Managing a pool of rules for credit card fraud detection by a Game Theory based approach

In the automatic credit card transaction classification there are two phases: in the Real-Time (RT) phase the system decides quickly, based on the bare transaction information, whether to authorize the transaction; in the subsequent Near-Real-Time (NRT) phase, the system enacts a slower ex-post evaluation, based on a larger information context. The classification rules in the NRT phase trigger alerts on suspicious transactions, which are transferred to human investigators for final assessment. The management criteria used to select the rules, to be kept operational in the NRT pool, are traditionally based mostly on the performance of individual rules, considered in isolation; this approach disregards the non-additivity of the rules (aggregating rules with high individual precision does not necessarily make a high-precision pool). In this work, we propose to apply, to the rule selection for the NRT phase, an approach which assigns a normalized score to the individual rule, quantifying the rule influence on the overall performance of the pool. As a score we propose to use a power-index developed within Coalitional Game Theory, the Shapley Value (SV), summarizing the performance in collaboration. Such score has two main applications: (1) it can be used, within the periodic rule assessment process, to support the decision of whether to keep or drop the rule from the pool; (2) it can be used to select the k top-ranked rules, so as to work with a more compact rule set. Using real-world credit card fraud data containing approximately 300 rules and 3×10⁵ transactions records, we show that: (1) this score fares better – in granting the performance of the pool – than the one assessing the rules in isolation; (2) that the same performance of the whole pool can be achieved keeping only one tenth of the rules — the top-k SV-ranked rules. We observe that the latter application can be reframed in terms of Feature Selection (FS) task for a classifier: we show that our approach is comparable w.r.t benchmark FS algorithms, but argue that it presents an advantage for the management, consisting in the assignment of a normalized score to the individual rule. This is not the case for most FS algorithms, which only focus in yielding a high-performance feature-set solution.