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Evidential Uncertainty Probes for Graph Neural Networks

Linlin Yu, Kangshuo Li, Pritom Kumar Saha, Yifei Lou, Feng Chen

TL;DR

This work tackles reliable uncertainty quantification for Graph Neural Networks by introducing the Evidential Probing Network (EPN), a plug-and-play head that attaches to pre-trained GNNs to produce Dirichlet-distributed predictions without retraining the base model. The authors propose two uncertainty-propagation schemes and two regularizations, ICE and PCL, forming the EPN-reg framework that improves epistemic uncertainty estimation. Theoretical results show limitations of using uncertainty cross-entropy alone and demonstrate that ICE can enforce correct ID vs OOD ordering under sufficient class separation. Empirically, EPN-reg achieves state-of-the-art or competitive performance across diverse datasets for OOD and misclassification detection while maintaining real-time efficiency, highlighting its practicality for high-stakes deployment.

Abstract

Accurate quantification of both aleatoric and epistemic uncertainties is essential when deploying Graph Neural Networks (GNNs) in high-stakes applications such as drug discovery and financial fraud detection, where reliable predictions are critical. Although Evidential Deep Learning (EDL) efficiently quantifies uncertainty using a Dirichlet distribution over predictive probabilities, existing EDL-based GNN (EGNN) models require modifications to the network architecture and retraining, failing to take advantage of pre-trained models. We propose a plug-and-play framework for uncertainty quantification in GNNs that works with pre-trained models without the need for retraining. Our Evidential Probing Network (EPN) uses a lightweight Multi-Layer-Perceptron (MLP) head to extract evidence from learned representations, allowing efficient integration with various GNN architectures. We further introduce evidence-based regularization techniques, referred to as EPN-reg, to enhance the estimation of epistemic uncertainty with theoretical justifications. Extensive experiments demonstrate that the proposed EPN-reg achieves state-of-the-art performance in accurate and efficient uncertainty quantification, making it suitable for real-world deployment.

Evidential Uncertainty Probes for Graph Neural Networks

TL;DR

This work tackles reliable uncertainty quantification for Graph Neural Networks by introducing the Evidential Probing Network (EPN), a plug-and-play head that attaches to pre-trained GNNs to produce Dirichlet-distributed predictions without retraining the base model. The authors propose two uncertainty-propagation schemes and two regularizations, ICE and PCL, forming the EPN-reg framework that improves epistemic uncertainty estimation. Theoretical results show limitations of using uncertainty cross-entropy alone and demonstrate that ICE can enforce correct ID vs OOD ordering under sufficient class separation. Empirically, EPN-reg achieves state-of-the-art or competitive performance across diverse datasets for OOD and misclassification detection while maintaining real-time efficiency, highlighting its practicality for high-stakes deployment.

Abstract

Accurate quantification of both aleatoric and epistemic uncertainties is essential when deploying Graph Neural Networks (GNNs) in high-stakes applications such as drug discovery and financial fraud detection, where reliable predictions are critical. Although Evidential Deep Learning (EDL) efficiently quantifies uncertainty using a Dirichlet distribution over predictive probabilities, existing EDL-based GNN (EGNN) models require modifications to the network architecture and retraining, failing to take advantage of pre-trained models. We propose a plug-and-play framework for uncertainty quantification in GNNs that works with pre-trained models without the need for retraining. Our Evidential Probing Network (EPN) uses a lightweight Multi-Layer-Perceptron (MLP) head to extract evidence from learned representations, allowing efficient integration with various GNN architectures. We further introduce evidence-based regularization techniques, referred to as EPN-reg, to enhance the estimation of epistemic uncertainty with theoretical justifications. Extensive experiments demonstrate that the proposed EPN-reg achieves state-of-the-art performance in accurate and efficient uncertainty quantification, making it suitable for real-world deployment.

Paper Structure

This paper contains 33 sections, 6 theorems, 91 equations, 1 figure, 22 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminary
  4. Problem Formulation
  5. Uncertainty Quantification in EGNN
  6. Optimization of EGNN
  7. Methodology
  8. Evidential Probe Network
  9. Optimization of EPN
  10. Theoretical Analysis
  11. Experiment
  12. Setup
  13. OOD and Misclassification Detection
  14. Ablation Study
  15. Conclusion
  16. ...and 18 more sections

Key Result

Theorem 1

For any $\epsilon > 0$, there exists a positive constant $\digamma > 0$ such that, for any data distribution satisfying Gaussian data assumption with $\|\bm{\mu}\|_2 > \digamma$, the probability that the epistemic uncertainty obtained by an optimal single-layer EGNN based on an upper bound of UCE lo

Figures (1)

  • Figure 1: The flow chart of our proposed EPN network and its interaction with the two regularization terms, including the Intra-Class Evidence-based (ICE) and Positive-Confidence Learning (PCL).

Theorems & Definitions (15)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Definition 1: Single-layer ENN
  • Definition 2: Upper Bound of the UCE Loss
  • Proposition 1: Optimal Epistemic Uncertainty
  • proof
  • proof
  • proof
  • Lemma 1
  • ...and 5 more