[Paper Review] PGM-Explainer: Probabilistic Graphical Model Explanations for Graph Neural Networks

Minh N. Vu, My T. Thai|arXiv (Cornell University)|Oct 12, 2020

Explainable Artificial Intelligence (XAI)Computer Science92 citations

TL;DR

PGM-Explainer introduces a model-agnostic explainer for GNNs that uses Bayesian networks to approximate predictions, capturing feature dependencies via conditional probabilities and Markov-blanket guarantees. It demonstrates superior explanations on synthetic and real-world datasets compared to baselines.

ABSTRACT

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.

Motivation & Objective

• Motivate transparent explanations for GNN predictions given the complex graph structure.
• Propose a model-agnostic explainer that uses probabilistic graphical models to approximate predictions.
• Ensure explanations capture dependencies among explained features beyond linear attributions.
• Provide theoretical guarantees relating the produced PGM to the target prediction’s Markov-blanket.
• Empirically evaluate on synthetic and real-world tasks to demonstrate effectiveness and intuition of the explanations.

Proposed method

• Define an explanation as a Bayesian network that approximates the GNN's target prediction.
• Use data generation by perturbing input graphs and recording predictions to build a sampled data set.
• Perform variable selection to constrain the PGM to a Markov-blanket containing the target, using pairwise dependency tests.
• Learn the PGM structure and parameters with a BIC-score-based approach and hill-climbing optimization.
• Optionally enforce a no-child constraint to make the target a leaf, improving interpretability.
• Provide theoretical results showing inclusion of the Markov-blanket and I-equivalence under a perfect map.

Experimental results

Research questions

• RQ1 Can a probabilistic graphical model faithfully approximate a GNN's target prediction while remaining interpretable?
• RQ2 Does restricting the explanation to a compact Markov-blanket capture all necessary information for the target prediction?
• RQ3 How does a PGM-based explainer compare to existing additive-attribute explainers in accuracy and interpretability?
• RQ4 What theoretical guarantees hold for PGM-Explainer regarding Markov-blanket inclusion and I-equivalence?

Key findings

• PGM-Explainer yields explanations that capture non-linear dependencies among graph components, unlike linear attribution methods.
• Theoretical results show the generated PGM includes the Markov-blanket of the target prediction, preserving all statistical information.
• Empirical results on synthetic and real-world datasets show PGM-Explainer often outperforms SHAP and GNNExplainer in accuracy/precision of explanations.
• In node and graph classification tasks, explanations provide intuitive probabilistic insights into how nearby nodes and motifs influence the target prediction.