Rule-State Inference (RSI): A Bayesian Framework for Compliance Monitoring in Rule-Governed Domains

Existing machine learning frameworks for compliance monitoring – Markov Logic Networks, Probabilistic Soft Logic, supervised models – share a fundamental paradigm: they treat observed data as ground truth and attempt to approximate rules from it. This assumption breaks down in rule-governed domains such as taxation or regulatory compliance, where authoritative rules are known a priori and the true challenge is to infer the latent state of rule activation, compliance, and parametric drift from partial and noisy observations. We propose Rule-State Inference (RSI), a Bayesian framework that inverts this paradigm by encoding regulatory rules as structured priors and casting compliance monitoring as posterior inference over a latent rule-state space S = {(a_i, c_i, delta_i)}, where a_i captures rule activation, c_i models the compliance rate, and delta_i quantifies parametric drift. We prove three theoretical guarantees: (T1) RSI absorbs regulatory changes in O(1) time via a prior ratio correction, independently of dataset size; (T2) the posterior is Bernstein-von Mises consistent, converging to the true rule state as observations accumulate; (T3) mean-field variational inference monotonically maximizes the Evidence Lower BOund (ELBO). We instantiate RSI on the Togolese fiscal system and introduce RSI-Togo-Fiscal-Synthetic v1.0, a benchmark of 2,000 synthetic enterprises grounded in real OTR regulatory rules (2022-2025). Without any labeled training data, RSI achieves F1=0.519 and AUC=0.599, while absorbing regulatory changes in under 1ms versus 683-1082ms for full model retraining – at least a 600x speedup.

💡 Research Summary

The paper tackles a fundamental mismatch in many compliance‑monitoring applications: while regulatory rules are publicly known and fixed, most machine‑learning approaches treat the observed data as ground truth and try to learn the rules from it. This “data‑to‑rule” paradigm works well for domains where the underlying logic is unknown, but it collapses in rule‑governed settings such as tax administration, medical protocol adherence, or financial regulation, where the real problem is to infer whether entities are complying with already‑specified rules despite noisy, incomplete, and possibly strategically manipulated observations.

To address this, the authors introduce Rule‑State Inference (RSI), a Bayesian framework that inverts the conventional direction. Rules are encoded as structured priors, and the latent state for each rule i is defined as a triple s_i = (a_i, c_i, δ_i): a_i∈{0,1} indicates whether the rule is active for the population under study, c_i∈