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SimCalib: Graph Neural Network Calibration based on Similarity between Nodes
Machine Learning · Submitted 19 Dec 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Additionally, we conduct extensive experiments investigating different design factors and demonstrate the effectiveness of our proposed SimCalib framework for GNN calibration by achieving state-of-the-art performance on 14 out of 16 benchmarks.
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The abstract, sentence by sentence
Graph neural networks (GNNs) have exhibited impressive performance in modeling graph data as exemplified in various applications. Recently, the GNN calibration problem has attracted increasing attention, especially in cost-sensitive scenarios. Previous work has gained empirical insights on the issue, and devised effective approaches for it, but theoretical supports still fall short. In this work, we shed light on the relationship between GNN calibration and nodewise similarity via theoretical analysis. A novel calibration framework, named SimCalib, is accordingly proposed to consider similarity between nodes at global and local levels. At the global level, the Mahalanobis distance between the current node and class prototypes is integrated to implicitly consider similarity between the current node and all nodes in the same class. At the local level, the similarity of node representation movement dynamics, quantified by nodewise homophily and relative degree, is considered. Informed about the application of nodewise movement patterns in analyzing nodewise behavior on the over-smoothing problem, we empirically present a possible relationship between over-smoothing and GNN calibration problem. Experimentally, we discover a correlation between nodewise similarity and model calibration improvement, in alignment with our theoretical results. Additionally, we conduct extensive experiments investigating different design factors and demonstrate the effectiveness of our proposed SimCalib framework for GNN calibration by achieving state-of-the-art performance on 14 out of 16 benchmarks.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Graph neural networks (GNNs) have exhibited impressive performance in modeling graph data as exemplified in various applications. | background 1.00 | 0.05 | 0.01 | asserted 0.99 |
| s1 | Recently, the GNN calibration problem has attracted increasing attention, especially in cost-sensitive scenarios. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s2 | Previous work has gained empirical insights on the issue, and devised effective approaches for it, but theoretical supports still fall short. | gap 0.97 | 0.05 | 0.03 | asserted 1.00 |
| s3 | In this work, we shed light on the relationship between GNN calibration and nodewise similarity via theoretical analysis. | contribution 0.99 | 0.91 | 0.10 | asserted 0.97 |
| s4 | A novel calibration framework, named SimCalib, is accordingly proposed to consider similarity between nodes at global and local levels. | contribution 0.68 | 0.93 | 0.12 | asserted 1.00 |
| s5 | At the global level, the Mahalanobis distance between the current node and class prototypes is integrated to implicitly consider similarity between the current node and all nodes in the same class. | method 0.99 | 0.86 | 0.06 | asserted 0.99 |
| s6 | At the local level, the similarity of node representation movement dynamics, quantified by nodewise homophily and relative degree, is considered. | method 0.99 | 0.85 | 0.05 | asserted 1.00 |
| s7 | Informed about the application of nodewise movement patterns in analyzing nodewise behavior on the over-smoothing problem, we empirically present a possible relationship between over-smoothing and GNN calibration problem. | contribution 0.56 | 0.87 | 0.07 | hedged possibility 0.98 |
| s8 | Experimentally, we discover a correlation between nodewise similarity and model calibration improvement, in alignment with our theoretical results. | result 0.96 | 0.96 | 0.35 | asserted 0.98 |
| s9 | Additionally, we conduct extensive experiments investigating different design factors and demonstrate the effectiveness of our proposed SimCalib framework for GNN calibration by achieving state-of-the-art performance on 14 out of 16 benchmarks. | result 0.94 | 0.98 | 0.57 | asserted 1.00 |
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The paper
Original abstract
Graph neural networks (GNNs) have exhibited impressive performance in modeling graph data as exemplified in various applications. Recently, the GNN calibration problem has attracted increasing attention, especially in cost-sensitive scenarios. Previous work has gained empirical insights on the issue, and devised effective approaches for it, but theoretical supports still fall short. In this work, we shed light on the relationship between GNN calibration and nodewise similarity via theoretical analysis. A novel calibration framework, named SimCalib, is accordingly proposed to consider similarity between nodes at global and local levels. At the global level, the Mahalanobis distance between the current node and class prototypes is integrated to implicitly consider similarity between the current node and all nodes in the same class. At the local level, the similarity of node representation movement dynamics, quantified by nodewise homophily and relative degree, is considered. Informed about the application of nodewise movement patterns in analyzing nodewise behavior on the over-smoothing problem, we empirically present a possible relationship between over-smoothing and GNN calibration problem. Experimentally, we discover a correlation between nodewise similarity and model calibration improvement, in alignment with our theoretical results. Additionally, we conduct extensive experiments investigating different design factors and demonstrate the effectiveness of our proposed SimCalib framework for GNN calibration by achieving state-of-the-art performance on 14 out of 16 benchmarks.
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What this paper does with the arXiv papers it cites
What it cites · 9 sentences without a confident label
Cites as support 1 paper
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Furthermore, aware of correlation between ECE and distances to training nodes [ref] , we estimate nodewise homophily and apply it to graph attention: [equation] where $η_i$ is the distance from $v_i$ to the nearest training node, and $σ:=LeakyReLU$ [ref] .
Empirical Evaluation of Rectified Activations in Convolutional Network · Representation movement similarity · 0.96
Cites as background 5 papers
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To mitigate the issue, a variety of calibration methods [ref] have been proposed to calibrate pretrained deep neural networks (DNNs).
Calibration of Neural Networks using Splines · Introduction · 0.84
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A plethora of methods based on evidential theory [ref] , model ensembling [ref] , adversarial calibration [ref] and Bayesian approach [ref] belongs to the category.
Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches · Calibration for standard multi-class classification · 0.97
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Recently, uncertainty quantification is also considered via conformal prediction [ref] .
Uncertainty Quantification over Graph with Conformalized Graph Neural Networks · GNN calibration · 0.96
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