Heavy-tail-aware representation learning and dynamic Bayesian state modelling to derive an operational proxy definition of problem gambling risk from routine online gambling data

Abstract Background: Problem gambling causes harm, but operational identification often relies on heuristic thresholds or sparse manual reviews. Routine online gambling logs are heavy-tailed and temporally structured, complicating risk definition and early detection. Methods: We analysed de-identified records from an online gambling operator across four streams (transactions, bets, sessions, payments). Time series were summarised into leakage-audited 30-day windows with heavy-tail-aware exceedance frequency and magnitude features. Window embeddings were learned using a hierarchical conditional variational autoencoder: a teacher trained on responsible-gambling proxy signals, then a student fine-tuned on sparse manual analyst assessments on the training split only. To address missing-not-at-random assessments, backlog-aware label inference conservatively augmented training data. Dynamic regimes were inferred from embeddings using a regularised Gaussian hidden Markov model, yielding a three-class operational proxy definition. Agreement with analyst assessments and early-warning utility under explicit capacity constraints were evaluated on held-out labels. Results: Balanced accuracy on labelled test windows ranged from 0.38 (transactions) to 0.62 (payments), with best macro-averaged F1-score in bets (0.54). Under a capacity-constrained top-10-per-week queue, escalation detection ranged from 0.39 (sessions) to 0.62 (bets), with median lead times of 42–290 days. Conclusions: Heavy-tail-aware representations combined with dynamic regime modelling can derive an auditable operational proxy definition of gambling-related risk from routine data and support realistic, capacity-constrained monitoring.