RSI: Rule-State Inference

A Bayesian Framework for Compliance Monitoring in Rule-Governed Domains

Evidence from Francophone African Fiscal Systems

Abdou-Raouf Atarmla — Togo DataLab / INPT Rabat

---

What is RSI?

Most ML frameworks for compliance monitoring learn rules from data. RSI inverts this paradigm: known regulatory rules are encoded as Bayesian priors, and compliance monitoring is cast as posterior inference over a latent rule-state space.

RSI operates at two complementary levels:

• Population-level Bayesian inference estimates the compliance rate for each rule across the population, with calibrated uncertainty. "63% of taxpayers comply with VAT, ± 3%."

• Entity-level deterministic scoring identifies non-compliant entities per rule using continuous compliance signals, without any labeled data. The aggregation strategy (flag if 1 rule violated, 2+, etc.) is a domain policy choice.

On individual Bayesian inference: The current version provides deterministic entity scoring. Sequential RSI, where the posterior at period t becomes the prior at t+1, will enable full entity-level Bayesian tracking over time. This is the natural next step and is under active development.

Three theoretical guarantees are proven:

• T1 — Regulatory changes absorbed in O(1) time (no retraining)
• T2 — Bernstein-von Mises posterior consistency (uncertainty shrinks at 1/√N)
• T3 — Monotone ELBO convergence under mean-field VI

---

Key Results (Togo Fiscal Instance)

Per-Rule Performance (zero-shot, no labels)

Rule	RSI F1	RSI AUC	RBS F1	Advantage
R1_TVA	0.865	0.874	0.765	+0.100
R2_IS	0.739	0.892	0.740	-0.001
R3_IMF	0.545	0.914	0.541	+0.005
R4_TPU	0.825	0.691	0.720	+0.105
R5_IRPP	0.690	0.879	0.690	+0.000
R6_PAT	0.841	0.876	0.783	+0.058
R7_DECL	0.630	0.879	0.621	+0.009
R8_BANK	0.791	0.867	0.739	+0.053
Mean	0.741	0.859	0.700	+0.041

• T1: RSI absorbs regulatory changes in ~0.002ms vs ~1,000ms for retraining (around 500,000x speedup; exact ratio is hardware-dependent, the O(1) guarantee is machine-independent)
• T2: Posterior uncertainty decreases at 1/√N (ratios 1.86-2.03 vs theoretical 2.0)
• T3: ELBO gain = +815, monotone, converges in 1 sweep
• Missing data: At 50% missing, RSI advantage over RBS widens to +0.25-0.37 per rule

---

Quick Start

pip install numpy scipy scikit-learn pandas
python experiments/togo-fiscal/run.py

---

Dataset: RSI-Togo-Fiscal-Synthetic v2.0

2,000 synthetic enterprises across 2 regulatory periods, grounded in real OTR fiscal rules (2022-2025):

• 8 fiscal rules (6 threshold-based + 2 universal)
• 4 market segments (informal 45%, small formal 25%, medium 18%, large 12%)
• Realistic noise: under-declaration ratio ~0.70, 18% missing data
• Regulatory change event: VAT threshold 60M → 100M FCFA (Law n°2024-007)
• Fully reproducible: seed=42

---

Applying RSI to a New Domain

RSI is domain-agnostic. The core (src/core.py) never changes. You only write a domain adapter. Example for medical protocol compliance:

from core import PopulationRSI, EntityScorer

# 1. Define rules as priors (institutional knowledge)
priors = {
    'HbA1c_control':   {'alpha': 6, 'beta': 4, 'sigma_drift': 1.0},
    'Annual_eye_exam': {'alpha': 5, 'beta': 5, 'sigma_drift': 0.5},
    'Metformin_first': {'alpha': 7, 'beta': 3, 'sigma_drift': 0.5},
}

# 2. Compliance signals: 1 = compliant, 0 = non-compliant, NaN = unknown
signals = {
    'HbA1c_control':   {'patient_001': 1, 'patient_002': 0, 'patient_003': float('nan')},
    'Annual_eye_exam': {'patient_001': float('nan'), 'patient_002': 1, 'patient_003': 0},
    'Metformin_first': {'patient_001': 1, 'patient_002': 1, 'patient_003': 0},
}

# 3. Applicability: which rules apply to which entities
applicability = {
    'HbA1c_control':   {'patient_001': True, 'patient_002': True, 'patient_003': True},
    'Annual_eye_exam': {'patient_001': True, 'patient_002': True, 'patient_003': False},
    'Metformin_first': {'patient_001': True, 'patient_002': True, 'patient_003': True},
}

# 4. Run
rsi = PopulationRSI(priors)
results = rsi.fit(signals, applicability)

# Population result: E[c_HbA1c] = 0.63 ± 0.04
# "63% of diabetic patients have controlled HbA1c, with calibrated uncertainty"
for rule, post in results['population'].items():
    print(f"{rule}: E[c]={post['E_c']:.3f} ± {post['std_c']:.3f}")

Any domain with (i) known rules, (ii) observable signals, (iii) definable applicability is a candidate. Immediate extensions include environmental regulation, anti-money-laundering, and legal contract monitoring.

---

Citing

@article{atarmla2026rsi,
  title   = {Rule-State Inference ({RSI}): A Bayesian Framework
             for Compliance Monitoring in Rule-Governed Domains},
  author  = {Atarmla, Abdou-Raouf},
  journal = {arXiv preprint arXiv:2603.21610},
  year    = {2026},
  url     = {https://arxiv.org/abs/2603.21610}
}

---

License

MIT — see LICENSE.

Contact

Abdou-Raouf Atarmla — achilleatarmla@gmail.com | abdou-raouf.atarmla@datalab.gouv.tg | atarmla.abdouraouf@ine.inpt.ac.ma