Rule-to-Data Knowledge Transfer via Optimal Transport for Weakly Supervised Anomaly Detection on Transaction Graphs

Technical Summary: Rule-to-Data Knowledge Transfer via Optimal Transport for Weakly Supervised Anomaly Detection on Transaction Graphs

Problem Statement
Transaction-graph anomaly detection, particularly in Anti-Money Laundering (AML), faces significant challenges due to the scarcity of high-quality labeled data, which requires costly expert investigation. While weakly supervised methods attempt to leverage expert-defined rules or heuristic labels to generate pseudo-labels for unlabeled data, existing approaches suffer from three fundamental limitations:

1. Loss of Hierarchical Structure: Rules are often reduced to flat labeling functions, ignoring the hierarchical decision paths and shared conditions that define related behavioral patterns.
2. Semantic Mismatch: There is a gap between symbolic, discrete rule representations and continuous, data-driven transaction embeddings, making reliable knowledge transfer difficult.
3. Noise Propagation: Pseudo-labels generated from limited and imbalanced labeled samples are inherently uncertain. Treating them as hard supervision can propagate errors throughout the learning process.

Methodology
The authors propose a unified weakly supervised framework designed to bridge the gap between rule-based knowledge and data-driven representations while mitigating noise. The architecture consists of a dual-branch design and a three-stage training process:

1. Dual-Branch Representation Learning:

   • Rule Branch: A decision tree is trained on limited labeled data. Instead of using leaf predictions as isolated labels, the decision paths are transformed into a Rule Graph. In this graph, transaction nodes and decision condition nodes are connected based on shared traversal paths. A Graph Neural Network (GNN) with attention mechanisms encodes this graph to capture hierarchical rule semantics and aggregate rule-consistent information, producing rule prototypes for illicit and licit classes.
   • Data Branch: Raw transaction features are encoded into dense embeddings using a Multi-Layer Perceptron (MLP).

2. Cross-Domain Optimal Transport (OT) Alignment:

   • To address the semantic gap between the symbolic rule space and the continuous data space, the framework employs Optimal Transport.
   • OT establishes soft correspondences between the rule prototypes (source distribution) and transaction embeddings (target distribution) by minimizing a cost matrix (e.g., Euclidean distance) with entropy regularization.
   • The resulting transport plan generates soft pseudo-labels (probability distributions over rule types) for unlabeled transactions, rather than hard binary assignments.

3. Pseudo-Label Contrastive Refinement:

   • A Cross-Domain Contrastive Learning (CCL) objective refines the pseudo-labels.
   • Based on the OT transport plan, high-confidence pairs (transactions strongly aligned with a specific rule prototype) are treated as positive pairs, while mismatched pairs are treated as negative pairs.
   • The contrastive loss pulls semantically consistent rule-data pairs closer in the embedding space while pushing apart inconsistent ones, thereby sharpening decision boundaries and reducing the impact of noisy pseudo-labels.

The total training objective combines the cross-entropy loss for classification, the OT loss for distribution alignment, and the contrastive loss for representation refinement.

Key Contributions

• Unified Weakly Supervised Framework: The paper introduces a dual-branch architecture that structurally represents hierarchical rule knowledge (via a Rule Graph) and jointly learns rule-based and data-driven representations.
• Rule-to-Data Knowledge Transfer Mechanism: The authors develop a novel mechanism combining Optimal Transport and Contrastive Learning. This approach aligns heterogeneous representation spaces (symbolic rules vs. continuous embeddings) to generate reliable soft pseudo-labels for unlabeled transactions.
• Empirical Validation: Extensive experiments on four benchmark datasets (Elliptic, Libra Bank, Reddit, and Amazon) demonstrate the framework's effectiveness, robustness, and generalizability across diverse domains and graph structures.

Experimental Results
The proposed model was evaluated against traditional machine learning models (SVM, LSTM, MLP), graph-based deep learning methods (GCN, GIN, GAT, FraudGT), and advanced weakly supervised baselines (CPL, BWGNN).

• Performance: The model consistently outperformed existing weakly supervised and supervised baselines across the four datasets.
  • On the Elliptic dataset (highly imbalanced cryptocurrency transactions), the model improved AUC-PRC by 24.7% and top-10% F1-score by 8.1% over the strongest baseline (BWGNN).
  • On Reddit and Amazon datasets, the model achieved the best AUC-PRC and tied for the best AUC-ROC, precision, and F1-scores.
  • On the Libra Bank dataset, while feature-driven models performed well due to direct feature-label associations, the proposed framework remained competitive, achieving perfect top-10% recall.
• Ablation Studies: Experiments confirmed that:
  • Using Decision Trees to generate hierarchical rules is superior to random or flat rule generation.
  • Graph Convolution (specifically GCN) on the Rule Graph is critical for capturing topological dependencies.
  • Optimal Transport alignment significantly outperforms simple concatenation or averaging of features.
  • Balanced weighting of OT and contrastive losses yields the best trade-off between distribution alignment and class separability.
• Visualization: t-SNE and cosine similarity analyses on the Elliptic dataset showed that while the Rule Branch preserves local topology and the Data Branch captures discriminative features, the OT-guided fusion effectively bridges these spaces, creating a more robust representation for illicit transactions.

Significance and Claims
The paper claims that its primary significance lies in addressing the "semantic gap" and "structural loss" inherent in current weakly supervised anomaly detection. By explicitly modeling the hierarchical structure of rules and using Optimal Transport to softly align them with data embeddings, the framework enables reliable knowledge transfer even under conditions of limited supervision, class imbalance, and distribution shifts. The authors assert that this design improves robustness in real-world AML scenarios where labeled data is scarce and laundering strategies are evolving. The work validates that preserving rule semantics and aligning heterogeneous spaces are critical for effective graph anomaly detection beyond traditional financial domains.