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CUQ-GNN: Committee-based Graph Uncertainty Quantification using Posterior Networks

Clemens Damke, Eyke Hüllermeier

TL;DR

This work tackles predictive uncertainty in graph-based node classification and critiques the axiomatic Graph Posterior Network (GPN) framework. It introduces CUQ-GNN, a committee-based, behavioral pooling approach that blends a Graph Neural Network with Posterior Network uncertainty to propagate a second-order distribution $Q$ through the graph via personalized PageRank, removing fixed pooling axioms. The proposed formulation $CUQ-GNN(X,A) = PostNet( GNN(h_{enc}(X), A) W_{lat} )$ enables domain-adaptive uncertainty properties while remaining flexible to graph structure. Across six node-classification benchmarks, CUQ-GNN delivers competitive accuracy and improved uncertainty quality (via $TU$, $AU$, $EU$, and $EU_{PC}$) with robust out-of-distribution detection compared to GPN and LopGPN.

Abstract

In this work, we study the influence of domain-specific characteristics when defining a meaningful notion of predictive uncertainty on graph data. Previously, the so-called Graph Posterior Network (GPN) model has been proposed to quantify uncertainty in node classification tasks. Given a graph, it uses Normalizing Flows (NFs) to estimate class densities for each node independently and converts those densities into Dirichlet pseudo-counts, which are then dispersed through the graph using the personalized Page-Rank algorithm. The architecture of GPNs is motivated by a set of three axioms on the properties of its uncertainty estimates. We show that those axioms are not always satisfied in practice and therefore propose the family of Committe-based Uncertainty Quantification Graph Neural Networks (CUQ-GNNs), which combine standard Graph Neural Networks with the NF-based uncertainty estimation of Posterior Networks (PostNets). This approach adapts more flexibly to domain-specific demands on the properties of uncertainty estimates. We compare CUQ-GNN against GPN and other uncertainty quantification approaches on common node classification benchmarks and show that it is effective at producing useful uncertainty estimates.

CUQ-GNN: Committee-based Graph Uncertainty Quantification using Posterior Networks

TL;DR

This work tackles predictive uncertainty in graph-based node classification and critiques the axiomatic Graph Posterior Network (GPN) framework. It introduces CUQ-GNN, a committee-based, behavioral pooling approach that blends a Graph Neural Network with Posterior Network uncertainty to propagate a second-order distribution through the graph via personalized PageRank, removing fixed pooling axioms. The proposed formulation enables domain-adaptive uncertainty properties while remaining flexible to graph structure. Across six node-classification benchmarks, CUQ-GNN delivers competitive accuracy and improved uncertainty quality (via , , , and ) with robust out-of-distribution detection compared to GPN and LopGPN.

Abstract

In this work, we study the influence of domain-specific characteristics when defining a meaningful notion of predictive uncertainty on graph data. Previously, the so-called Graph Posterior Network (GPN) model has been proposed to quantify uncertainty in node classification tasks. Given a graph, it uses Normalizing Flows (NFs) to estimate class densities for each node independently and converts those densities into Dirichlet pseudo-counts, which are then dispersed through the graph using the personalized Page-Rank algorithm. The architecture of GPNs is motivated by a set of three axioms on the properties of its uncertainty estimates. We show that those axioms are not always satisfied in practice and therefore propose the family of Committe-based Uncertainty Quantification Graph Neural Networks (CUQ-GNNs), which combine standard Graph Neural Networks with the NF-based uncertainty estimation of Posterior Networks (PostNets). This approach adapts more flexibly to domain-specific demands on the properties of uncertainty estimates. We compare CUQ-GNN against GPN and other uncertainty quantification approaches on common node classification benchmarks and show that it is effective at producing useful uncertainty estimates.
Paper Structure (20 sections, 10 equations, 4 figures, 1 table)

This paper contains 20 sections, 10 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Uncertainty Quantification
  3. Entropy-based Uncertainty Measures
  4. Least-confidence and Count-based Uncertainty Measures
  5. Posterior and Graph Posterior Networks
  6. Posterior Networks
  7. Graph Posterior Networks
  8. GPN as an Opinion Pooling Model
  9. Committee-based Graph Uncertainty Quantification
  10. The Irreducibility of Conflicts Assumption
  11. Resolving Conflicts via Behavioral Pooling
  12. Evaluation
  13. Experimental Setup
  14. Datasets
  15. Models
  16. ...and 5 more sections

Figures (4)

  • Figure 1: Illustration of how *gpn aggregates the predictions (opinions) of different nodes (agents).
  • Figure 2: Examples for graphs obtained via bounded and unbounded degree sampling.
  • Figure 3: Illustration of how *cuqgnn can flexibly resolve conflicts.
  • Figure 4: *arc for different uncertainty measures. The x-axis represents the fraction of rejected test instances; the y-axis represents the test accuracy for a given rejection rate. The (small) shaded areas behind the curves represent the estimate's standard error.