Uncertainty quantification of machine learning and deep learning methods plays an important role in enhancing trust to the obtained result. In recent years, a numerous number of uncertainty quantification methods have been introduced. Monte Carlo dropout (MC-Dropout) is one of the most well-known techniques to quantify uncertainty in deep learning methods. In this study, we propose two new loss functions by combining cross entropy with Expected Calibration Error (ECE) and Predictive Entropy (PE). The obtained results clearly show that the new proposed loss functions lead to having a calibrated MC-Dropout method. Our results confirmed the great impact of the new hybrid loss functions for minimising the overlap between the distributions of uncertainty estimates for correct and incorrect predictions without sacrificing the model's overall performance.

Countless research works of deep neural networks (DNNs) in the task of credit card fraud detection have focused on improving the accuracy of point predictions and mitigating unwanted biases by building different network architectures or learning models. Quantifying uncertainty accompanied by point estimation is essential because it mitigates model unfairness and permits practitioners to develop trustworthy systems which abstain from suboptimal decisions due to low confidence. Explicitly, assessing uncertainties associated with DNNs predictions is critical in real-world card fraud detection settings for characteristic reasons, including (a) fraudsters constantly change their strategies, and accordingly, DNNs encounter observations that are not generated by the same process as the training distribution, (b) owing to the time-consuming process, very few transactions are timely checked by professional experts to update DNNs. Therefore, this study proposes three uncertainty quantification (UQ) techniques named Monte Carlo dropout, ensemble, and ensemble Monte Carlo dropout for card fraud detection applied on transaction data. Moreover, to evaluate the predictive uncertainty estimates, UQ confusion matrix and several performance metrics are utilized. Through experimental results, we show that the ensemble is more effective in capturing uncertainty corresponding to generated predictions. Additionally, we demonstrate that the proposed UQ methods provide extra insight to the point predictions, leading to elevate the fraud prevention process.