Abstract:

In response to the weak applicability of backpropagation neural network models with Cross Entropy as the objective function to imbalanced samples， especially the low recognition accuracy of default samples that financial institutions focus on， the ACPL （Adaptive Class Perception Loss） function in the field of image recognition is introduced into credit risk assessment to construct a BPNN-ACPL （Back Propagation Neural Network-Adaptive Class Perception Loss） imbalanced credit evaluation model with adaptive adjustment function for sample loss weights.In order to evaluate the performance and robustness of the credit risk prediction model， three real credit data， seven comparative models， five model evaluation criteria， and two different training and testing set partitioning ratios are used. The three empirical data are 1298 farmer data from a small credit institution in China， 2044 farmer data from a large commercial bank in China， and 1000 German credit data publicly released by UCI. The seven comparative models are BPNN-CBCE （Back Propagation Neural Network-Class Balanced Cross Entropy）， BPNN-CE （Back Propagation Neural Network-Cross Entropy）， XGBoost （eXtreme Gradient Boosting）， SVM （Support Vector Machine）， DT （Decision Tree）， RF （Random Forest）， and KNN （K-Nearest Neighbors）. The five evaluation criteria are ACC （Accuracy）， AUC （Area under the ROC curve）， NDR （Non-default recall）， DR （Default recall）， and GM （Geometric mean）. The ratio of dividing the two different training and testing sets is 9∶1 and 7∶3， respectively. Empirical findings show that compared to the BPNN-CBCE model constructed based on sample loss reweighting， the proposed model has advantages in improving the recognition of default samples and avoiding misjudgment of non-default samples； Compared with traditional backpropagation neural network models and shallow machine learning models， the proposed model has significant effects in identifying defaulting customers and effectively distinguishing between the two types of customers； The proposed model demonstrates robust credit risk prediction performance on multiple credit datasets. Introducing an adjustment term in the Cross Entropy function that can adaptively adjust the loss of two types of samples. Its essence is to determine whether the sample has been misjudged based on the predicted value of sample default， and then adaptively calculate the gradient suitable for accurate identification of the sample. When the sample is misjudged， it retains both the positive gradient accumulated by itself and the negative gradient applied to the opposite class sample. When the sample is accurately identified， only the sample is retained as its own accumulated positive gradient. The introduction of the adjustment term in the ACPL function can not only improve the learning strength and prediction accuracy of the model for default samples， but also avoid misjudgment of non-default samples， providing a new reference for credit risk evaluation of non-equilibrium samples.

Key words: credit evaluation, imbalance, ACPL loss, cross entropy