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× 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.
Related
- Variational objectives for amortized Bayesian inference in inverse problems: The role of posterior conditioning
- Differentiable Systematic Resampling for Variational Sequential Monte Carlo
- From Variational Optimization to Flow-Based Transport: Posterior-Geometry Regularization for Ill-Conditioned Data Assimilation
- Sampling-Based Batch Sequential Design by Stein Variational Gradient Descent
- Convergence of Coordinate Ascent Variational Inference for log-concave measures via optimal transport
BibTeX
@misc{obukofe2026posterior,
title = {{Posterior Regimes and Latent Deception: Variational Bayesian Inference in Hidden Markov Models for Sequential Fraud Detection in Financial Transactions}},
author = {Joseph Uririoghene Obukofe and Anthony O'Hare and Chioma Sandra Dike},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34031},
eprint = {2609.34031},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34031},
}
RIS
TY - UNPB
TI - Posterior Regimes and Latent Deception: Variational Bayesian Inference in Hidden Markov Models for Sequential Fraud Detection in Financial Transactions
AU - Joseph Uririoghene Obukofe
AU - Anthony O'Hare
AU - Chioma Sandra Dike
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.34031
UR - https://arxiv.org/abs/2609.34031
AB - 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× 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.
ER -