## 5 Results and Discussion
### Effect of Noise Level, Informative Level, and Number of Features on All Feature Importance
As the percentage of feature informative level increases the feature importance errors increases. The higher number of contributing (non-zero) features to the output increases the difficulty of quantifying feature importance leading to higher errors. Figure 9 depicts the average of all SME and the MME Framework with fusion methods across 20, 60, and 100 features. The results on the effect of number of features on ensemble feature importance using the RMSE and \(R^{2}\) metrics are shown in Sections S1.7 and S1.8 of the Supplementary Material. Similar to the effect of noise level and the percentage of informative features on feature importance errors, the MME Framework with majority vote has the lowest error across all features. The error bar for the effect of feature number in Figure 9 has a smaller range compared with the feature importance errors of the effect of noise but larger than the effect of number of features. From Table 6, we observe that, when there are 20 and 40 features, the method with the lowest feature importance errors is the MME Framework with majority vote, and it outperforms the best SME method--SHAP by 8.2% and 26.2%, respectively. For 100 features, the MME Framework using the mode is the most accurate method, and it outperforms the best SME method, PI by 20.5%. For SME, PI has lower feature importance errors compared with SHAP as the number of informative features and features increases. \begin{table}
\begin{tabular}{l l c c c c c} \hline \hline  & \multirow{2}{*}{**Models**} & \multicolumn{5}{c}{**Feature Informative Level (\%)**} \\ \cline{3-7}  & & **20 (10\({}^{-2}\))** & **40 (10\({}^{-2}\))** & **60 (10\({}^{-2}\))** & **80 (10\({}^{-2}\))** & **100 (10\({}^{-2}\))** \\ \hline \multirow{4}{*}{SME} & PI & 2.7 \(\pm\) 0.4 & 6.7 \(\pm\) 0.8 & 11.2 \(\pm\) 2.0 & 13.8 \(\pm\) 1.0 & 16.5 \(\pm\) 1.3 \\  & SHAP & 2.2 \(\pm\) 0.4 & 5.8 \(\pm\) 0.8 & 9.7 \(\pm\) 1.0 & 14.2 \(\pm\) 1.5 & 17.3 \(\pm\) 1.9 \\  & IG & 6.3 \(\pm\) 7.2 & 10.7 \(\pm\) 7.2 & 15.8 \(\pm\) 7.2 & 22.2 \(\pm\) 7.2 & 26.7 \(\pm\) 7.2 \\ \hline \multirow{4}{*}{MME} & RATE (Kendall) & 2.1 \(\pm\) 0.4 & **5.4 \(\pm\) 1.1** & **9.3 \(\pm\) 1.5** & 12.3 \(\pm\) 1.6 & 15.9 \(\pm\) 3.0 \\  & RATE (Spearman) & 2.1 \(\pm\) 0.5 & **5.4 \(\pm\) 1.1** & **9.3 \(\pm\) 1.5** & 12.3 \(\pm\) 1.6 & 15.9 \(\pm\) 3.0 \\  & Median & **2.0 \(\pm\) 0.6** & 5.9 \(\pm\) 1.4 & 10.2 \(\pm\) 1.8 & 13.0 \(\pm\) 2.4 & 16.7 \(\pm\) 3.5 \\  & Mean & 2.1 \(\pm\) 0.5 & **5.4 \(\pm\) 1.1** & 9.4 \(\pm\) 1.5 & 12.3 \(\pm\) 1.6 & 15.7 \(\pm\) 3.0 \\  & Mode & 7.0 \(\pm\) 2.0 & 9.0 \(\pm\) 3.1 & 12.4 \(\pm\) 3.1 & 13.3 \(\pm\) 1.9 & 15.0 \(\pm\) 3.0 \\  & Box-whiskers & 2.1 \(\pm\) 0.6 & 5.6 \(\pm\) 1.1 & 9.5 \(\pm\) 1.4 & 12.9 \(\pm\) 1.7 & 16.1 \(\pm\) 2.9 \\  & Tau test & **2.0 \(\pm\) 0.6** & 5.6 \(\pm\) 1.2 & 9.5 \(\pm\) 1.5 & 12.4 \(\pm\) 1.7 & 15.7 \(\pm\) 3.0 \\  & Majority vote & 3.1 \(\pm\) 0.9 & 6.5 \(\pm\) 1.5 & 9.4 \(\pm\) 1.6 & **10.3 \(\pm\) 2.1** & **12.7 \(\pm\) 3.4** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of feature importance MAE between different SME and our the MME Framework for different percentages of informative level. Figure 8: Effect of feature informative levels on ensemble feature importance methods. Figure 10 shows the relationship between the MAE of feature importance and the number of features as they increase. The higher number of features increases the difficulty of quantifying feature importance accurately.