## 5 Results and Discussion
### Effect of Noise Level, Informative Level, and Number of Features on All Feature Importance  
Figure 5 shows the feature importance results of SME and the MME Framework with different fusion strategies averaged across three different noise levels in the data. The results on the effect of noise in data on ensemble feature importance using the RMSE and \(R^{2}\) metrics  
Figure 4: Average feature importance error between SME and our MME Framework with the training and test datasets. \begin{table}
\begin{tabular}{c c} \hline \hline
**Models** & **Interpretability Methods** \\ \hline Random Forest & Permutation Importance, SHAP \\ \hline Gradient Boosted Trees & Permutation Importance, SHAP \\ \hline Support Vector Regressor & Permutation Importance, SHAP \\ \hline Deep Neural Network & Permutation Importance, SHAP, and Integrated Gradient \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Interpretability methods employed by each ML model for feature importance fusion. are shown in Sections S1.3 and S1.4 of the Supplementary Material. The best performing ensemble method averaged across all noise levels is MME Framework using majority vote. The MME Framework that uses majority vote outperforms the best SME method, SHAP, by 14.2%. In addition, Table 4 and Figure 6 show how the feature importance errors change for all SME and MME Framework methods as the noise level increases. In Table 4, we observe that the MAE decreases marginally, from a noise level of 0 standard deviations to 2 standard deviations, and then, it increases again by four times the standard deviation. The addition of 2 standard deviation noise to the dataset improves the generalisation performance of ML models, leading to lower errors [51]. However, the feature importance errors increase when the noise in the dataset reaches four times the standard deviation, indicating that the noise level has negatively impacted ML model performance. Overall, however, the noise levels have little effect on the feature importance errors. The results also reveal that the M  
Figure 7 presents the feature importance MAE error for all SME and the MME Framework with different fusion strategies averaged across five different feature informative levels in the data. The results on the effect of feature informative levels on ensemble feature importance using the RMSE and \(R^{2}\) metrics are shown in Sections S1.5 and S1.6 of the Supplementary Material. The best performing method is MME with majority vote followed by MME with mean and RATE. All MME Framework methods except for that with the mode outperform SME by more accurately quantifying the feature importance. The error bar (standard deviation) for the effect of feature informative levels in Figure 7 has a smaller range than the effect of noise and the effect of number of features. The low standard deviation indicates that the feature informative levels explain most of the variances. From Table 5, we observe that, when 20% of the features are informative, the best feature importance methods are MME Framework with Modified Thompson tau test and median, and they outperform the best SME method, SHAP, by 9.1%. For the 40% feature informative level, the MME Framework with RATE (Kendall and Spearman) and mean have the lowest errors, with 6.9% improvement over SME with SHAP. For the 60% feature informative level, the MME Framework using RATE (Kendall and Spearman) have the best results, with a 4.1% improvement over SME with SHAP. Furthermore, the MME Framework with majority vote obtains the lowest error for both 80% and 100% feature informative level. The best performing SME is using PI. MME with majority votes outperforms SME's best results by 25.4% and 23.0% for 80% and 100% feature informative level, respectively. Figure 6: Effect of noise levels on ensemble feature importance. Figure 7: Effect of feature informative level on all ensemble feature importance methods. Figure 8 shows the relationship between the MAE of feature importance errors and the percentage of feature informative level.