Fraud Detection by Integrating Multisource Heterogeneous Presence-Only Data

In credit fraud detection practice, certain fraudulent transactions often evade detection because of the hidden nature of fraudulent behavior. To address this issue, an increasing number of positive-unlabeled (PU) learning techniques have been employed by more and more financial institutions. However, most of these methods are designed for single data sets and do not take into account the heterogeneity of data when they are collected from different sources. In this paper, we propose an integrative PU learning method (I-PU) for pooling information from multiple heterogeneous PU data sets. A novel approach that penalizes group differences is developed to explicitly and automatically identify the cluster structures of coefficients across different data sets, thus offering a plausible interpretation of heterogeneity. Furthermore, we apply a bilevel selection method to detect the sparse structure at both the group level and within-group level. Theoretically, we show that our proposed estimator has the oracle property. Computationally, we design an expectation-maximization (EM) algorithm framework and propose an alternating direction method of multipliers (ADMM) algorithm to solve it. Simulation results show that our proposed method has better numerical performance in terms of variable selection, parameter estimation, and prediction ability. Finally, a real-world application showcases the effectiveness of our method in identifying distinct coefficient clusters and its superior prediction performance compared with direct data merging or separate modeling. This result also offers valuable insights for financial institutions in developing targeted fraud detection systems.