1. Introduction

2. Related Works

3. Methodology

3.2. Data Analysis

Descriptive analysis, such as count, mean, median, and standard deviation were used to summarise the numerical features and identify errors, furthermore, data visualisation was used to analyse the features and remove the ones that do not add any information. Which allowed some features to be excluded, and the state information ‘addr_state’ to be converted to region, so as not to completely miss out on any benefit that the location might have. Additionally, the descriptive analysis showed that there were outliers and possible errors in some features, for instance, ‘annual_inc’ had a maximum value of $9,522,972, which is a possible error, which would likely affect the debt-to-income ratio ‘dti’, which showed a maximum DTI of 999.00%. The errors and outliers were handled in the data pre-processing stage.

Table 1. Descriptive Analysis of Annual Income and DTI.

Table 1. Descriptive Analysis of Annual Income and DTI.

Features	count	mean	std	50%	max
annual_inc	403,593	76,278.3	71,140.2	65,000	9,522,972
dti	403,593	18.26	10.38	17.62	999

3.4. Addressing Class Imbalance

There are several techniques that can be used to tackle the issue of class imbalance, but no single one is regarded as the best. While popular techniques like SMOTE and ADASYN are used frequently, this research requires that the best technique to make use of is identified, therefore, different techniques were tested as shown below:

Figure 2. Class Imbalance Handling Techniques.

Figure 2. Class Imbalance Handling Techniques.

The techniques evaluated are:

Random Over-Sampling (ROS): It works by randomly adding data samples from the minority class to the dataset until the whole data is balanced [33,34]. It can be represented as

$$\mathrm{New}{\mathrm{S}}_{\mathrm{minority}}={\mathrm{S}}_{\mathrm{minority}}\cup \text{{}{\mathrm{S}}_{\mathrm{minority}}\mathrm{duplicated}\mathrm{until}\left|{\mathrm{S}}_{\mathrm{minority}}\right|={\mathrm{N}}_{\mathrm{majority}}\text{}}$$

(11)

where,

${\mathrm{S}}_{\mathrm{minority}}$ = minority class samples.

${\mathrm{N}}_{\mathrm{majority}}$ = Number of majority class samples.

$\left|{\mathrm{S}}_{\mathrm{minority}}\right|$ = Current size of the minority class.

Random Under-Sampling (RUS): It works by filling the minority class with data from the majority class, thereby reducing the majority class until the whole data is balance [34]. It can be shown as:

$$\mathrm{New}{\mathrm{S}}_{\mathrm{majority}}={\mathrm{S}}_{\mathrm{minority}}\cup \text{{}{\mathrm{S}}_{\mathrm{majority}}\mathrm{duplicated}\mathrm{until}\left|{\mathrm{S}}_{\mathrm{majority}}\right|={\mathrm{N}}_{\mathrm{minority}}\text{}}$$

(12)

SMOTE: It works by generating synthetic data through interpolating between the existing minority class data samples and their nearest neighbour, thereby adding new data point without adding duplicates [9,36]. It generates synthetic data (${\mathrm{x}}_{\mathrm{new}})$with:

$${\mathrm{x}}_{\mathrm{new}}={\mathrm{x}}_{\mathrm{i}}+\text{⋋}*({\mathrm{x}}_{\mathrm{nn}}-{\mathrm{x}}_{\mathrm{i}})$$

(13)

where,

${\mathrm{x}}_{\mathrm{i}}$ = minority class.

${\mathrm{x}}_{\mathrm{nn}}$= one of the nearest neighbours.

$\text{⋋}$ = a random value between [0, 1].

ADASYN: It works in a similar way to SMOTE, but it focuses on generating more synthetic samples for the harder to classify minority class, the number of the synthetic sampled $\mathrm{i}$, $\left({\mathrm{G}}_{\mathrm{i}}\right)$ is calculated as:

$${\mathrm{G}}_{\mathrm{i}}={\mathrm{d}}_{\mathrm{i}}*\mathrm{G}$$

(14)

where,

${\mathrm{d}}_{\mathrm{i}}$ = ratio of the majority neighbours.

$\mathrm{G}$ = total synthetic samples needed.

Tomek-Links is an under-sampling technique that cleans up the data by locating and removing ambiguous or noisy data samples that are near the decision boundary [36,37]. Given a majority class (${\mathrm{x}}_1)$ and a minority class (${\mathrm{x}}_2)$, if they are the nearest neighbours and they belong to different classes, they form a Tomek Link and removing them will help to clean the boundary between classes.

SMOTE-Tomek: It is a combination of SMOTE and Tomek Links, firstly, SMOTE is used to generate the synthetic data samples for the minority class, then Tomek Links are removed to clean up the boundaries between classes, thereby improving the quality of the synthetic data [38].

SMOTE+ENN: It is a hybrid technique that improves the quality of the synthetic data created by SMOTE, as Edited Nearest Neighbour (ENN) is used to remove instances of misclassification of the nearest neighbour [35,36,37,38,39,40].

To address the issue of class imbalance in the LendingClub dataset, the resampling techniques were tested using XGBoost and evaluated using accuracy, precision, recall and AUC. After the data has been balanced, the next step involved testing various splits to determine the best split to use, with 20%, 25%, 30%, 35% and 40% test ratios evaluated. Subsequently, the selected split 80:20 was used in selecting the appropriate features for the model development in the next stage.

3.6. Model Development Process

This process involved using the selected features in the development of predictive models, so as to identify the best performing model that can be used to identify credit default risk. Additionally, methods like hyperparameter tuning and ensemble methods are further used to optimise the models.

3.6.1. Predictive Models

Decision Tree, which has a tree structure that works by recursively splitting the data into subsets of the tree based on a decision rule [1]. It selects the best feature to split based on criteria like Gini index – the impurity of a node and the values closer to 0 are the purer nodes, it is calculated and is calculated as:

$$\mathrm{Gini}=1-\sum _{\mathrm{i}=1}^{\mathrm{c}}{(\mathrm{p}}_{\mathrm{i}}{)}^2$$

(15)

where,

${\mathrm{p}}_{\mathrm{i}}$ = proportion of the data sample that belongs to the class $i$ in a tree node.

$\mathrm{c}$ = number of classes.

Random Forest, an ensemble learning method that combines the predictions gotten from training multiple decision trees to get the final predictions [37,42]. The final predictions are made using majority voting. Since it is a combination of decision trees, it uses the Gini as well for splitting.

SVM, finds the optimal hyperplane that separates the data into different classes [23]. It uses kernel functions to handle non-linear separation by mapping input features into high-dimensional spaces. The hyperplane:

$$\mathrm{h}({\mathrm{x}\text{}}_{\mathrm{i}})=\mathrm{sign}(\mathrm{w}\text{⋅}{\mathrm{x}}_{\mathrm{i}}\text{}+\mathrm{b})$$

(16)

XGBoost, builds an ensemble of weak learners in an iterative manner in order to improve on the models’ performance [17]. It uses gradient boosting with specific loss functions $l$ and regularisation terms $\mathsf{\Omega }\left(f\right)$:

$${\mathrm{L}}^{\left(\mathrm{t}\right)}=\sum _{\mathrm{i}=1}^{\mathrm{n}}\mathrm{l}\left({\mathrm{y}}_{\mathrm{i}},{{\widehat{\mathrm{y}}}_{\mathrm{i}}}^{\left(\mathrm{t}-1\right)}+{\mathrm{f}}_{\mathrm{t}}\left({\mathrm{X}}_{\mathrm{i}}\right)\right)+\mathsf{\Omega }\left({\mathrm{f}}_{\mathrm{t}}\right)$$

(17)

where,

$L^{\left(t\right)}$ = total loss at iteration $t$.

$n$ = data points.

$l\left(y_i,{{\widehat{y}}_i}^{\left(t-1\right)}+f_t\left(X_i\right)\right)$ represents the loss function that measures the difference between the true and predicted labels.

${{\widehat{y}}_i}^{\left(t-1\right)}$ is the previous iteration’s predicted class.

$f_t\left(X_i\right)$, is the current model’s prediction.

ADABoost, focuses on creating strong classifiers by combining multiple weak classifiers [43]. It trains weaker learners on the errors made by the previous ones, and when there is a misclassification, it assigns more weight to them. Final predictions are calculated by:

$$\mathrm{H}\left(\mathrm{x}\right)=\mathrm{sign}\left[\sum _{\mathrm{t}=1}^{\mathrm{T}}{\mathsf{\alpha }}_{\mathrm{t}}{\mathrm{h}}_{\mathrm{t}}\left(\mathrm{x}\right)\right]$$

(18)

where,

$T$ = weak classifiers.

${\alpha }_t$= weight for the weak classifier.

$h_t\left(x\right)$ = predictions for the weak classifier.

$sign$ = determines the final prediction

MLP, is a feedforward type of ANN that consist of the inner layer, multiple hidden layers and an outer layer, and each layer is made up of neurons connected to those in the previous and following layers. Each connection has a weight, and MLP uses backpropagation to adjust the weights based on the error in the output, and gradually increases the predictions. Furthermore, this model is capable of learning complex patterns in data.

3.6.2. Hyperparameter Tuning

This process can help in getting the best performance from each model, and similar to [41], GridSearchCv was used to get the parameters used for the model development. Some of the parameters used for GridSearchCV are shown in Table A2, the values were predominantly chosen to strike a balance between reducing overfitting and increasing the performance of the models, for instance, the max_depth limits the depth of the tree, therefore, the values chosen may capture complexity and make the model efficient. Additionally, for reg_alpha and reg_lambda, which are Lasso (L1) and Ridge (L2) regularisation terms, they allow XGBoost control sparsity as well as the magnitude of the model’s weights. The best parameters identified and used for the model development are shown in Table 3:

3.6.3. Ensemble Techniques

In this stage, some of the models, as well as the top three best performing models are combined using the voting and stacking method. The first method, soft voting, takes the average probability predictions from the models as the final prediction. Additionally, the second method uses the stacking method for the combination, here, a meta-model is used to get the final prediction, the meta-model learns how best to aggregate the predictions to make the final prediction. The ensemble methods used in this work and how they are combined is shown in Figure 3 and Figure 4 respectively.

Figure 3. Ensemble Methods.

Figure 3. Ensemble Methods.

Figure 4. Methods used in combining the model predictions.

Figure 4. Methods used in combining the model predictions.

4. Results

Figure 4. Features Selected.

Figure 4. Features Selected.

Figure 5. Feature Importance.

Figure 5. Feature Importance.

4.1. Model Performance Evaluation

4.1.1. Individual Model Performance

The metrics discussed in Section 3.3.3 were used in the evaluation of the model performance, with the performance of the individual models presented in Table 5:

Table 5. Individual Model Result.

Table 5. Individual Model Result.

Model	Accuracy	Precision	Recall	AUC
Random Forest*	0.8987	0.8996	0.9656	0.9589
Decision Tree	0.7778	0.7743	0.9713	0.7256
SVM	0.7318	0.9476	0.6601	0.8824
XGBoost*	0.9156	0.9478	0.9330	0.9726
ADABoost	0.8458	0.8548	0.9439	0.9305
MLP*	0.8775	0.9008	0.9305	0.9229
*Indicates models part of the ensemble with 3 base-learners

Models with ensembled techniques like Random Forest and XGBoost outperformed simpler models like Decision Tree and SVM, which shows the advantages of combining model predictions to improve their effectiveness. The models – Random Forest and XGBoost showed strong performances with an accuracy of 89.87% and 91.56% respectively. Additionally, the recall, which indicates that the models can effectively identify default cases are 96.56% (Random Forest) and 93.30% (XGBoost), with high AUC scores of 95.89% and 97.29%, which suggests that the models are able to effectively distinguish between the defaulters and the non-defaulters. Similarly, with a recall of 92.48%, MLP had a solid performance, however, SVM had the lowest score, despite having a high precision value of 94.76%, which may suggest that SVM is not able to address the complexity of the credit default data.

The ROC curve in Figure 6 shows the performance of the individual models across different thresholds, displaying how well the models separate the non-default and the default class, furthermore, it shows that all the models performed well.

For the individual models XGBoost with an accuracy of 91.56%, precision of 94.78% and AUC of 97.26% achieved the best results, which shows how effective the model is at handling complex credit default data, with the performance being attributed to XGBoost’s ability to create better predictions by combining the predictions from weaker learners, as well as the built-in regularisation that helps to prevent overfitting, giving it an edge, especially when compared to the other models:

Figure 7. Comparative Result (Individual Model).

Figure 7. Comparative Result (Individual Model).

4.1.2. Ensemble Model Performance

As detailed in Section 3.6.3, the predictions from the individuals can be combined to create stronger learners. The result of combining the models’ predictions is shown below:

Table 6. Ensemble Model Result.

Table 6. Ensemble Model Result.

Model	Accuracy	Precision	Recall	AUC
Voting A	0.9109	0.9099	0.9710	0.9703
Voting B	0.9166	0.9314	0.9532	0.9687
Stacking A	0.9369	0.9559	0.9555	0.9781
Stacking B	0.9188	0.9409	0.9454	0.9708

Combining the models led to an overall increase in the performance, especially when the predictions are combined with the ensemble model which uses a learner model (meta-model) – Stacking. The method A, which combines the predictions from all the models achieved the highest result overall (Staking A), with an accuracy of 93.69%, precision of 95.59 and AUC of 97.81%, which suggests that combining the models with the stacking technique led to an improvement in the performance.

Although XGBoost and the ensemble methods – Voting A, B and Stacking A, B performed well, as seen in Figure 8, however, Stacking A’s performance is impressive, as it is identified as the best model with the ability to effectively separate the classes. This demonstrates the need for the inclusion of more algorithms in the ensemble process, therefore, we propose this technique for the classification of credit default risk. Furthermore, with a precision and recall of approximately 96%, the model shows how well the technique can enhance the individual models, as it uses a meta-model to learn how best to combine predictions.

The comparative result can be seen below, with Stacking A outperforming the other models, with an AUC of 98%, thereby showing how effective ensemble methods can be at optimising the performance of the models.

Figure 9. Comparative Result (All Models).

Figure 9. Comparative Result (All Models).

4.2. Comparison with Baseline Results

The performance of the proposed model is compared with other related works, which served as the baseline for further evaluation. The result can be seen below:

Table 5. Baseline Comparison.

Table 5. Baseline Comparison.

Reference	Dataset	Total Record	Model	Result
Proposed Method	LendingClub	394,073	Stacking	93.7%
[9]	Taiwan Credit-Client	30,000	GBDT*	88.7%
	South German Credit-Client	1,000		83.5%
	Belgium Credit-Client	285,299		86.3%
[10]	LendingClub	282,763	XGBoost	87.9%
[11]	Data from Kaggle (Chatterjee, 2021)	614	Voting	87.3%
[12]	Auto-Finance	25,383	Deep Learning-Optimised Stacking	92.7%
*Gradient Boosted Decision Tree (GBDT)

The proposed method displays a higher accuracy when compared with the other results, [9] achieved accuracy scores ranging from 83.5% to 88.7% using GBDT, with results varying across the different datasets, additionally, [10] achieved an accuracy of 87.9% with the XGBoost model on LendingClub dataset, moreover, [12] achieved an accuracy of 92.7% with Deep Learning-Optimised Stacking, an ensemble model. However, the proposed result performed better with a score of 93.7%, showing how well the model is at predicting credit default.

Finally, SHAP (SHapley Additive exPlanations) with XGBoost model was used to analyse and explain the features as shown in Table A3, with the features resulting in negative values, contributing to the predictions being lower, thereby increasing the likelihood of defaults, for instance, a negative ‘int_rate’ means that higher interest rate pushes the prediction towards default, while positive values, contributes to the predictions being higher, for instance, positive ‘fico_range_low’ means that higher credit scores move the prediction away from being classed as a default. With the proposed model developed, tested and evaluated, this research shows how well the methodology used worked, as testing the techniques to identify the most suitable one contributed to the overall performance of the models, additionally, combining the predictions from wearker classifiers contributed as well.

5. Conclusion and Recommendations

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