Conformal prediction (CP) provides distribution-free coverage guarantees and has emerged as a principled tool for uncertainty quantification. In edge-level fraud detection on temporal interaction graphs, where false positives and false negatives both carry substantial cost, such coverage guarantees are particularly appealing for risk-aware decision making. However, directly applying existing graph conformal predictors yields inefficient prediction sets due to two recurring properties of fraud data. Fraudulent interactions are often embedded in benign-dominated neighborhoods that dilute calibration signals, while extreme class imbalance leaves scarce labeled-fraud support in the calibration split and leads to overly conservative class-conditional thresholds. To address these issues, we propose ProtoCP, a conformal prediction framework for edge-level fraud detection on temporal graphs. ProtoCP improves calibration efficiency by focusing calibration on fraud-relevant subgraph context and producing more stable nonconformity scores under class imbalance and temporal drift. Specifically, it leverages learned prototypes to suppress benign-dominated noise in the calibration context and introduces a neighborhood-relative scoring mechanism with temporal score diffusion for stable class-conditional calibration. Experiments on four fraud benchmarks (YelpChi, S-FFSD, FTFD, and BankSim) show that ProtoCP achieves the target coverage with consistently smaller prediction sets than state-of-the-art baselines. Our codes are available at https://github.com/Picard1701ent/ProtoCP.git
Figures & tables
Figure 1. Two graph-specific challenges for conformal prediction in fraud detection. (a) Fraudulent edges are structurally camouflaged within benign neighborhoods, which distorts neighborhood-based calibration and increases uncertainty. (b) With few fraud-labeled calibration edges, extreme nonconformity scores from overconfident errors can disproportionately raise the fraud–class calibration quantile, especially under calibration–test distribution shift.
Figure 2. Overall pipeline of Prototype-based Temporal Graph Conformal Prediction
Category
Method
YelpChi
S-FFSD
FTFD
BankSim
Coverage
Efficiency( ↓ )
Coverage
Efficiency( ↓ )
Coverage
Efficiency( ↓ )
Coverage
Efficiency( ↓ )
Traditional
TPS
0.89 ± 0.00 ×
1.52 ± 0.02
0.94 ± 0.02 ×
1.44 ± 0.04
0.78 ± 0.01 ×
1.51 ± 0.01
0.88 ± 0.01 ×
1.57 ± 0.01
APS
0.91 ± 0.01 ×
1.52 ± 0.07
0.96 ± 0.02 ✓
1.53 ± 0.08
0.92 ± 0.03 ×
1.48 ± 0.09
0.92 ± 0.02 ×
1.67 ± 0.10
RAPS
0.94 ± 0.03 ×
1.48 ± 0.08
0.96 ± 0.02 ✓
1.65 ± 0.09
0.93 ± 0.03 ×
1.32 ± 0.06
0.95 ± 0.02 ✓
1.37 ± 0.07
Graph-based
DAPS
0.93 ± 0.01 ×
1.44 ± 0.08
0.94 ± 0.02 ×
1.60 ± 0.07
0.89 ± 0.03 ×
1.38 ± 0.09
0.90 ± 0.02 ×
1.34 ± 0.08
CF-GNN
0.93 ± 0.03 ×
1.40 ± 0.08
0.94 ± 0.03 ×
1.29 ± 0.05
0.97 ± 0.03 ✓
1.17 ± 0.08
0.96 ± 0.03 ✓
1.13 ± 0.06
Table 1. Comparison of methods across four fraud detection datasets in terms of Coverage and Efficiency (set size). ✓ indicates that the coverage meets the target, while × indicates the opposite.
Category
Method
YelpChi
S-FFSD
FTFD
BankSim
Fraud
Benign
Fraud
Benign
Fraud
Benign
Fraud
Benign
Cov.
Eff.( ↓ )
Cov.
Eff.( ↓ )
Cov.
Eff.( ↓ )
Cov.
Eff.( ↓ )
Cov.
Eff.( ↓ )
Cov.
Eff.( ↓ )
Cov.
Eff.( ↓ )
Cov.
Eff.( ↓ )
Traditional
TPS
0.71 ×
1.68
0.92 ×
1.50
0.90 ×
1.75
0.96 ✓
1.21
0.73 ×
1.69
0.78 ×
1.51
0.80 ×
1.79
0.88 ×
1.57
APS
0.78 ×
1.77
0.93 ×
1.48
0.92 ×
1.79
0.98 ✓
1.33
0.90 ×
1.89
0.92 ×
1.48
0.83 ×
1.80
0.92 ×
1.67
RAPS
0.85 ×
1.83
0.95 ✓
1.43
0.92 ×
1.91
0.99 ✓
1.44
0.85 ×
1.71
0.93 ×
1.32
0.86 ×
1.84
0.95 ✓
1.36
Graph-based
DAPS
0.89 ×
1.73
0.94 ×
1.40
0.92 ×
1.76
0.96 ✓
1.47
0.81 ×
1.79
0.90 ×
1.38
0.89 ×
1.74
0.90 ×
1.34
Table 2. Comparison of methods across four fraud detection datasets in terms of positive/negative coverage and set size. ✓ denotes that the coverage reaches the target, while × denotes the opposite.
Method
Calib.
Fraud
Benign
Coverage
Efficiency( ↓ )
Coverage
Efficiency( ↓ )
TPS
Global
0.90 ×
1.75
0.96 ✓
1.21
TPS
+LC
0.95 ✓
1.95
0.95 ✓
1.34
APS
Global
0.92 ×
1.79
0.98 ✓
1.33
APS
+LC
0.94 ×
1.88
0.97 ✓
1.59
CF-GNN
Global
0.89 ×
1.47
0.98 ✓
1.15
Table 3. Effect of label-conditioned calibration on S-FFSD. +LC calibrates class-specific thresholds using label-conditioned calibration scores.
Figure 3. Visualization of sensitivity analysis under different hyperparameters and data size
Figure 4. Visualization of temporal neighborhood subgraphs for a fraud (a) and a benign (b) target edge. Tables report ΔT , amount, and the neighbor-importance weight αij (shown as Score ).
Figure 5. Visualization of KS distance of Nonconformity Score(NCS) distributions over temporal windows on S-FFSD. (a) Benign class. (b) Fraud class.
Window
NCPNet
ProtoCP
Coverage
Efficiency
Coverage
Efficiency
1
0.98
1.42
0.97
1.22
2
0.98
1.45
0.97
1.24
3
0.95
1.57
0.96
1.27
4
0.92
1.66
0.95
1.29
Table 4. Fraud-class coverage and efficiency across temporal test windows on S-FFSD. Lower efficiency indicates smaller prediction sets.
Method
Pre. Time
Pre. Mem.
Cal. Mem.
Cal. Time
(s)
(GiB)
(GiB)
(s/epoch)
CF-GNN
N/A
N/A
0.85
0.315
NCPNet
N/A
N/A
0.33
0.641
ProtoCP
79.43
1.88
2.18
0.947
Table 5. Runtime and memory comparison on S-FFSD. N/A indicates that the baseline does not require the corresponding preprocessing stage.
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Metric
YelpChi
S-FFSD
FTFD
BankSim
Accuracy
F1
Accuracy
F1
Accuracy
F1
Accuracy
F1
TGN
79.75
65.57
89.43
77.82
98.15
90.32
96.74
84.48
Appendix
Table 6. Performance of the backbone model (TGN) across four fraud detection datasets in terms of Accuracy and F1 Score.
Dataset
Accuracy
F1 Score
S-FFSD
89.64
78.02
YelpChi
81.43
66.32
Appendix
Table 7. Performance of the TGAT backbone on S-FFSD and YelpChi.
Method
S-FFSD
YelpChi
Coverage
Efficiency
Coverage
Efficiency
NCPNet
0.95
1.47
0.95
1.42
ProtoCP
0.96
1.31
0.96
1.35
Appendix
Table 8. Fraud-class coverage and efficiency with TGAT backbone. Lower efficiency indicates smaller prediction sets.
Dataset
Accuracy
F1 Score
HI-SMALL
99.81
75.78
Appendix
Table 9. Backbone performance on HI-SMALL.
Method
Fraud Cov.
Fraud Eff.
Benign Cov.
Benign Eff.
TPS
0.93
1.92
0.95
1.13
APS
0.95
1.96
0.95
1.23
RAPS
0.92
1.94
0.96
1.19
DAPS
0.93
1.56
0.95
1.09
CF-GNN
0.94
1.73
0.96
1.09
NCPNet
0.95
1.52
0.98
1.07
Appendix
Table 10. Class-wise coverage and efficiency on HI-SMALL. Lower efficiency indicates smaller prediction sets.
Variant
S-FFSD
YelpChi
Fraud Cov.
Fraud Eff.
Fraud Cov.
Fraud Eff.
w/o one-step diffusion
0.93
1.35
0.95
1.61
ProtoCP
0.96
1.26
0.98
1.52
Appendix
Table 11. Ablation of the one-step temporal diffusion component. Lower efficiency indicates smaller prediction sets.
Statistic
YelpChi
S-FFSD
FTFD
BankSim
# Samples
67,395
77,881
5,000,000
594,643
# Fraud (Positive)
8,916
5,256
179,553
7,200
# Benign (Negative)
58,479
24,387
4,820,447
587,443
# Unknown
–
48,238
–
–
Fraud Ratio (%)
13.23%
17.73%
3.59%
1.21%
Domain
Review
Payment
Transaction
Transaction
Appendix
Table 12. Summary statistics of the four fraud detection datasets.
Financial fraud in corporate transaction networks has grown more coordinated and harder to detect with rule-based engines and with classical learning models that treat each transaction in isolation. This paper presents GTFD, a graph-transformer fraud detector that fuses structural and temporal evidence from a corporation's payment graph. GTFD encodes the graph with a multi-head graph attention network, encodes ordered transaction sequences with a gated transformer, and combines both views through a cross-modal gating layer. A conformal risk-control head converts the fused representation into threshold-free anomaly scores with finite-sample coverage guarantees, and the network is trained with self-supervised link-mask pretraining plus adversarial augmentation so it remains stable under scarce labels and under adversarial perturbation. On a corporate transaction benchmark enriched with coordinated fraud rings, GTFD reaches an AUROC of 0.990, an F1-score of 96.1% (precision 96.3%, recall 95.9%), and an accuracy of 98.4%. It reduces the false-positive rate by about 29% relative to the strongest baseline while raising coordinated fraud-ring recall from 85.1% to 96.5%. Ablations attribute roughly 2.0 AUROC points to self-supervised pretraining and 1.9 AUROC points to the conformal head, and adversarial stress tests show GTFD retains 89.2% accuracy at perturbation magnitude 0.20 where the next-best model falls to 76.4%.
Conformal prediction (CP) provides a distribution-free approach to uncertainty quantification with finite-sample guarantees. However, applying CP to graph neural networks (GNNs) remains challenging as the combinatorial nature of graphs often leads to insufficiently certain predictions and indiscriminative embeddings. Existing methods primarily rely on embedding-space proximity for localization, which can be unreliable for graphs and yield inefficient prediction sets. We propose GRAPHLCP, a proximity-based localized CP framework that explicitly incorporates graph topology and inter-node dependencies into localization and weighting. Our approach introduces a feature-aware densification step to mitigate locality bias in sparse graphs, followed by a Personalized PageRank-based kernel computation to model structural proximity. This enables topology-dependent anchor sampling and calibration weighting that captures both local and long-range dependencies. Extensive experiments on several regression and classification datasets demonstrate that GRAPHLCP guarantees marginal coverage with finite samples while efficiently attaining favorable test conditional coverage across various conditioning scenarios.
Illicit transaction detection is often driven by transaction level attributes however, fraudulent behavior may also manifest through network structure such as central hubs, high flow intermediaries, and coordinated neighborhoods. This paper presents a time respecting, leakage safe (causal) graph feature extraction protocol for temporal transaction networks and evaluates its utility for illicit entity classification. Using the Elliptic dataset, we construct directed transaction graphs and compute interpretable structural descriptors, including degree statistics, PageRank, HITS hub or authority scores, k-core indices, and neighborhood reachability measures. To prevent look ahead bias, we additionally compute causal variants of graph features using only edges observed up to each timestep. A Random Forest classifier trained with strict temporal splits achieves strong discrimination on a held out future test period (ROC-AUC about 0.85, Average Precision about 0.54). Although transaction attributes remain the dominant predictive signal, graph derived features provide complementary interpretability and enable risk context analysis for investigation workflows. We further assess operational utility using Precision at k and evaluate probability reliability via calibration curves and Brier scores, showing that calibrated models yield better aligned probabilities for triage. Overall, the results support causal graph feature extraction as a practical and interpretable augmentation for temporal fraud detection pipelines.