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

arXiv: https://arxiv.org/abs/2504.02248 · HTML: https://mlsanity.com/paper/2504.02248/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 3 Apr 2025.

## Builds on (most cited first, 21 of 21)

- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Enhancing Graph Neural Network-based Fraud Detectors against Camouflaged Fraudsters](https://mlsanity.com/paper/2008.08692/) (2020)
- [A Comprehensive Survey on Graph Anomaly Detection with Deep Learning](https://mlsanity.com/paper/2106.07178/) (2021)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [Bayesian graph convolutional neural networks for semi-supervised classification](https://mlsanity.com/paper/1811.11103/) (2018)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Hiding Individuals and Communities in a Social Network](https://mlsanity.com/paper/1608.00375/) (2016)
- [Fast Gradient Attack on Network Embedding](https://mlsanity.com/paper/1809.02797/) (2018)
- [DGraph: A Large-Scale Financial Dataset for Graph Anomaly Detection](https://mlsanity.com/paper/2207.03579/) (2022)
- [GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection](https://mlsanity.com/paper/2306.12251/) (2023)
- [Attacking Fake News Detectors via Manipulating News Social Engagement](https://mlsanity.com/paper/2302.07363/) (2023)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Partitioning Message Passing for Graph Fraud Detection](https://mlsanity.com/paper/2412.00020/) (2024)
- [A General Black-box Adversarial Attack on Graph-based Fake News Detectors](https://mlsanity.com/paper/2404.15744/) (2024)
- [Towards Reliable Rare Category Analysis on Graphs via Individual Calibration](https://mlsanity.com/paper/2307.09858/) (2023)

## Abstract (arXiv)

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.