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CRC-SGAD: Conformal Risk Control for Supervised Graph Anomaly Detection

Songran Bai, Xiaolong Zheng, Daniel Dajun Zeng

TL;DR

CRC-SGAD establishes a paradigm for statistically rigorous anomaly detection in graph-structured security applications and introduces a Dual-Threshold Conformal Risk Control mechanism that provides theoretically guaranteed bounds for both False Negative Rate (FNR) and False Positive Rate (FPR) through providing prediction sets.

Abstract

Graph Anomaly Detection (GAD) is critical in security-sensitive domains, yet faces reliability challenges: miscalibrated confidence estimation (underconfidence in normal nodes, overconfidence in anomalies), adversarial vulnerability of derived confidence score under structural perturbations, and limited efficacy of conventional calibration methods for sparse anomaly patterns. Thus we propose CRC-SGAD, a framework integrating statistical risk control into GAD via two innovations: (1) A Dual-Threshold Conformal Risk Control mechanism that provides theoretically guaranteed bounds for both False Negative Rate (FNR) and False Positive Rate (FPR) through providing prediction sets; (2) A Subgraph-aware Spectral Graph Neural Calibrator (SSGNC) that optimizes node representations through adaptive spectral filtering while reducing the size of prediction sets via hybrid loss optimization. Experiments on four datasets and five GAD models demonstrate statistically significant improvements in FNR and FPR control and prediction set size. CRC-SGAD establishes a paradigm for statistically rigorous anomaly detection in graph-structured security applications.

CRC-SGAD: Conformal Risk Control for Supervised Graph Anomaly Detection

TL;DR

CRC-SGAD establishes a paradigm for statistically rigorous anomaly detection in graph-structured security applications and introduces a Dual-Threshold Conformal Risk Control mechanism that provides theoretically guaranteed bounds for both False Negative Rate (FNR) and False Positive Rate (FPR) through providing prediction sets.

Abstract

Graph Anomaly Detection (GAD) is critical in security-sensitive domains, yet faces reliability challenges: miscalibrated confidence estimation (underconfidence in normal nodes, overconfidence in anomalies), adversarial vulnerability of derived confidence score under structural perturbations, and limited efficacy of conventional calibration methods for sparse anomaly patterns. Thus we propose CRC-SGAD, a framework integrating statistical risk control into GAD via two innovations: (1) A Dual-Threshold Conformal Risk Control mechanism that provides theoretically guaranteed bounds for both False Negative Rate (FNR) and False Positive Rate (FPR) through providing prediction sets; (2) A Subgraph-aware Spectral Graph Neural Calibrator (SSGNC) that optimizes node representations through adaptive spectral filtering while reducing the size of prediction sets via hybrid loss optimization. Experiments on four datasets and five GAD models demonstrate statistically significant improvements in FNR and FPR control and prediction set size. CRC-SGAD establishes a paradigm for statistically rigorous anomaly detection in graph-structured security applications.

Paper Structure

This paper contains 25 sections, 18 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Graph Anomaly Detection
  4. Uncertainty Quantification for GNNs
  5. Preliminaries
  6. Supervised Graph Anomaly Detection
  7. Conformal Risk Control
  8. Methodology
  9. Dual-Threshold Conformal Risk Control (DTCRC)
  10. Risk Functions and Set-Valued Predictors in SGAD
  11. Exchangeability of Risk Functions
  12. FNR and FPR Control
  13. Subgraph-aware Spectral Graph Neural Calibrator
  14. Dynamic Routing Mechanism
  15. Chebyshev Graph Convolution
  16. ...and 10 more sections

Figures (3)

  • Figure 1: The unreliable prediction confidence of BWGNN on Amazon dataset. (a) and (b) Figures depict the calibration error plots for anomalous nodes and normal nodes, respectively. (c) Figure illustrates the confidence distribution of misclassified nodes (both normal and anomalous) following a global attack. (d) Figure demonstrates the confidence variation of attacked nodes under a targeted attack scenario .
  • Figure 2: The overall framework of our proposed CRC-SGAD.
  • Figure 3: The distribution of Neighborhood Inefficiency entropy of the BWGNN model on the weibo dataset after CRC.