# Extreme Learning Machine Enhanced Gradient Boosting for Credit Scoring
## 4 Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Dataset** & **Algorithm** & **Accuracy** & **AUC** & **Precision** & **Recall** & **F1** & **BS** \\ \hline \multirow{6}{*}{Australian} & XGBoost & 0.8633 & 0.9394 & 0.8449 & 0.8487 & 0.8468 & 0.0992 \\  & LightGBM & 0.8624 & 0.9371 & 0.8476 & 0.8422 & 0.8449 & **0.0942** \\  & AugBoost-RP & 0.8633 & 0.9416 & 0.8449 & 0.8487 & 0.8468 & 0.0991 \\  & AugBoost-PCA & **0.8681** & 0.9415 & 0.8533 & 0.8497 & **0.8515** & 0.0951 \\  & AugBoost-NN & 0.8645 & **0.9424** & 0.8435 & **0.8539** & 0.8487 & 0.0984 \\  & AugBoost-ELM & 0.8635 & 0.9422 & **0.8485** & 0.8439 & 0.8462 & 0.0993 \\ \hline \multirow{6}{*}{German} & XGBoost & 0.7582 & 0.7811 & 0.7757 & 0.9208 & 0.842 & 0.1652 \\  & LightGBM & 0.7615 & 0.7776 & **0.7887** & 0.9007 & 0.841 & 0.1657 \\  & AugBoost-RP & 0.7519 & 0.7707 & 0.7862 & 0.8867 & 0.8335 & 0.1694 \\  & AugBoost-PCA & 0.7605 & 0.7735 & 0.7956 & 0.8852 & 0.838 & 0.1702 \\  & AugBoost-NN & 0.7604 & 0.7843 & 0.7766 & 0.9237 & 0.8438 & 0.1644 \\  & AugBoost-ELM & **0.7617** & **0.7861** & 0.7775 & **0.9245** & **0.8446** & **0.1637** \\ \hline \multirow{6}{*}{Japanese} & XGBoost & 0.8678 & 0.9362 & 0.8959 & 0.8625 & 0.8789 & 0.095 \\  & LightGBM & 0.8634 & 0.9349 & 0.8829 & **0.8696** & 0.8762 & 0.0957 \\  & AugBoost-RP & 0.8669 & 0.9398 & 0.8964 & 0.8599 & 0.8778 & 0.095 \\  & AugBoost-PCA & 0.8676 & 0.9388 & 0.8957 & 0.8622 & 0.8786 & 0.0949 \\  & AugBoost-NN & 0.8676 & 0.9395 & 0.9004 & 0.8567 & 0.878 & 0.0944 \\  & AugBoost-ELM & **0.8687** & **0.9399** & **0.901** & 0.8582 & **0.8791** & **0.0942** \\ \hline \multirow{6}{*}{Taiwan} & XGBoost & 0.6945 & 0.7504 & 0.7301 & 0.6175 & 0.6691 & 0.2006 \\  & LightGBM & 0.6954 & 0.7494 & 0.7292 & **0.6218** & **0.6712** & 0.201 \\ \cline{1-1}  & AugBoost-RP & 0.6941 & 0.7508 & 0.7295 & 0.617 & 0.6686 & 0.2007 \\ \cline{1-1}  & AugBoost-PCA & 0.6943 & 0.7508 & 0.7297 & 0.6174 & 0.6689 & 0.2006 \\ \cline{1-1}  & AugBoost-NN & 0.6933 & 0.7514 & 0.7285 & 0.616 & 0.6677 & 0.2005 \\ \cline{1-1}  & AugBoost-ELM & **0.6963** & **0.7516** & **0.7322** & 0.6194 & 0.6711 & **0.2005** \\ \hline \end{tabular}
\end{table} 
Table 8: Performance comparison of advanced ensemble models for credit datasets. Since each credit scoring metric has its advantages and limitations, to give a view of the statistical ranks for credit scoring models, we perform a significance test procedure. Because parametric significance test method computers statistic value based on the assumption that credit scoring datasets follow a normal distribution, we adopt a simple and powerful non-parametric way for significance test. In this study, Friedman test, a rank-based non-parametric significance test, is introduced to investigate the statistical performance of credit scoring algorithms. The Friedman statistic value is calculated as:  
\[\chi^{2}=\frac{12D}{K(K+1)}\left[\sum_{k=1}^{K}AvR_{k}^{2}-\frac{K(K+1)^{2}}{4} \right], \tag{20}\]  
where \(K\) denotes the number of classifiers, \(D\) represents the number of datasets. \(AvR_{k}=\frac{1}{D}\sum_{d=1}^{D}r_{k,d}\) is the average rank of \(k\)-th classifier, and \(r_{k,d}=\frac{1}{4}(r_{k,d,ACC}+r_{k,d,AUC}+r_{k,d,F1}+r_{k,d,BS})\), \(r_{k,d,ACC}\), \(r_{k,d,AUC}\), \(r_{k,d,F1}\), \(r_{k,d,BS}\) are the ranks of \(k\)-th classifier on \(d\)-th dataset that are computed based on accuracy score, AUC, F1, and BS, respectively. By calculating the Friedman statistic value, the issue of whether there is a significant difference among credit scoring models is detected. Specifically, when \(\chi\) is larger than a critical value at a significance level, the null hypothesis (there is no significant difference between credit scoring models) is rejected, and a post hoc test, Nemenyi test, is further performed for pair-wise comparison.