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Temporal Graph Prototype-conditioned Conformal Prediction for Fraud Detection

Xudong Chen, Shengbo Gong, Lu Cheng, Wei Jin

arXiv:2608.15768v1cs.LGcs.AI

TL;DR

Temporal edge-level fraud detection needs uncertainty estimates despite benign-dominated neighborhoods and severe class imbalance. ProtoCP uses prototype-conditioned calibration and temporal scoring, achieving target coverage with tighter prediction sets across four fraud datasets.

  • Problem

    Existing temporal graph fraud detectors largely overlook uncertainty quantification, while deceptive benign-dominated neighborhoods complicate neighborhood-based calibration.

  • Method

    ProtoCP constructs fraud-informative calibration subgraphs with learned prototypes and stabilizes class-conditional calibration using neighborhood-relative scores with temporal diffusion.

  • Results

    ProtoCP achieves target coverage with consistently tighter prediction sets across four fraud datasets, with particularly improved class-wise validity on fraud edges.

  • Takeaways & Limitations

    ProtoCP provides more efficient uncertainty control for temporal graph fraud detection while maintaining target coverage, including across fraud and benign classes.

  • Takeaways & Limitations

    Label-conditioned calibration can improve fraud-class coverage while producing more conservative prediction sets with inflated set sizes.

Abstract

from arXiv · show

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

1 Introduction

ProtoCP targets inefficient conformal prediction for temporal edge-level fraud detection by addressing benign-dominated neighborhoods and scarce, drifting fraud calibration data. It uses prototype-guided calibration contexts and prototype-conditioned scoring to improve calibration stability while preserving CP’s coverage guarantees.

  • Background: Conformal prediction generates prediction sets with finite-sample, distribution-free coverage by thresholding nonconformity scores at an empirical calibration quantile.The guarantee relies on exchangeability between calibration and test examples.
  • Challenge 1: Fraudulent edges can be camouflaged in heterogeneous benign neighborhoods, diluting fraud-relevant evidence and making neighborhood-based calibration overly conservative.This conservatism biases procedures toward larger prediction sets while still satisfying marginal coverage.
  • Challenge 2: Extreme fraud rarity leaves class-conditional calibration thresholds estimated from few positive samples, producing high-variance quantiles that overconfident errors can further destabilize under temporal shift.The figure passage notes that extreme nonconformity scores can disproportionately raise the fraud-class calibration quantile.
  • ProtoCP: ProtoCP constructs fraud-informative calibration contexts with prototype-guided subgraph extraction to address coordination and camouflage.The framework is designed for uncertainty quantification on fraud graphs.
  • ProtoCP: ProtoCP uses prototype-conditioned nonconformity scoring to stabilize conformal calibration when labeled-fraud support is scarce.The method learns class-specific prototype banks in its backbone.

2 Related Work

Related work establishes conformal prediction as a distribution-free framework for coverage-guaranteed prediction sets, while graph structure complicates exchangeability and fraud detection benefits from relational modeling. Existing approaches address these issues separately, leaving topological dependencies and temporal correlations insufficiently handled in graph-structured fraud detection.

  • Foundation of Conformal Prediction: Conformal prediction returns prediction sets containing the true label with user-chosen probability under exchangeability between calibration and test examples.Full CP requires refitting for every candidate label, whereas split CP uses a held-out calibration set for nonconformity scoring.
  • Conformal Prediction on Graphs: Existing conformal predictors do not address the topological dependencies and temporal correlations in graph-structured fraud detection.This limitation motivates methods that jointly account for graph topology and temporal behavior in fraud-focused uncertainty estimation.
  • Conformal Prediction on Graphs: Graph structure challenges exchangeability because nodes and edges are coupled through topology.Prior work studies transductive exchangeability, inductive recalculation, and score pooling or diffusion to improve graph conformal prediction efficiency.
  • Graph-based Fraud Detection: Graph-based fraud detection exploits relational structures to identify camouflage, collusion, heterophily, and abnormal interaction patterns.Representative methods use relation-aware aggregation, label-balanced sampling, spectral modeling, mask learning, cohort augmentation, and label-aware message passing.

3 Preliminary

This section introduces split conformal prediction for binary classification, where nonconformity scores determine prediction sets with finite-sample coverage guarantees under exchangeability. The method calibrates a threshold on held-out examples and includes candidate labels whose scores fall below it.

  • Conformal prediction: Conformal prediction transforms a predictive model into one that outputs prediction sets with finite-sample coverage guarantees.The setup uses binary labels Y∈{0, 1} and features X∈X.
  • Split conformal prediction: Split conformal prediction trains the model separately, then computes nonconformity scores on calibration examples.The score function s: X × {0, 1} → R measures how poorly an example fits a candidate label, with higher values indicating greater disagreement.
  • Threshold calibration: The calibration scores determine a threshold q̂ using the ⌈(n + 1)(1 − α)⌉-th smallest calibration value.This threshold is constructed from the calibration-score distribution after separate model training.
  • Prediction sets: The prediction set includes every candidate label whose nonconformity score falls below the calibrated threshold.Under exchangeability between calibration and test data, split conformal prediction guarantees marginal coverage for the test label.

4 Method

ProtoCP calibrates conformal prediction on prototype-conditioned temporal subgraphs that retain fraud-relevant context while suppressing benign noise. It combines neighborhood-relative nonconformity features, temporal score diffusion, and class-conditional calibration for stable, efficient fraud detection.

  • Prototype-conditioned calibration: ProtoCP uses learned prototypes to extract fraud-relevant subgraphs, suppress benign-dominated neighbors, and support pattern-aware calibration across relational contexts.Prototypes act as class-specific anchors in edge-embedding space and are refined jointly with the subgraph-level calibration objective.
  • Prototype-conditioned calibration: Prototype-conditioned subgraphs are built from k-hop temporal neighborhoods using only interactions with timestamps t≤t_i, preventing information leakage from future events.Neighboring edges receive normalized importance weights, which are pooled into a subgraph representation centered on the target interaction.
  • Relative-aware nonconformity: Relative nonconformity encodes prediction discrepancies, degree statistics, and motif counts by comparing each edge with its weighted neighborhood.The resulting relative difference vector is combined with the backbone probability-based score through a learnable scalar λ.
  • Temporal calibration: Temporal graph score diffusion smooths intermediate nonconformity over each prototype-conditioned historical neighborhood, combining center-edge and weighted contextual information without future interactions.The method uses one-step diffusion with β=0.5 by default.
  • Temporal calibration: Class-conditional Mondrian calibration estimates separate class-wise thresholds and constructs prediction sets by including labels whose temporal-graph-aware scores meet their thresholds.Prototype and conformal objectives are jointly optimized using sigmoid and hinge relaxations, with a smooth efficiency loss as a proxy for prediction-set size.

5 Theoretical Analysis

ProtoCP’s theoretical analysis decomposes empirical class-wise miscoverage into finite-sample discretization and calibration–test score-distribution shift. It motivates prototype conditioning and temporal diffusion as mechanisms for reducing this shift and tightening prediction sets at target coverage.

  • Scope of the analysis: Because temporal fraud graphs may exhibit relational dependence and temporal shift, the analysis targets empirical efficiency rather than establishing a new finite-sample coverage guarantee.
  • Miscoverage-gap decomposition: The empirical miscoverage gap separates a typically small quantile discretization error from calibration–test score-distribution shift.The analysis focuses on the latter as the empirical shift.
  • Miscoverage-gap decomposition: Reducing |b𝛿𝑦| is the central objective because smaller shift yields tighter prediction sets at target coverage.
  • Prototype conditioning: Prototype conditioning reduces |b𝛿𝑦| by grouping behaviorally similar edges into more homogeneous score distributions and reducing prototype-frequency mismatch.The class-conditional CDF is decomposed as a mixture over prototypes, motivating these two reduction mechanisms.
  • Temporal diffusion: Temporal diffusion further stabilizes sfinal by smoothing each edge’s score over its temporal neighborhood, empirically reducing |b𝛿𝑦|.

6 Experiment

ProtoCP is evaluated across four fraud benchmarks under temporally separated calibration and testing, achieving target coverage with smaller prediction sets and improved class-wise and temporal robustness. Ablations and runtime results further show the contributions and moderate cost of its prototype-conditioned calibration.

  • Conformal Prediction Performance: ProtoCP achieves target coverage of 0.97–0.99 across YelpChi, S-FFSD, FTFD, and BankSim, with the smallest prediction sets on three datasets.Experiments use TGN with temporal splits; TGAT is additionally used to examine backbone transferability.
  • Conformal Prediction Performance: On S-FFSD, ProtoCP achieves set size 1.04 versus 1.14 for the comparison method, showing reduced conservativeness under deceptive neighborhoods.The passage attributes inflated thresholds to deceptive neighborhoods that raise nonconformity scores.
  • Label-Conditioned Calibration: ProtoCP achieves fraud-class coverage 0.96 with set size 1.26, outperforming NCPNet +LC at 1.53 under the same validity requirement.Label-conditioned calibration improves fraud coverage but often inflates prediction sets; TPS +LC rises from 1.75 to 1.95 and CF-GNN +LC from 1.47 to 1.62.
  • Ablation: Removing prototypes increases average set size by +0.09, +0.11, +0.17, and +0.15 on YelpChi, S-FFSD, FTFD, and BankSim, respectively.Removing prototypes preserves target-level coverage, while neighborhood-relative discrepancies provide complementary information beyond absolute backbone confidence.
  • Temporal Robustness: Across temporal windows, ProtoCP maintains fraud-class coverage from 0.97 to 0.95 and efficiency from 1.22 to 1.29, while NCPNet changes from 0.98 to 0.92 and 1.42 to 1.66.Prototype-based nonconformity scores show smaller, more slowly growing KS distances than standard scores under temporal drift.
  • Runtime and Memory: On S-FFSD, preprocessing takes 79.43 seconds with 1.88 GiB peak memory, while calibration takes 0.947 seconds per epoch with 2.18 GiB peak GPU memory.ProtoCP is more expensive than CF-GNN and NCPNet because of prototype-conditioned subgraph extraction and relative structural encoding, but the overhead remains moderate.

7 Conclusion

ProtoCP addresses calibration inefficiency in temporal-graph fraud detection caused by benign-dominated neighborhoods and extreme class imbalance. It uses learned prototypes, neighborhood-relative nonconformity scores, and temporal diffusion to construct fraud-informative calibration subgraphs and stabilize calibration.

  • 7 Conclusion: ProtoCP targets calibration inefficiency arising from benign-dominated neighborhoods and extreme class imbalance in temporal interaction-graph fraud detection.These properties degrade calibration efficiency.
  • 7 Conclusion: Learned prototypes construct fraud-informative calibration subgraphs by focusing calibration on relevant graph context.The prototype-based framework is designed to reduce the influence of benign-dominated neighborhoods.
  • 7 Conclusion: Neighborhood-relative nonconformity scores and temporal diffusion stabilize calibration under temporal interaction-graph conditions.These mechanisms are core components of ProtoCP’s calibration procedure.
  • 7 Conclusion: Experiments on four fraud datasets evaluate whether ProtoCP improves calibration efficiency.The supplied passage states that these experiments show ProtoCP achieves the target c, but the result is truncated.

A Backbone and Dataset Robustness

ProtoCP is evaluated across backbone choices and datasets to test the reliability and robustness of its temporal graph foundation. It remains effective with TGAT on S-FFSD and YelpChi and is additionally assessed on the HI-SMALL AML benchmark.

  • Backbone performance: The TGN backbone is evaluated using Accuracy and F1 Score across YelpChi, S-FFSD, FTFD, and BankSim.These results assess whether TGN provides a reliable foundation for ProtoCP.
  • Backbone transfer: ProtoCP is additionally evaluated with TGAT on S-FFSD and YelpChi using the same temporal split and class-conditional calibration protocol.This tests whether ProtoCP depends on a specific temporal encoder.
  • Backbone transfer: With TGAT, ProtoCP achieves higher fraud-class coverage and smaller prediction sets than NCPNet on both S-FFSD and YelpChi.Lower efficiency indicates smaller prediction sets.
  • Supplementary AML benchmark: ProtoCP is further assessed on the HI-SMALL AML Laundering Dataset as a supplementary transaction-style benchmark.HI-SMALL better matches continuous temporal edge-level transactions than Elliptic or node-labeled DGraphFin.

B Additional Component Ablation

The additional ablation isolates ProtoCP’s one-step temporal score diffusion while retaining prototype-conditioned relative-difference scoring. Removing diffusion lowers fraud-class coverage and enlarges fraud-class prediction sets on S-FFSD and YelpChi, showing its stabilizing role under temporal dependence.

  • One-step temporal diffusion ablation: The ablation removes only the one-step history-only temporal diffusion step while keeping prototype-conditioned relative-difference scoring unchanged.This isolates the contribution of temporal score diffusion from the other ProtoCP components.
  • One-step temporal diffusion ablation: Removing temporal diffusion reduces fraud-class coverage and increases fraud-class prediction set size on both S-FFSD and YelpChi.The result indicates that diffusion provides complementary stabilization for class-conditional calibration under temporal dependence.

C Dataset Introduction · D Evaluation Metric

The evaluation uses four fraud-detection datasets spanning review spam, simulated financial fraud, synthetic transactions, and bank payments. ProtoCP is assessed by coverage and efficiency, with empty prediction sets penalized as full-label-set predictions for efficiency.

  • C Dataset Introduction: YelpChi is a Yelp.com review dataset covering recommended benign and filtered spam or suspicious reviews, users, and businesses.It is widely used for review spam detection experiments.
  • C Dataset Introduction: S-FFSD is a small-scale simulated financial-fraud dataset with transaction records and partially observed fraud labels.It is widely used for financial fraud detection.
  • C Dataset Introduction: FTFD 2 contains 5 million synthetically generated financial transactions designed to simulate real-world behavior.The dataset supports fraud-detection research and machine-learning applications.
  • C Dataset Introduction: BankSim is an agent-based synthetic bank-payment dataset calibrated on aggregated statistics from a real Spanish bank.It provides multi-month card-payment records with injected fraud behaviors without exposing sensitive personal or proprietary transaction data.
  • D Evaluation Metric: ProtoCP is evaluated using coverage and efficiency, measured as average prediction-set size over test edges.For each test edge e_i in Dtest, the prediction set is Γ(e_i).
  • D Evaluation Metric: When Γ(e_i) = ∅, coverage remains unchanged while efficiency assigns |Γ(e_i)| = |Y|, treating the empty set as the full label set.This explicitly penalizes empty prediction sets in efficiency calculations.

E Detailed Experiment Setup

ProtoCP is evaluated under a strictly temporal protocol, with fixed backbone and prototype configurations, staged loss weighting, and repeated runs reporting mean and standard deviation. The setup prevents future-information leakage and specifies the main optimization, calibration, and computational conditions.

  • Data Splitting: All datasets use a temporal 55%/25%/20% split for backbone training, calibration, and testing, with no future information accessible at any stage.The split follows interaction chronology throughout the experimental pipeline.
  • Backbone Training: TGN is the shared backbone, trained with binary crossentropy and Adam at a validation-selected learning rate of {1e-3, 1e-4}, for up to 200 epochs with validation-F1 early stopping.Backbone parameters are frozen after training for calibration and evaluation.
  • ProtoCP Configuration: ProtoCP uses default prototype counts M=15 and N=10, margin γ=1.0, a 3-hop history-constrained temporal neighborhood, diffusion coefficient β=0.5, and target miscoverage α=0.05.These values define the prototype, subgraph, diffusion, and calibration configuration unless otherwise specified.
  • ProtoCP Configuration: The first 50 epochs optimize only prototype loss; thereafter, coverage and efficiency losses use λ_cov=1.0 and λ_eff=0.5, while λ_proto decays from 0.1.This staged weighting strategy is used to stabilize prototype learning.
  • Computational Environment: Experiments run on a single NVIDIA V100 GPU (32GB) with PyTorch 2.6, using 5 random seeds and reporting the mean and standard deviation.The repeated-seed protocol quantifies variability across runs.
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