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GETS: Ensemble Temperature Scaling for Calibration in Graph Neural Networks
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Proposes GETS, a Graph Mixture-of-Experts post-hoc calibrator that combines input ensembles (logits, node features, degree embeddings) and model ensembles with top-k gating to produce node-wise temperature-like calibration for GNNs.
Problem
GNN classifiers are often miscalibrated (overconfident or underconfident), and existing post-hoc graph calibrators (TS, ETS, CaGCN, GATS) do not jointly exploit diverse input information and model ensembles or graph structure such as node degree.
Approach
Treat each calibration expert as a GNN calibrator trained on a different combination of inputs (logits, node features, degree embeddings), and use a noisy top-k sparse gating network over nodes to weight experts, yielding node-wise calibrated logits that preserve accuracy.
Key results
- GETS achieves the lowest ECE on most dataset/classifier pairs, e.g., Physics GIN 0.44 vs 0.90 for GATS and Reddit GAT 0.62 vs 0.81 for CaGCN.
- Reports average ECE improvements of 28.60% over CaGCN, 26.62% over GATS, and 28.09% over ETS across datasets.
- GATS runs out of memory on Reddit while GETS runs (GCN classifier, 7208 MB GPU memory).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use GETS instead of the strongest baseline for GCN calibration | GCN classifier · Across 10 datasets | ECE | Mixed |
| replace GCN experts with GAT experts (ablation) | GETS · Across datasets | ECE | Mixed |
| replace GCN experts with GIN experts (ablation) | GETS · Across datasets | ECE | Mixed |
| replace GCN experts with MLP experts (ablation) | GETS · Across datasets | ECE | Mixed |
| exclude logits from the input ensemble (ablation) | GETS · Across datasets | ECE | Hurt |
| exclude node features from the input ensemble (ablation) | GETS · Across datasets | ECE | Hurt |
| exclude degree information from the input ensemble (ablation) | GETS · Across datasets | ECE | Mixed |
| replace degree embeddings with betweenness centrality (ablation) | GETS input ensemble · Available datasets | ECE | Hurt |
| replace degree embeddings with clustering coefficient (ablation) | GETS input ensemble · Available datasets | ECE | Hurt |
| replace degree embeddings with PageRank centrality (ablation) | GETS input ensemble · Available datasets | ECE | Mixed |
| replace degree embeddings with Node2Vec embeddings (ablation) | GETS input ensemble · Available datasets | ECE | Mixed |
Surprising findings
- Using only logits as expert input is not preferred by the gating function, suggesting value in input ensembling.
- GETS does not beat all baselines on every setting; e.g., CaGCN is best on Computers GCN and SimCalib outperforms GETS on several GCN settings in the appendix.
Limitations
- Gains are not uniform; GETS is weaker on Computers, Cora, and Cora-full in several settings.
- Training multiple experts makes GETS less time-efficient than single-calibrator baselines.
- Fairness analysis is limited and shows negative improvement on some datasets (Ogbn-arxiv, Physics).
Experimental setup
Datasets: Citeseer Computers Cora Cora-full CS Ogbn-arxiv Photo Physics Pubmed Reddit
Benchmarks: Citeseer Computers Cora Cora-full CS Ogbn-arxiv Photo Physics Pubmed Reddit
Metrics: ECE (10 bins) VarECE GPU memory elapsed time
Baselines: TS VS ETS CaGCN GATS SimCalib
Builds on: temperature scaling ensemble temperature scaling CaGCN GATS noisy top-k gating mixture of experts
Closest papers by meaning
- HoTS: Homophily-Aware Temperature Scaling for Graph Neural Network Calibration (NeurIPS 2026 · similarity 0.91)
- Towards Precise Prediction Uncertainty in GNNs: Refining GNNs with Topology-grouping Strategy (AAAI 2025 · similarity 0.90)
- Understanding and Mitigating Under-Confidence in GNNs from the Final Layer (NeurIPS 2026 · similarity 0.88)
- SimCalib: Graph Neural Network Calibration Based on Similarity between Nodes (AAAI 2024 · similarity 0.88)
- Improving GNN Calibration with Discriminative Ability: Insights and Strategies (AAAI 2024 · similarity 0.88)
- MaxEnt Loss: Calibrating Graph Neural Networks under Out-of-Distribution Shift (Student Abstract) (AAAI 2024 · similarity 0.86)
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