# A Novel Ensemble Belief Rule-Based Model for Online Payment Fraud Detection
###### Abstract
Traditional methods tend to prioritize the normal transaction samples that are not fraud. Consequently, addressing imbalanced classification becomes very important. Over the past few decades, various approaches have been proposed at data and model level to address class imbalance problems in fraud detection. These approaches include data resampling, class weight adjustments, threshold tuning, sample weighting and so on. For data resampling methods, this category of approaches is highly versatile and can be applied independently of the algorithm type. However, the drawback of this kind of method is the potential of overfitting (oversampling) and loss of important information (undersampling) [9]. The former makes the model perform well on training fraud dataset, while it can hardly predict fraud samples in test datasets. The latter may make the model perform poorly in general since the dataset loses important information. For model level methods such as adjusting class weight, threshold tuning and cost-sensitive learning methods, these are capable of enhancing the model's performance in minority class instances while preserving the original data distribution. However, in practical applications of fraud detection, determining the specific parameters such as weights, classification boundaries and cost sensitivity coefficients for these methods is often challenging and prone to subjective influences. In the latest research within this field, ensemble learning methods [10] have started to gain widespread adoption for tackling fraud detection tasks, especially in solving the class imbalance problems in fraud detection. Ensemble learning is a framework that combines multiple models. After combination, ensemble learning can achieve more accurate classification results than a single model. By applying ensemble methods, the model excels at capturing the feature of a minority class. As a result, it achieves better performance in a minority class. There are mainly three types of ensemble learning [11]: bagging, boosting and stacking. In boosting-based ensemble learning, the current trend involves embedding data preprocessing methods into the boosting algorithm. This approach trains each classifier on the entire dataset, focusing more attention on challenging examples after each training round. The weight distribution used to train the next classifier is adjusted in each iteration. Key algorithms in this category include SMOTEBoost [12], DataBoost [13], MSMOTEBoost [14], RUSBoost [15], among others. However, resampling the original dataset in this manner may lead to sample distortion or loss of important information. Additionally, training on the complete dataset each time can be time-consuming and resource-intensive, especially for large datasets like fraud detection, offering no significant advantage. By contrast, the bagging algorithm enhances the training speed by splitting the dataset into multiple subsets and independently training each subset. It reduces the impact of noise on the model by employing random sampling with replacement, thereby improving model stability and robustness. Additionally, by training multiple models on different subsets and averaging their results, the bagging method reduces variance, mitigating the risk of overfitting and enhancing model generalization. Hence, it is widely applied in various domains and is suitable for fraud detection. Based on the bagging algorithm, ensemble methods do not require reweighting or adjusting weights. The focus is on the process of collecting each bootstrap replica, which involves generating multiple sub-training sets through random sampling with replacement. Each sub-training set is used to independently train a base classifier. The predictions from multiple base classifiers are then combined using weighted methods to obtain the final result. For datasets with multiple attributes, bagging methods randomly select different attributes, reducing the correlation between attributes and improving the diversity and performance of the ensemble model.