# PGM-Explainer: Probabilistic Graphical Model Explanations for Graph Neural Networks

arXiv: https://arxiv.org/abs/2010.05788 · HTML: https://mlsanity.com/paper/2010.05788/

## Key facts

- Cited by 211 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2020.

## Built on by (most cited first, 30 of 211)

- [From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AI](https://mlsanity.com/paper/2201.08164/) (2022)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism](https://mlsanity.com/paper/2201.12987/) (2022)
- [Generative Causal Explanations for Graph Neural Networks](https://mlsanity.com/paper/2104.06643/) (2021)
- [CF-GNNExplainer: Counterfactual Explanations for Graph Neural Networks](https://mlsanity.com/paper/2102.03322/) (2021)
- [A Comprehensive Survey on Trustworthy Graph Neural Networks: Privacy, Robustness, Fairness, and Explainability](https://mlsanity.com/paper/2204.08570/) (2022)
- [ProtGNN: Towards Self-Explaining Graph Neural Networks](https://mlsanity.com/paper/2112.00911/) (2021)
- [Trustworthy Graph Neural Networks: Aspects, Methods and Trends](https://mlsanity.com/paper/2205.07424/) (2022)
- [Evaluating Explainability for Graph Neural Networks](https://mlsanity.com/paper/2208.09339/) (2022)
- [Debiasing Graph Neural Networks via Learning Disentangled Causal Substructure](https://mlsanity.com/paper/2209.14107/) (2022)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Robust Counterfactual Explanations on Graph Neural Networks](https://mlsanity.com/paper/2107.04086/) (2021)
- [Graph-Based Deep Learning for Medical Diagnosis and Analysis: Past, Present and Future](https://mlsanity.com/paper/2105.13137/) (2021)
- [Global Explainability of GNNs via Logic Combination of Learned Concepts](https://mlsanity.com/paper/2210.07147/) (2022)
- [GraphSVX: Shapley Value Explanations for Graph Neural Networks](https://mlsanity.com/paper/2104.10482/) (2021)
- [Interpretable Graph Neural Networks for Connectome-Based Brain Disorder Analysis](https://mlsanity.com/paper/2207.00813/) (2022)
- [GraphFramEx: Towards Systematic Evaluation of Explainability Methods for Graph Neural Networks](https://mlsanity.com/paper/2206.09677/) (2022)
- [GStarX: Explaining Graph Neural Networks with Structure-Aware Cooperative Games](https://mlsanity.com/paper/2201.12380/) (2022)
- [A Survey on Graph-Based Deep Learning for Computational Histopathology](https://mlsanity.com/paper/2107.00272/) (2021)
- [Towards Understanding the Generalization of Graph Neural Networks](https://mlsanity.com/paper/2305.08048/) (2023)
- [Towards Self-Interpretable Graph-Level Anomaly Detection](https://mlsanity.com/paper/2310.16520/) (2023)
- [Probing GNN Explainers: A Rigorous Theoretical and Empirical Analysis of GNN Explanation Methods](https://mlsanity.com/paper/2106.09078/) (2021)
- [Zorro: Valid, Sparse, and Stable Explanations in Graph Neural Networks](https://mlsanity.com/paper/2105.08621/) (2021)
- [GCExplainer: Human-in-the-Loop Concept-based Explanations for Graph Neural Networks](https://mlsanity.com/paper/2107.11889/) (2021)
- [Explaining the Explainers in Graph Neural Networks: a Comparative Study](https://mlsanity.com/paper/2210.15304/) (2022)
- [Reinforced Causal Explainer for Graph Neural Networks](https://mlsanity.com/paper/2204.11028/) (2022)
- [GNNInterpreter: A Probabilistic Generative Model-Level Explanation for Graph Neural Networks](https://mlsanity.com/paper/2209.07924/) (2022)
- [OrphicX: A Causality-Inspired Latent Variable Model for Interpreting Graph Neural Networks](https://mlsanity.com/paper/2203.15209/) (2022)
- [Global Concept-Based Interpretability for Graph Neural Networks via Neuron Analysis](https://mlsanity.com/paper/2208.10609/) (2022)

## Abstract (arXiv)

In Graph Neural Networks (GNNs), the graph structure is incorporated into the learning of node representations. This complex structure makes explaining GNNs' predictions become much more challenging. In this paper, we propose PGM-Explainer, a Probabilistic Graphical Model (PGM) model-agnostic explainer for GNNs. Given a prediction to be explained, PGM-Explainer identifies crucial graph components and generates an explanation in form of a PGM approximating that prediction. Different from existing explainers for GNNs where the explanations are drawn from a set of linear functions of explained features, PGM-Explainer is able to demonstrate the dependencies of explained features in form of conditional probabilities. Our theoretical analysis shows that the PGM generated by PGM-Explainer includes the Markov-blanket of the target prediction, i.e. including all its statistical information. We also show that the explanation returned by PGM-Explainer contains the same set of independence statements in the perfect map. Our experiments on both synthetic and real-world datasets show that PGM-Explainer achieves better performance than existing explainers in many benchmark tasks.