# Extreme Learning Machine Enhanced Gradient Boosting for Credit Scoring
## 4 Experimental Results
The same as the results on the previous credit datasets, ensemble credit scoring algorithms get a larger ROC curve area compared with other credit scoring models further proves ensemble learning approaches are the good choice to improve the performance of credit scoring. On the Taiwan dataset, as can be observed from Figure 2d, the ROC curve of AugBoost-ELM is close to that of GBDT. To reveal the concrete performance of credit scoring models, we further investigate the quantitative evaluation results of various credit scoring models on the credit datasets. In this study, we selected six metrics to comprehensively compare the performance of the credit scoring model, which include accuracy score, AUC score, precision score, recall score, F1 score, Brier loss. Accuracy score computes the ratio of samples that are correctly classified, which is defined as:  
\[ACC=\frac{TP+TN}{TP+TN+FP+FN}. \tag{15}\]  
AUC score calculates the area under the ROC curve and measures the overall predictive performance of credit scoring models. The precision score represents the ratio of samples whose predicted result is \"bad\" while its label is \"bad\", which can be calculated as:  
\[prec=\frac{TP}{TP+FP}. \tag{16}\]  
Recall score measures how many \"bad\" applicants are correctly predicted, which can be defined as:  
\[recall=\frac{TP}{TP+FN}. \tag{17}\]  
F1 is a comprehensive metric of precision score and recall score, which can be calculated as:  
\[\text{F1}=\frac{2\times precision\times recall}{precision+recall}. \tag{18}\]  
Brier loss score describes the average error between the predicted result and the label, which can be calculated as:  
\[BS=\frac{1}{N}\sum_{i=1}^{N}(p_{i}-y_{i})^{2}, \tag{19}\]  
where \(p_{i}\) represents the predicted probability of the \(i\)-th sample, \(y_{i}\) is the label of the \(i\)-th sample, and \(N\) is the number of samples. Table 4 presents the performance comparison of credit scoring models for the Australian dataset. As can be seen from Table 4, AugBoost-ELM gets the best AUC, which is consistent with the ROC curves in Figure 2a, demonstrating AugBoost-ELM is a good choice to recognize good and bad applicants. On the Australian dataset, LR performs well,  
it achieves the best accuracy score. Therefore, if we are aiming at finding an efficient and effective credit scoring model for the Australian dataset, LR is the best choice. KNN gets the best precision score and worst recall score, leading to the comprehensive performance on the AUC score, F1 score, and BS poor. Moreover, compared with ML-based individual classifiers, RF and GBDT get better AUC score, F1 score, and BS, indicating the effectiveness of ensemble strategy. Compared with GBDT, though AugBoost-ELM gets better AUC score and precision score, its poor recall score results in a small F1 and large BS. In other words, if we focus on the discrimination of good/bad applicants, LR is the best choice; if we are concerned more about the prediction of the PD, AugBoost-ELM is a better choice. Table 5 shows the performance comparison of credit scoring models for the German dataset. As can be seen from Table 5, AugBoost-ELM gets the optimal AUC score, F1 score, and BS score, revealing that ELM-based supervised feature augmentation is able to enhance the discrimination ability of good/bad applicants. Furthermore, Table 5 further demonstrates statistical-based credit scoring models are the alternative solution to achieve accurate credit scoring compared with ML-based individual classifiers. Furthermore, as is shown in Table 5, in the comparison among ML-based individual classifiers, NN outperforms other ML-based credit scoring algorithms such as DT, KNN, and SVM. This is because NN is a robust algorithm that can learn nonlinear relationships from complex credit datasets. Compared with the bagging-based ensemble method RF, the superior performance of GBDT shows that boosting ensemble strategy is more suitable for the modeling of PD.