BetaExplainer: A Probabilistic Method to Explain Graph Neural Networks

TL;DR

The paper tackles explainability for Graph Neural Networks by producing edge-level explanations with quantified uncertainty. BetaExplainer uses a Beta-distributed edge mask and a variational ELBO objective to learn $P(M|f(X,G))$, yielding probabilistic edge importance scores. It demonstrates improved fidelity and uncertainty-aware rankings across seven simulated datasets, notably in sparse-feature settings, when compared to GNNExplainer and SubgraphX. The framework provides a scalable, priors-aware explanation approach that supports hypothesis generation and can reduce downstream costs by focusing on high-confidence edges.

Abstract

Graph neural networks (GNNs) are powerful tools for conducting inference on graph data but are often seen as "black boxes" due to difficulty in extracting meaningful subnetworks driving predictive performance. Many interpretable GNN methods exist, but they cannot quantify uncertainty in edge weights and suffer in predictive accuracy when applied to challenging graph structures. In this work, we proposed BetaExplainer which addresses these issues by using a sparsity-inducing prior to mask unimportant edges during model training. To evaluate our approach, we examine various simulated data sets with diverse real-world characteristics. Not only does this implementation provide a notion of edge importance uncertainty, it also improves upon evaluation metrics for challenging datasets compared to state-of-the art explainer methods.

Figures (7)

• Figure 1: BetaExplainer returns a mask for the important edges of a graph for a GNN's classification. As it learns a probabilistic model to represent these important edges, the mask contains a level of uncertainty quantification to indicate the importance of each edge to a GNN missing or limited in other models
• Figure 2: Given a trained GNN, the original graph, and Beta distribution parameters $\alpha$ and $\beta$, BetaExplainer is trained by learning the masked-out graph minimizing the KL-Divergence Loss between the model output on the masked out graph and original graph. It will return the learned edge mask representing a probabilistic importance score for each edge when complete
• Figure 3: We calculate the mean and standard errors of the Jaccard Index (a), F1 Score (b), and unfaithfulness (c) results and whether explainer differences are significant (ns: $0.05 < p \le 1$, *: $0.01 < p \le 0.05$, **: $0.001 < p \le 0.01$, ***: $0.0001 < p \le 0.001$, and ****: $p \le 0.0001$). We graph the best subgraphs for the datasets for each explainer versus the groundtruth (d), denoting true positive (blue), false positive (red), and false negative (pink) edges and weighting BetaExplainer edges by probabilities and empirical cumulative distribution (eCDF) of BetaExplainer probabilities for true and false positives with respect to the groundtruth (e, f, g, h, i)
• Figure 4: We calculate the mean and standard errors of the accuracy (a), F1 score (b), and unfaithfulness (c) and the significant differences between explainer results (ns: $0.05 < p \le 1$, *: $0.01 < p \le 0.05$, **: $0.001 < p \le 0.01$, ***: $0.0001 < p \le 0.001$, and ****: $p \le 0.0001$). We graph best results per explainer for datasets (if true positives are returned) (d), denoting true positive (blue), false positive (red), and false negative (pink) edges and weighting BetaExplainer edges by probabilities and the eCDF of the BetaExplainer probabilities for true and false positives with respect to the groundtruth (e, f)
• Figure 5: The architecture for the input GNNs for the explainers are recorded for reproducibility