# ADDAEIL: Anomaly Detection with Drift-Aware Ensemble-Based Incremental Learning
## 4 Results
### Sensitivity Analysis on Key Hyperparameters  
This subsection evaluates the robustness of ADDAEIL with respect to three key hyperparameters: the sliding window size \(W\), the number of base detectors \(N\), and the update ratio range \([r_{\text{min}},r_{\text{max}}]\). In each experiment, one parameter is varied while the others are fixed at their default values: \(W=48\), \(N=100\), and \([r_{\text{min}},r_{\text{max}}]=[0.1,0.6]\). The results on the Yahoo A3 dataset are summarized in Table 4.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{Dataset} & \multicolumn{4}{c}{iForest (No Update)} & \multicolumn{4}{c}{Performance-only} & \multicolumn{4}{c}{Distribution-only} \\ \cline{2-13}  & **AUC** & **F1** & **Recall** & **Precision** & **AUC** & **F1** & **Recall** & **Precision** & **AUC** & **F1** & **Recall** & **Precision** \\ \hline Yahoo & 0.62 & 0.31 & 0.64 & 0.29 & 0.91 & 0.74 & 0.98 & 0.72 & 0.89 & 0.71 & 0.98 & 0.68 \\ NAB & 0.83 & 0.47 & **0.95** & 0.41 & 0.84 & 0.59 & 0.95 & 0.55 & 0.85 & 0.60 & 0.94 & 0.57 \\ CEMACS & 0.92 & 0.89 & 0.88 & 0.85 & **0.94** & 0.89 & 0.91 & 0.92 & **0.94** & **0.90** & 0.91 & **0.93** \\ \hline
**Average** & 0.79 & 0.56 & 0.82 & 0.52 & 0.90 & 0.74 & 0.95 & 0.73 & 0.89 & 0.74 & 0.94 & 0.73 \\ \hline \multicolumn{13}{c}{**ADDAEIL (Proposed)**} \\ \cline{2-13}  & **AUC** & **F1** & **Recall** & **Precision** & & & & & & & & \\ \hline Yahoo & **0.92** & **0.77** & **0.98** & **0.75** & & & & & & & & \\ NAB & **0.85** & **0.61** & **0.95** & **0.58** & & & & & & & & \\ CEMACS & **0.94** & **0.90** & **0.92** & **0.92** & & & & & & & & \\ \hline
**Average** & **0.90** & **0.76** & **0.95** & **0.75** & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Ablation study on update strategies across benchmark datasets. Bold values indicate the best performance among all compared methods for each metric in each dataset.  
The results show that ADDAEIL remains stable across a range of parameter values. When adjusting the window size, the model achieves the highest F1-score (0.80) at \(W=24\), along with a slight increase in recall. In contrast, a larger window size (\(W=96\)) results in a minor drop in both recall and F1-score. This indicates that larger window sizes may slightly reduce model adaptability and accuracy, as long windows may encompass multiple or complex concept drifts, thereby increasing the difficulty for the model to promptly adapt to distributional changes.  
The number of base detectors also shows limited influence on performance. All three configurations (\(N=50\), 100, and 200) yield nearly identical results. This suggests that the ensemble size can be flexibly adjusted to match resource constraints, without significantly compromising accuracy.  
Adjusting the update ratio range likewise has only a modest effect. Increasing the maximum update rate to \(r_{\max}=0.8\) improves precision and F1-score slightly. Meanwhile, a more conservative setting (\(r_{\max}=0.5\)) leads to a slight decrease in precision, from 0.77 to 0.74.  
Overall, the results indicate that ADDAEIL is robust to variations in all three parameters. This robustness reduces the need for extensive hyperparameter tuning and supports practical deployment in streaming anomaly detection tasks.