models in purple. Error bars indicate standard deviation across cross-validation folds.  
When we tested model predictions against actual values, the Random Forest model achieved an R\({}^{2}\) of 0.604 and RMSE of 0.05089 on the test data. The residuals were normally distributed (Shapiro-Wilk W = 0.971, \(p\) = 0.093), indicating well-behaved errors.  
The analysis of key structural features revealed optimal configuration patterns (Figure 22). For p_spread, the optimal value was consistently around 0.3 across both discussion and non-discussion networks. For network density, values around 0.18 for discussion networks and 0.15 for non-discussion networks maximized coverage. These findings provide practical guidelines for optimizing information spread.  
Figure 21: Feature importance in real data analysis.  
Figure 22: Optimal values of key structural features. Red stars indicate optimal p_spread values for each delay type in Discussion (**left**) and Non-Discussion (**right**) graphs.  
The statistical tests confirmed that spread probability had a significant effect on coverage (F = 12.195, \(p<\,0.001\)), while the effects of graph type (t = 1.765, \(p\) = 0.082) and delay type (F = 0.172, \(p\) = 0.843) were not statistically significant. This suggested that transmission probability was more influential than network structure or delay mechanism in this dataset.