PAGE: Parametric Generative Explainer for Graph Neural Network

TL;DR

The paper addresses the challenge of explaining graph neural networks with faithful, scalable explanations. It introduces PAGE, a parametric generative explainer built from an autoencoder and a discriminator that isolates latent causal features $Z_c$ to generate a graph-substructure explanation without perturbations, via a two-stage training regime that maximizes mutual information with predictions. PAGE demonstrates superior fidelity, accuracy, and efficiency on both synthetic and real-world datasets compared with GNNExplainer, PGExplainer, Gem, and OrphicX, while avoiding extensive perturbation or sampling. The approach is model-agnostic, post-hoc, and scalable, offering a practical path toward reliable interpretability in diverse GNN applications, though it currently relies on autoencoders as the interpreter for explanations.

Abstract

This article introduces PAGE, a parameterized generative interpretive framework. PAGE is capable of providing faithful explanations for any graph neural network without necessitating prior knowledge or internal details. Specifically, we train the auto-encoder to generate explanatory substructures by designing appropriate training strategy. Due to the dimensionality reduction of features in the latent space of the auto-encoder, it becomes easier to extract causal features leading to the model's output, which can be easily employed to generate explanations. To accomplish this, we introduce an additional discriminator to capture the causality between latent causal features and the model's output. By designing appropriate optimization objectives, the well-trained discriminator can be employed to constrain the encoder in generating enhanced causal features. Finally, these features are mapped to substructures of the input graph through the decoder to serve as explanations. Compared to existing methods, PAGE operates at the sample scale rather than nodes or edges, eliminating the need for perturbation or encoding processes as seen in previous methods. Experimental results on both artificially synthesized and real-world datasets demonstrate that our approach not only exhibits the highest faithfulness and accuracy but also significantly outperforms baseline models in terms of efficiency.

Figures (6)

• Figure 1: Methods using autoencoder as explainer: (a) GemlinGenerativeCausalExplanations2021, (b) OrphicXlinOrphicXCausalityInspiredLatent2022, (c) PAGE(Ours)
• Figure 2: Basic framework of PAGE. The causal part of the latent features related to GNN prediction is used to generate explanations, while the non-causal part is discarded. An additional discriminator is employed to maximize the mutual information between causal features and prediction results. The training process consists of two steps: the first step (indicated by the blue arrows) involves training the autoencoder and the discriminator, and the parameters of the discriminator will be fixed to constrain the encoder in generating better causal features in the second step.
• Figure 3: Fidelity and 1-Infidelity vs. Sparsity on BA-Shapes.
• Figure 4: Fidelity and 1-Infidelity vs. Sparsity on Mutagenicity.
• Figure 5: Visualized explanations on Mutagenicity. The explanation results of different methods are highlighted with black edges, where the gray edges are regarded as non-casual parts for the prediction. "P" under each graph/subgraph denotes the probability of being classified into the mutagenic class, which is obtained by feeding the associated graph/subgraph into the target GNN.

Theorems & Definitions (7)

• Proposition 1
• proof
• Proposition 2
• Proposition 3
• Definition 1
• Proposition 4
• proof