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RR-PU: A Synergistic Two-Stage Positive and Unlabeled Learning Framework for Robust Tax Evasion Detection
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Proposes RR-PU, a two-stage positive-unlabeled learning framework that estimates tax-evasion label frequency with a regrouping-enhanced MPE and then jointly refines it with a trainable slack transition-matrix variable while training the classifier.
Problem
Tax evasion detection from few identified evaders and many unidentified taxpayers, where the label frequency is unknown and two-stage estimate-then-classify pipelines accumulate estimation bias.
Approach
Combines Regrouping-MPE (duplicating low-negative-posterior unlabeled instances into the positive set to make the mixture irreducible) with a revision stage that learns a slack variable on the transition matrix jointly with the classifier, using a validation set to stop, so label frequency and classifier are refined synergistically.
Key results
- On TaxS, RR-PU reaches 90.286% accuracy, 0.9088 F1 and 0.9643 AUC, beating the best baseline by 3.567% accuracy, 0.0929 F1 and 0.0231 AUC (per the paper's analysis section).
- On TaxH and TaxZ, RR-PU reports 93.658% and 96.726% accuracy respectively, the highest among compared methods in Table 1.
- Ablation on TaxS: base AlphaMax 87.611% accuracy, adding regrouping 89.451%, adding regrouping plus revision 90.847%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use RR-PU instead of the strongest baseline | Tax evasion detection · TaxS | Accuracy (%): 86.719 -> 90.286 | Helped |
| use RR-PU instead of the strongest baseline | Tax evasion detection · TaxH | Accuracy (%): 93.327 -> 93.658 | Helped |
| use RR-PU instead of the strongest baseline | Tax evasion detection · TaxZ | Accuracy (%): 95.813 -> 96.726 | Helped |
| use RR-PU instead of the strongest baseline | Tax evasion detection · TaxS | F1-score: 0.8159 -> 0.9088 | Helped |
| use RR-PU instead of the strongest baseline | Tax evasion detection · TaxH | F1-score: 0.7337 -> 0.7834 | Helped |
| use RR-PU instead of the strongest baseline | Tax evasion detection · TaxZ | F1-score: 0.8966 -> 0.9182 | Helped |
| add regrouping technique (ablation) | AlphaMax-based classifier · TaxS, TaxH, TaxZ | Accuracy (%): 87.611 -> 89.451; 92.471 -> 92.597; 95.615 -> 96.161 | Helped |
| add regrouping technique (ablation) | AlphaMax-based classifier · TaxS, TaxH, TaxZ | F1-score: 0.8536 -> 0.8749; 0.7155 -> 0.7268; 0.8893 -> 0.9067 | Helped |
| add revision stage to regrouping (ablation) | AlphaMax-based classifier · TaxS, TaxH, TaxZ | Accuracy (%): 89.451 -> 90.847; 92.597 -> 93.517; 96.161 -> 96.734 | Helped |
| add revision stage to regrouping (ablation) | AlphaMax-based classifier · TaxS, TaxH, TaxZ | F1-score: 0.8749 -> 0.8938; 0.7268 -> 0.7645; 0.9067 -> 0.9219 | Helped |
| add regrouping technique and revision stage (ablation) | RR-PU label-frequency estimation · TaxS, TaxH, TaxZ | estimation error | Helped |
Surprising findings
- Standard MPE methods degrade badly on TaxS because positive and unlabeled distributions overlap, violating the irreducibility assumption.
Limitations
- Relies on kernel density estimation inside MPE, so estimation error inflates with high-dimensional inputs.
- Evaluated only on three proprietary Chinese tax datasets; no public tax benchmark is available.
Experimental setup
Datasets: TaxS TaxH TaxZ
Benchmarks: TaxS TaxH TaxZ
Metrics: Accuracy F1-score AUC label frequency estimation error
Baselines: Biased PU nnPU uPU RankPruning WSVM VPU FBNE-PU Eagle Dist-PU EN KM1 KM2
Builds on: Regrouping-MPE nnPU DEDPUL AlphaMax Eagle
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