# Statistical Test for Saliency Maps of Graph Neural Networks via Selective Inference

arXiv: https://arxiv.org/abs/2505.16893 · HTML: https://mlsanity.com/paper/2505.16893/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 22 May 2025.

## Builds on (most cited first, 30 of 32)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [GraphLIME: Local Interpretable Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2001.06216/) (2020)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [GraphSVX: Shapley Value Explanations for Graph Neural Networks](https://mlsanity.com/paper/2104.10482/) (2021)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [Zorro: Valid, Sparse, and Stable Explanations in Graph Neural Networks](https://mlsanity.com/paper/2105.08621/) (2021)
- [EEG-GNN: Graph Neural Networks for Classification of Electroencephalogram (EEG) Signals](https://mlsanity.com/paper/2106.09135/) (2021)
- [More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming](https://mlsanity.com/paper/2105.04920/) (2021)
- [Computing Valid p-values for Image Segmentation by Selective Inference](https://mlsanity.com/paper/1906.00629/) (2019)
- [Quantifying Statistical Significance of Neural Network-based Image Segmentation by Selective Inference](https://mlsanity.com/paper/2010.01823/) (2020)
- [Graph Neural Network-based EEG Classification: A Survey](https://mlsanity.com/paper/2310.02152/) (2023)
- [Graph Neural Network Explanations are Fragile](https://mlsanity.com/paper/2406.03193/) (2024)
- [Selecting the number of principal components: estimation of the true rank of a noisy matrix](https://mlsanity.com/paper/1410.8260/) (2014)
- [A significance test for forward stepwise model selection](https://mlsanity.com/paper/1405.3920/) (2014)
- [Valid P-Value for Deep Learning-Driven Salient Region](https://mlsanity.com/paper/2301.02437/) (2023)
- [Tree-Values: selective inference for regression trees](https://mlsanity.com/paper/2106.07816/) (2021)
- [Unifying approach to selective inference with applications to cross-validation](https://mlsanity.com/paper/1703.06559/) (2017)
- [Statistical Test for Anomaly Detections by Variational Auto-Encoders](https://mlsanity.com/paper/2402.03724/) (2024)
- [Explainable Graph Neural Networks Under Fire](https://mlsanity.com/paper/2406.06417/) (2024)
- [si4onnx: A Python package for Selective Inference in Deep Learning Models](https://mlsanity.com/paper/2501.17415/) (2025)

## Built on by (most cited first, 1 of 1)

- [Statistical Testing for Multiple Instance Learning via Selective Inference with Applications to Computational Pathology](https://mlsanity.com/paper/2609.31712/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have gained prominence for their ability to process graph-structured data across various domains. However, interpreting GNN decisions remains a significant challenge, leading to the adoption of saliency maps for identifying salient subgraphs composed of influential nodes and edges. Despite their utility, the reliability of GNN saliency maps has been questioned, particularly in terms of their robustness to input noise. In this study, we propose a statistical testing framework to rigorously evaluate the significance of saliency maps. Our main contribution lies in addressing the inflation of the Type I error rate caused by double-dipping of data, leveraging the framework of Selective Inference. Our method provides statistically valid p-values while controlling the Type I error rate, ensuring that identified salient subgraphs contain meaningful information rather than random artifacts. The method is applicable to a variety of saliency methods with piecewise linearity (e.g., Class Activation Mapping). We validate our method on synthetic and real-world datasets, demonstrating its capability in assessing the reliability of GNN interpretations.