Posterior Regimes and Latent Deception: Variational Bayesian Inference in Hidden Markov Models for Sequential Fraud Detection in Financial Transactions

Abstract:We present a three-tier progression of Hidden Markov Models: maximum-likelihood (Baum-Welch), variational Bayesian (VBEM), and a neural variational extension (Neural VBEM), that model each customer's transaction history as a trajectory through a small number of latent behavioural regimes, one of which is empirically identified as fraud-associated. The Neural VBEM HMM replaces the fixed Gaussian-multinomial emission family with a learned encoder, compressing a 741-dimensional transaction representation into a 64-dimensional latent space in which the VBEM HMM's posterior operates; a UMAP projection of this space reveals that the discovered regimes are not discrete clusters but ordered segments of a single continuous behavioural manifold, with confirmed fraud concentrated at its extreme. We show that the model's natural output, that is, the posterior probability of regime membership, is routinely mistaken for a fraud probability, and quantify the resulting miscalibration (the regime-membership interpretation error, MRIE); a corrected posterior-predictive score, closes most of this gap. We further distinguish batch (smoothed) inference, which uses look-ahead unavailable at deployment time, from filtered (forward-only) inference, and report both. On IEEE-CIS transaction data, the neural tier achieves a 14.4$\times$ fraud enrichment in its identified regime; while its AUPRC trails a discriminative XGBoost baseline, we show this gap is structural and not incidental, and argue the model is best positioned as a calibrated triage and interpretability layer rather than a drop-in ranking replacement.

44 pages, 10 figures. Adapted from the primary author's MSc dissertation, University of Stirling, Scotland

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2609.34031 [cs.LG]

(or arXiv:2609.34031v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.34031 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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