Incremental learning strategies for credit cards fraud detection

Abstract

Every second, thousands of credit or debit card transactions are processed in financial institutions. This extensive amount of data and its sequential nature make the problem of fraud detection particularly challenging. Most analytical strategies used in production are still based on batch learning, which is inadequate for two reasons: Models quickly become outdated and require sensitive data storage. The evolving nature of bank fraud enshrines the importance of having up-to-date models, and sensitive data retention makes companies vulnerable to infringements of the European General Data Protection Regulation. For these reasons, evaluating incremental learning strategies is recommended. This paper designs and evaluates incremental learning solutions for real-world fraud detection systems. The aim is to demonstrate the competitiveness of incremental learning over conventional batch approaches and, consequently, improve its accuracy employing ensemble learning, diversity and transfer learning. An experimental analysis is conducted on a full-scale case study including five months of e-commerce transactions and made available by our industry partner, Worldline.

Appendices

A Appendix: Additional metrics

As explained in Sect. 2, taking into account the Pr@100 can be more relevant because of the limited number of investigators or investigations per day. Figures 6 and 7 summarize the results in the form of F/N tests ([37]).

Another interesting indicator can be obtained by calibrating the AUPRC. Indeed, the number of fraud to detect per day ranges from 0.095 to 0.335% (the coefficient of variation is 21%.). The AUPRC is calibrated in such a way that it is invariant to the fraud prior (see [42] for details). Figures 8 and 9 summarize the results in the form of F/N tests ([37]).

The purpose of those two additional metrics is to be extensive on the results and to provide different points of view for the evaluation. For the sake of conciseness, we will not comment all the results once again. This appendix shows that the conclusions are the same, in terms of statistical tests, regardless of the metric used: Pr@100, uncalibrated AUPRC and calibrated AUPRC. However, since those three metrics do not measure exactly the same quantities, there are small variations in the actual ordering of the methods in terms of average results.

Fig. 6

F/N test based on the metric Pr@100. See caption of Fig. 2 for details

Fig. 7

F/N test based on the metric Pr@100. See caption of Fig. 3 for details

Fig. 8

F/N test based on the metric calibrated AUPRC. See caption of Fig. 2 for details

Fig. 9

F/N test based on the metric calibrated AUPRC. See caption of Fig. 3 for details

B Appendix: Transfer learning in details

This description is based on [38] and is here to make the paper self-contained. Algorithm 4 details how transfer learning is embedded into the continuous approach. In our case, the target domain is the data used to initialize the incremental NN model and the source domain is the new batch of data. We consider here only the univariate case where each feature is transferred independently of the others.

The transfer process is a nonlinear monotonous transformation of the values of a continuous random variable X (the source data), such that the cumulative distribution function (CDF) of X after transformation matches a given CDF F (the target data).

First, we compute the value of the empirical CDF of X (noted $\hat{F}$) at each observed value $x_i, i=1,\dots , n$. The transferred value $x_i^\prime$ is then chosen such that $F(x_i^\prime ) = \hat{F}(x_i)$. We denote source examples by $x_i^{(s)}, i = 1,\dots ,n^{(s)}$ and target examples by $x_j^{(t)}, j = 1,\dots ,n^{(t)}$, with $n^{(s)}$ and $n^{(t)}$, respectively, the number of source and target examples. We also note the value of the empirical CDF as $p_i^{(s)}=\hat{F}^{(s)}(x_i^{(s)})$ and $p_j^{(t)}=\hat{F}^{(t)}(x_j^{(t)})$.

The source examples $x_i^{(s)}$ are transformed to a CDF that matches the empirical CDF $\hat{F}^{(t)}$ of the target examples. The target examples are left unmodified. For each source example $x_i^{(s)}$ and the corresponding empirical CDF value $p_i^{(s)}$, we find the two consecutive empirical CDF values $p_{j_1}^{(t)}$ and $p_{j_2}^{(t)}$ framing $p_i^{(s)}$ in the target domain:

$$\begin{aligned} p_{j_1}^{(t)} \le p_i^{(s)} < p_{j_2}^{(t)} \end{aligned}$$

with $j_1 + 1 = j_2$. $x_i^{(s)\prime }$ is then computed as the linear interpolation between the values $x_{j_1}^{(t)}$ and $x_{j_2}^{(t)}$.