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Uncertainty in Graph Neural Networks: A Survey

Fangxin Wang, Yuqing Liu, Kay Liu, Yibo Wang, Sourav Medya, Philip S. Yu

TL;DR

This work addresses predictive uncertainty in $PU = AU + EU$ for Graph Neural Networks and emphasizes the decomposition $EU = MU + DU$ to distinguish model-based epistemic uncertainty from distributional shifts. It proposes a three-stage framework—identify sources, quantify uncertainty, and utilize uncertainty—for systematic study and practical guideposts. By surveying a taxonomy of methods (direct, Bayesian/random-parameter, and other approaches) and detailing evaluation metrics, the paper highlights gaps such as the lack of ground-truth uncertainty and the need for task-aligned evaluation. The authors outline real-world applications and future directions to foster efficient, robust, and trustworthy graph learning across communities and domains.

Abstract

Graph Neural Networks (GNNs) have been extensively used in various real-world applications. However, the predictive uncertainty of GNNs stemming from diverse sources such as inherent randomness in data and model training errors can lead to unstable and erroneous predictions. Therefore, identifying, quantifying, and utilizing uncertainty are essential to enhance the performance of the model for the downstream tasks as well as the reliability of the GNN predictions. This survey aims to provide a comprehensive overview of the GNNs from the perspective of uncertainty with an emphasis on its integration in graph learning. We compare and summarize existing graph uncertainty theory and methods, alongside the corresponding downstream tasks. Thereby, we bridge the gap between theory and practice, meanwhile connecting different GNN communities. Moreover, our work provides valuable insights into promising directions in this field.

Uncertainty in Graph Neural Networks: A Survey

TL;DR

This work addresses predictive uncertainty in for Graph Neural Networks and emphasizes the decomposition to distinguish model-based epistemic uncertainty from distributional shifts. It proposes a three-stage framework—identify sources, quantify uncertainty, and utilize uncertainty—for systematic study and practical guideposts. By surveying a taxonomy of methods (direct, Bayesian/random-parameter, and other approaches) and detailing evaluation metrics, the paper highlights gaps such as the lack of ground-truth uncertainty and the need for task-aligned evaluation. The authors outline real-world applications and future directions to foster efficient, robust, and trustworthy graph learning across communities and domains.

Abstract

Graph Neural Networks (GNNs) have been extensively used in various real-world applications. However, the predictive uncertainty of GNNs stemming from diverse sources such as inherent randomness in data and model training errors can lead to unstable and erroneous predictions. Therefore, identifying, quantifying, and utilizing uncertainty are essential to enhance the performance of the model for the downstream tasks as well as the reliability of the GNN predictions. This survey aims to provide a comprehensive overview of the GNNs from the perspective of uncertainty with an emphasis on its integration in graph learning. We compare and summarize existing graph uncertainty theory and methods, alongside the corresponding downstream tasks. Thereby, we bridge the gap between theory and practice, meanwhile connecting different GNN communities. Moreover, our work provides valuable insights into promising directions in this field.
Paper Structure (15 sections, 4 figures, 1 table)

This paper contains 15 sections, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Identifying Sources of Uncertainty in Gnns
  3. Quantifying Uncertainty in Gnns
  4. Single Deterministic Model
  5. Single Model with Parameters Being Random Variables
  6. Other Methods
  7. Evaluating Quantification Models
  8. Utilizing Uncertainty in Gnn Tasks
  9. Uncertainty-based Node Selection
  10. Uncertainty-based Abnormality Detection
  11. Uncertainty-aware Gnn Modeling
  12. Uncertainty for Trustworthy Gnn
  13. Uncertainty in Gnns: Real-world Applications
  14. Future directions
  15. Conclusions

Figures (4)

  • Figure 1: Overall Framework: (1) identifying sources of uncertainty (Section \ref{['2.2 sources']}), (2) quantifying uncertainty (Section \ref{['3. UQ methods']}) and (3) utilizing uncertainty for downstream tasks (Section \ref{['4. task']}). In the first subfigure, 'PU' refers to predictive/total uncertainty. 'AU' represents aleatoric/data/statistical uncertainty, 'EU' is in short for epistemic uncertainty. 'MU' and 'DU' represent model and distributional uncertainty, respectively.
  • Figure 2: Bridge uncertainty quantification models and evaluation methods by uncertainty sources. The diamond shape represents the separation of uncertainty sources. Quantification models linked to any diamond indicate their ability to separate the corresponding uncertainty source. We merge "Model Uncertainty" and "Data Uncertainty" in evaluation as they are complementary and share similar evaluation metrics in some cases.
  • Figure 3: Flowchart illustrating recommended quantification methods for various conditions. Diamond shapes represent conditions, while rectangular shapes indicate the recommended methods.
  • Figure 4: Illustration of representative usage of uncertainty in Gnn tasks. The darker the color, the greater the uncertainty/weight.