[Paper Review] Anomalous Edge Detection in Edge Exchangeable Social Network Models

Rui Luo, Buddhika Nettasinghe+1 more|arXiv (Cornell University)|Sep 27, 2021

Complex Network Analysis Techniques55 references4 citations

TL;DR

This paper proposes a conformal prediction-based anomaly detector for identifying anomalous edges in directed social networks using edge exchangeability as a statistical criterion. By modeling edge likelihoods via an edge exchangeable network model and applying conformal prediction, the method guarantees a user-specified upper bound on the false positive rate, outperforming baselines in Ethereum blockchain transaction data experiments.

ABSTRACT

This paper studies detecting anomalous edges in directed graphs that model social networks. We exploit edge exchangeability as a criterion for distinguishing anomalous edges from normal edges. Then we present an anomaly detector based on conformal prediction theory; this detector has a guaranteed upper bound for false positive rate. In numerical experiments, we show that the proposed algorithm achieves superior performance to baseline methods.

Motivation & Objective

• To address the challenge of detecting anomalous edges in dynamic, directed social networks with provable statistical guarantees.
• To leverage edge exchangeability as a principled criterion for identifying edges that deviate from normal network patterns.
• To develop an anomaly detection algorithm with a guaranteed upper bound on false positive rate, overcoming limitations of non-i.i.d. graph data in existing methods.
• To improve memory and time efficiency over snapshot-based or compression-based approaches while maintaining statistical rigor.

Proposed method

• Models the network using an edge exchangeable random graph model based on the asymmetric Dirichlet network distribution (ADND).
• Defines edge non-conformity using the negative log-likelihood of each edge given the rest of the network, ensuring exchangeability-preserving transformation.
• Applies conformal prediction to compute p-values for edge non-conformity, where uniform p-values under exchangeability ensure valid false positive control.
• Uses the rank of the non-conformity score of a candidate edge among all edges to compute a p-value, which determines anomaly classification.
• Employs a threshold ε on the p-value to classify edges as anomalous, with the guarantee that P(Anom_{N+1}^ε = 1) ≤ ε under exchangeability.
• Validates the method on real-world Ethereum blockchain transaction data, demonstrating robustness and efficiency.

Experimental results

Research questions

• RQ1 Can edge exchangeability serve as a reliable statistical criterion for detecting anomalous edges in directed social networks?
• RQ2 Can conformal prediction be effectively adapted to edge exchangeable models to provide provable false positive rate control in anomaly detection?
• RQ3 How does the proposed Conformal detector compare in performance and efficiency to existing edge anomaly detection baselines?
• RQ4 Does the method maintain statistical validity under the non-i.i.d. structure of real-world network data?

Key findings

• The proposed Conformal detector guarantees an upper bound on the false positive rate of ε, ensuring that normal edges are incorrectly flagged as anomalous with probability at most ε.
• The method achieves superior performance in detecting anomalous edges on Ethereum blockchain transaction data compared to baseline methods, as measured by detection accuracy and F1-score.
• The use of edge exchangeability and conformal prediction enables efficient, real-time anomaly detection with low memory and time overhead.
• Theoretical analysis confirms that the p-value computed via the rank of non-conformity scores is uniformly distributed under exchangeability, validating the method’s statistical reliability.
• Empirical results demonstrate that the algorithm effectively identifies bursty or low-probability edges that deviate from typical network behavior.