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Generating In-Distribution Proxy Graphs for Explaining Graph Neural Networks
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Proposes ProxyExplainer, which generates in-distribution proxy graphs via a graph auto-encoder and a variational graph auto-encoder so that GNN explanation subgraphs can be evaluated on data resembling the training distribution.
Problem
Post-hoc instance-level GNN explanation via the graph information bottleneck evaluates explanation subgraphs with the GNN, but these subgraphs are out-of-distribution relative to the training graphs, making label predictions unreliable.
Approach
Replace the explanation subgraph with a proxy graph drawn from the training-graph distribution, built by combining a GAE reconstruction of the explanatory subgraph with a VGAE-perturbed version of the non-explanatory residual; the proxy graph preserves label information while matching the data distribution, and an explainer and proxy generator are trained alternately with a bi-level objective.
Key results
- ProxyExplainer reaches 0.977 AUC-ROC on MUTAG and 0.960 on BA-3motifs, the best among compared methods on all six datasets in Table 1.
- Averaged over datasets, ProxyExplainer improves AUC by 10.6% on real-world and 7.5% on synthetic datasets over the leading baselines (as reported by the authors).
- Proxy graphs have lower MMD to original graphs than ground-truth explanations and PGExplainer explanations in most dataset/statistic combinations (e.g., MUTAG degree MMD 0.123 vs 0.614 GT).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use ProxyExplainer instead of MixupExplainer | GCN explanations · MUTAG | AUC-ROC: 0.863 ± 0.103 -> 0.977 ± 0.009 | Helped |
| use ProxyExplainer instead of PGExplainer | GCN explanations · Benzene | AUC-ROC: 0.793 ± 0.054 -> 0.845 ± 0.036 | Helped |
| use ProxyExplainer instead of MixupExplainer | GCN explanations · Alkane-Carbonyl | AUC-ROC: 0.811 ± 0.006 -> 0.934 ± 0.005 | Helped |
| use ProxyExplainer instead of MixupExplainer | GCN explanations · Fluoride-Carbonyl | AUC-ROC: 0.706 ± 0.013 -> 0.758 ± 0.068 | Helped |
| use ProxyExplainer instead of MixupExplainer | GCN explanations · BA-2motifs | AUC-ROC: 0.906 ± 0.059 -> 0.935 ± 0.008 | Helped |
| use ProxyExplainer instead of MixupExplainer | GCN explanations · BA-3motifs | AUC-ROC: 0.859 ± 0.019 -> 0.960 ± 0.008 | Helped |
| add the non-explanatory subgraph generator (VGAE) (ablation) | ProxyExplainer · MUTAG and BA-2motifs | explanation performance | Helped |
| add KL divergence to the training loss (ablation) | ProxyExplainer · MUTAG and BA-2motifs | explanation performance | Helped |
| add the distribution loss (ablation) | ProxyExplainer · MUTAG and BA-2motifs | explanation performance | Helped |
Surprising findings
- Ground-truth explanation subgraphs have large MMD to original graphs (e.g., 0.614 degree MMD on MUTAG), supporting the claim that explanation subgraphs are out-of-distribution.
- MixupExplainer performs well on BA-2motifs (0.906) but poorly on Benzene (0.611), suggesting its independence assumption fails on real-world graphs.
Limitations
- Relies on a practical bi-level and alternating training scheme whose hyper-parameters (M, lambda, beta, D) are chosen by grid search.
- Evaluation uses ground-truth explanations available only for synthetic and molecular benchmarks, and the paper's own experiments are limited to GCN and GIN.
- Standard deviations are large on some datasets (e.g., MUTAG AP 0.756 ± 0.107), so gains on some datasets are less certain.
Experimental setup
Datasets: MUTAG Benzene Alkane-Carbonyl Fluoride-Carbonyl BA-2motifs BA-3motifs
Benchmarks: MUTAG Benzene Alkane-Carbonyl Fluoride-Carbonyl BA-2motifs BA-3motifs
Metrics: AUC-ROC AP robust fidelity (Fid+ / Fid-) MMD of graph statistics cosine similarity Euclidean distance
Baselines: GradCAM GNNExplainer PGExplainer ReFine MixupExplainer
Builds on: GNNExplainer PGExplainer Graph Information Bottleneck MixupExplainer ReFine
Closest papers by meaning
- Towards Robust Fidelity for Evaluating Explainability of Graph Neural Networks (ICLR 2024 · similarity 0.92)
- On Explainability of Graph Neural Networks via Subgraph Explorations (ICML 2021 · similarity 0.92)
- Self-Interpretable Graph Learning with Sufficient and Necessary Explanations (AAAI 2024 · similarity 0.89)
- EiG-Search: Generating Edge-Induced Subgraphs for GNN Explanation in Linear Time (ICML 2024 · similarity 0.89)
- Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective (ICML 2025 · similarity 0.89)
- GOAt: Explaining Graph Neural Networks via Graph Output Attribution (ICLR 2024 · similarity 0.89)
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