## 1 Introduction  
As already stated in the companion paper [1], the rapid development of e-commerce online payment has become more and more popular, and therefore it also represents a challenge, not only to secure the transactions but also to avoid false positives in fraud detection algorithms. According to a report by The Alan Turing Institute [2], the number of transactions wrongly rejected due to suspected fraud can pose an equivalent threat to actual fraud in the industry of the financial services. Another study stated that transactions that were wrongly declined due to suspected fraud account for USD 118 billion in retail losses [3]. As a consequence, the banks are now forced to devote an increasing amount of resources to discriminate among legitimate transaction and fraud to cope with the difficult dilemma of avoiding impostors' actions while not limiting e-commerce's inexorable growth. However, this is not an easy task, since scammers try their best to ensure that the profiles of the transactions differ as little as possible from the real ones, trying to model extremely assimilated behavioral profiles [4]. To cope with this emerging new reality, financial institutions hire skilled expert fraud software engineers, who develop full packages of new and sophisticated strategies to pursue this purpose. Fraud detection primitive strategies, such as expert systems, were very much related to checklists of risk factors, e.g., repeated declined transactions, multiple failed attempts to enter a credit card number, or living beyond means. However, the emergence of machine learning (ML) techniques has allowed the creation of new schemes capable of providing more adequate and precise alternatives to respond to the potential (or actual) security threats based on historical transactional records. From a mathematical perspective, credit fraud detection (CFD) could be seen and analyzed as a novelty detection problem [2]. In this direction, a possible approach could be to find lower dimensional embeddings to model the original dataset, where anomalies are expected to be detached from normal data [5]. Autoencoders have recently emerged as a resourceful deep learning family of methods for dimensionality reduction and feature extraction. According to the literature, these techniques have shown to offer improvements in accuracy, computational efficiency, and the subsequent user satisfaction in their applications [6]. Even so, one of the big challenges, and a potential barrier, for autoencoders is the lack of visibility of the underlying model in the encoding and decoding sides. Therefore, these data-driven models are frequently considered as black boxes, meaning that although inputs and outputs are known, and regardless of the good results provided in many problems, the model itself exhibits relevant limitations to show the role played by each of the features in the final outcome. That is why the authorities and regulatory bodies have shown, to date, significant reluctance to accept a generalized use of these modern techniques [7]. Although this reality becomes a clear limitation, the wide consensus among researchers and financial institutions suggests that ML still has great potential, even though a number of challenges still require special attention [8]. As an example, in the case of the United States and in order to avoid any discrimination, the features such as race, sex, or marital status, or any related one, should be very carefully applied or even not used according to existing regulations [9]. Moreover, an algorithm to lend money could be found in violation of this prohibition even if the algorithm does not directly use any of the prohibited categories, but instead it uses data that can be highly correlated with the protected categories. Lack of transparency is becoming a real challenge in fact in the European Union, as the General Data Protection Regulation adopted in 2018 gives its citizens the right to receive an explanation of decisions based on automated processing [8].