Rule-State Inference (RSI): A Bayesian Framework for Compliance Monitoring in Rule-Governed Domains
Rule-State Inference (RSI) addresses compliance monitoring in domains like taxation where authoritative rules are known a priori but observations are partial, noisy, or strategically distorted. The paper proposes a Bayesian framework that inverts the standard ML paradigm: instead of learning rules from data, RSI encodes regulatory rules as structured priors and infers latent rule states (activation, compliance rate, parametric drift) via posterior inference. This enables zero-shot compliance assessment without labeled training data—a critical capability for low-resource environments where non-compliance labels are scarce or legally sensitive.
RSI presents a theoretically rigorous and practically motivated framework for rule-governed domains. The core innovation—treating rules as priors rather than learning targets—is well-articulated and addresses a genuine gap in existing approaches. The three theoretical guarantees (O(1) adaptability, BvM consistency, and monotone ELBO convergence) are formally proven and empirically validated on a synthetic Togolese fiscal dataset. However, the empirical evaluation is limited to synthetic data, and the zero-shot performance (F1=0.519) lags substantially behind supervised alternatives, raising questions about the practical trade-offs.
The theoretical contributions are the paper's strongest aspect. The O(1) regulatory adaptability claim (T1) is substantiated by a clean proof showing that updates require only computing a scalar prior ratio, independent of dataset size. The mean-field variational inference derivation is standard but correct, and the handling of missing data via unit likelihood preserves the prior without injecting bias—a practical necessity for African fiscal systems with 18–20% missing rates.
The empirical evaluation relies entirely on synthetic data, which the authors acknowledge "may not capture all idiosyncratic noise of administrative reality" (Section 6). While necessary for controlled experiments, this limits external validity. The zero-shot F1 of 0.519—though better than a rule-based system—is far below the 0.967 achieved by XGBoost with supervision, and the practical utility of this performance level for fiscal enforcement is unclear. The mean-field assumption ignores dependencies between rules, and the prior hyperparameters (e.g., $\pi_i=0.92$ for VAT activation) appear choosen post-hoc to match institutional intuition rather than derived from systematic calibration.
The evidence supports the O(1) adaptability claim both theoretically and empirically (under 1ms vs 683–1082ms for retraining). However, the comparison to related work is asymmetric: while MLNs and PSL are discussed extensively in Section 2 as learning-based approaches, no empirical comparison to these methods is provided in the experiments. The paper argues RSI treats rules as "inputs" versus MLN/PSL treating them as "outputs" to be learned, but without runtime or accuracy comparisons on the same benchmark, this distinction remains theoretical. The missing data robustness (50% missing) is impressive, though the baseline deterministic system is weak.
Reproducibility is well-supported. The dataset (RSI-Togo-Fiscal-Synthetic v1.0) is publicly released with detailed documentation in Appendix A, including the under-declaration model ($\hat{x}=x\cdot\beta\cdot\varepsilon$ with $\beta\sim\text{Beta}(7,3)$) and regulatory change event (VAT threshold 60M$\to$100M FCFA). Implementation hyperparameters are specified in Appendix C (learning rate $\eta=1.5$, max iterations 150, random seed 42). The computational environment is modest (standard desktop, no GPU), lowering barriers to replication. However, the specific code repository URL is not provided in the text, only a general claim of release.
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.
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