# On the Influence of Data Imbalance on Supervised Gaussian Mixture Models
## 5 Results
### Simulation Studies
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Method** & **Precision/** & **Recall/** & **F2** & **Sensitivity/** & **Specificity/** & **Balanced** \\  & **PPV** & **TPR** & **TPR** & **TNR** & **Accuracy** \\ \hline EDDA & 0.0289 (0.0094) & 0.0002 (0.0001) & 0.0003 (0.0001) & 0.0002 (0.0001) & 0.9999 (0.0000) & 0.5001 (0.0000) \\ EDDA+costSens & 0.0339 (0.0002) & 0.8347 (0.0025) & 0.1457 (0.0009) & 0.8347 (0.0025) & 0.7612 (0.0017) & 0.7979 (0.0010) \\ EDDA+adjPriorThreshold & 0.0254 (0.0011) & 0.9030 (0.0097) & 0.1113 (0.0041) & 0.9030 (0.0097) & 0.5488 (0.0273) & 0.7259 (0.0103) \\ EDDA+opTThreshold & 0.0350 (0.0005) & 0.8221 (0.0056) & 0.1489 (0.0015) & 0.8221 (0.0056) & 0.7685 (0.0040) & 0.7953 (0.0013) \\ EDDA+downSamp & 0.0330 (0.0004) & 0.8391 (0.0037) & 0.1421 (0.0014) & 0.8391 (0.0037) & 0.7503 (0.0034) & 0.7947 (0.0015) \\ EDDA+upSamp & 0.0335 (0.0003) & 0.8491 (0.0027) & 0.1446 (0.0011) & 0.8491 (0.0027) & 0.7535 (0.0023) & 0.8013 (0.0010) \\ EDDA+smote & 0.0335 (0.0003) & 0.8490 (0.0023) & 0.1442 (0.0012) & 0.8408 (0.0032) & 0.7551 (0.0027) & 0.7980 (0.0012) \\ MCLUSTDA & 0.1190 (0.0251) & 0.0009 (0.0022) & 0.0011 (0.00202) & 0.0009 (0.0002) & 1.0000 (0.0000) & 0.5004 (0.0001) \\ MCLUSTDA+costSens & 0.0335 (0.0003) & 0.8416 (0.0032) & 0.1434 (0.0011) & 0.8416 (0.0032) & 0.7553 (0.0025) & 0.7985 (0.0012) \\ MCLUSTDA+adjPriorThreshold & 0.0295 (0.0010) & 0.8685 (0.004) & 0.1272 (0.0039) & 0.8685 (0.0049) & 0.6380 (0.0293) & 0.7537 (0.0087) \\ MCLUSTDA+opThreshold & 0.0359 (0.0006) & 0.8144 (0.0068) & 0.1514 (0.0017) & 0.8144 (0.0068) & 0.7745 (0.0045) & 0.7944 (0.0017) \\ MCLUSTDA+downSamp & 0.0326 (0.0004) & 0.8472 (0.0039) & 0.1409 (0.0014) & 0.8472 (0.0039) & 0.7446 (0.0037) & 0.7959 (0.0016) \\ MCLUSTDA+upSamp & 0.0332 (0.0005) & 0.7019 (0.0072) & 0.1390 (0.0018) & 0.7019 (0.0072) & 0.7919 (0.0032) & 0.7469 (0.0033) \\ MCLUSTDA+smote & 0.0333 (0.0005) & 0.6867 (0.0071) & 0.1390 (0.0019) & 0.6867 (0.0071) & 0.7970 (0.0032) & 0. In this simulation study, much like in the previous case, it is evident that addressing class imbalance is important for both the EDDA and McustDA models. Class imbalance exerts a notable influence on model performance, reaffirming the need for the implementation of effective strategies to address this issue. In this simulated scenario, the relevance of the chosen adjustment becomes more apparent, particularly when dealing with a small prior probability for the minority class. Specifically, threshold adjustment emerges as the superior approach in comparison to sampling-based techniques to deal with class imbalance effectively, particularly in scenarios with severely imbalanced class distributions. Looking deeply at the results, notable improvement in sensitivity is evident, a crucial aspect in correctly identifying the minority class, while simultaneously maintaining a substantial level of specificity. This striking balance ultimately leads to an enhanced measure of balanced accuracy, demonstrating the efficacy of the investigated adjustments. However, it is essential to note that both thresholding and sampling-based adjustments come at a cost: a significant decrease in precision coupled with an increase in recall. This trade-off, while substantial, necessitates a careful consideration of the specific priorities and objectives of the classification task.