Robust Stochastic Graph Generator for Counterfactual Explanations

TL;DR

This work tackles the challenge of graph counterfactual explanations by introducing RSGG-CE, a robust stochastic graph generator that creates plausible counterfactual graphs from a learned latent space using a partially ordered edge-generation strategy. It combines a Graph Autoencoder with a residual GAN to learn edge perturbations conditioned on the explainee class, enabling zero-shot generation without retraining for new graphs. Through training with a class-conditioned discriminator and a specialized loss, and via inference-time partial-order sampling, RSGG-CE achieves higher correctness and lower graph edit distance (GED) compared to state-of-the-art methods on both synthetic Tree-Cycles and real ASD datasets. The method demonstrates strong robustness to topology complexity and scales well with graph size and dataset size, offering a practical, efficient approach for generating concise, plausible counterfactuals in graph domains and enabling extensions to node classification.

Abstract

Counterfactual Explanation (CE) techniques have garnered attention as a means to provide insights to the users engaging with AI systems. While extensively researched in domains such as medical imaging and autonomous vehicles, Graph Counterfactual Explanation (GCE) methods have been comparatively under-explored. GCEs generate a new graph similar to the original one, with a different outcome grounded on the underlying predictive model. Among these GCE techniques, those rooted in generative mechanisms have received relatively limited investigation despite demonstrating impressive accomplishments in other domains, such as artistic styles and natural language modelling. The preference for generative explainers stems from their capacity to generate counterfactual instances during inference, leveraging autonomously acquired perturbations of the input graph. Motivated by the rationales above, our study introduces RSGG-CE, a novel Robust Stochastic Graph Generator for Counterfactual Explanations able to produce counterfactual examples from the learned latent space considering a partially ordered generation sequence. Furthermore, we undertake quantitative and qualitative analyses to compare RSGG-CE's performance against SoA generative explainers, highlighting its increased ability to engendering plausible counterfactual candidates.

Figures (11)

• Figure 1: RSGG-CE's workflow during training (up) and inference (down) in a cyclic graph vs tree scenario. $(X_j,A_j) \in \mathcal{G}_{\text{cyclic}}$ is fed to the generator, which produces counterfactual residuals. The discriminator is trained on both real $(X_r,A_r) \in \mathcal{G}_{\text{tree}}$ and generated graphs $(X_g,A_g)$. The generator optimisation is guided via $\Phi$'s classification. The generator explains input instances $(X_*,A_*)$ at inference time by sampling edges according to a learned stochastic distribution of its latent space. In this scenario, we highlight the critical edges forming a cycle the generator needs to break so that the returned counterfactual candidate does not contain cycles. The sampled edges entail a counterfactual candidate that $\Phi$ needs to validate.
• Figure 2: GED $\downarrow$ and Correctness $\uparrow$ trends when varying the number of nodes in each cycle on TreeCycles with 128 nodes and 4 cycles per instance.
• Figure 3: GED $\downarrow$ and Correctness $\uparrow$ trends when varying the number of cycles per instance on TreeCycles with 128 nodes and 3 nodes per cycle.
• Figure 4: The trend of GED $\downarrow$ normalised by the number $n$ of nodes instance, and the trend of Correctness $\uparrow$ when $n$ increases.
• Figure 5: The trend of GED $\downarrow$ and Correctness $\uparrow$ when varying the number of instances in the dataset.