# JuryGCN: Quantifying Jackknife Uncertainty on Graph Convolutional Networks

arXiv: https://arxiv.org/abs/2210.05959 · HTML: https://mlsanity.com/paper/2210.05959/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 54 references that are in the map.
- First posted on arXiv 12 Oct 2022.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [A Semi-supervised Graph Attentive Network for Financial Fraud Detection](https://mlsanity.com/paper/2003.01171/) (2020)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [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)
- [Bayesian Graph Neural Networks with Adaptive Connection Sampling](https://mlsanity.com/paper/2006.04064/) (2020)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [Few-shot Network Anomaly Detection via Cross-network Meta-learning](https://mlsanity.com/paper/2102.11165/) (2021)
- [Active Learning for Graph Embedding](https://mlsanity.com/paper/1705.05085/) (2017)
- [Graph Policy Network for Transferable Active Learning on Graphs](https://mlsanity.com/paper/2006.13463/) (2020)
- [Discriminative Jackknife: Quantifying Uncertainty in Deep Learning via Higher-Order Influence Functions](https://mlsanity.com/paper/2007.13481/) (2020)
- [Bayesian Semi-supervised Learning with Graph Gaussian Processes](https://mlsanity.com/paper/1809.04379/) (2018)
- [RawlsGCN: Towards Rawlsian Difference Principle on Graph Convolutional Network](https://mlsanity.com/paper/2202.13547/) (2022)

## Built on by (most cited first, 15 of 15)

- [Class-Imbalanced Graph Learning without Class Rebalancing](https://mlsanity.com/paper/2308.14181/) (2023)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Unraveling Privacy Risks of Individual Fairness in Graph Neural Networks](https://mlsanity.com/paper/2301.12951/) (2023)
- [Towards Data-centric Graph Machine Learning: Review and Outlook](https://mlsanity.com/paper/2309.10979/) (2023)
- [Accurate and Scalable Estimation of Epistemic Uncertainty for Graph Neural Networks](https://mlsanity.com/paper/2401.03350/) (2024)
- [Towards Reliable Rare Category Analysis on Graphs via Individual Calibration](https://mlsanity.com/paper/2307.09858/) (2023)
- [Cross-Space Adaptive Filter: Integrating Graph Topology and Node Attributes for Alleviating the Over-smoothing Problem](https://mlsanity.com/paper/2401.14876/) (2024)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Active Learning for Graphs with Noisy Structures](https://mlsanity.com/paper/2402.02321/) (2024)
- [Shapley-Guided Utility Learning for Effective Graph Inference Data Valuation](https://mlsanity.com/paper/2503.18195/) (2025)
- [Accurate and Scalable Estimation of Epistemic Uncertainty for Graph Neural Networks](https://mlsanity.com/paper/2309.10976/) (2023)
- [Quantile-Free Uncertainty Quantification in Graph Neural Networks](https://mlsanity.com/paper/2605.04847/) (2026)
- [When does distribution shift break graph neural networks calibration?](https://mlsanity.com/paper/2607.10804/) (2026)
- [GATTA: Graph Active Learning with Test-Time Augmentation](https://mlsanity.com/paper/2608.15084/) (2026)

## Abstract (arXiv)

Graph Convolutional Network (GCN) has exhibited strong empirical performance in many real-world applications. The vast majority of existing works on GCN primarily focus on the accuracy while ignoring how confident or uncertain a GCN is with respect to its predictions. Despite being a cornerstone of trustworthy graph mining, uncertainty quantification on GCN has not been well studied and the scarce existing efforts either fail to provide deterministic quantification or have to change the training procedure of GCN by introducing additional parameters or architectures. In this paper, we propose the first frequentist-based approach named JuryGCN in quantifying the uncertainty of GCN, where the key idea is to quantify the uncertainty of a node as the width of confidence interval by a jackknife estimator. Moreover, we leverage the influence functions to estimate the change in GCN parameters without re-training to scale up the computation. The proposed JuryGCN is capable of quantifying uncertainty deterministically without modifying the GCN architecture or introducing additional parameters. We perform extensive experimental evaluation on real-world datasets in the tasks of both active learning and semi-supervised node classification, which demonstrate the efficacy of the proposed method.