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COMBINEX: A Unified Counterfactual Explainer for Graph Neural Networks via Node Feature and Structural Perturbations

Flavio Giorgi, Fabrizio Silvestri, Gabriele Tolomei

TL;DR

COMBINEX introduces a unified counterfactual explainer for Graph Neural Networks that jointly optimizes node feature and graph-structure perturbations to flip predictions with minimal changes. By using differentiable perturbation matrices and a tunable trade-off parameter α, the method balances topology and feature modifications and supports both discrete and continuous features. Empirical results across node and graph classification tasks demonstrate strong validity, competitive fidelity, and sparsity, outperforming several baselines while offering improved scalability via an edge-weight sparsification technique. The approach is versatile across multiple GNN architectures and datasets, with flexible α-scheduling policies enabling adaptation to dataset characteristics. This work advances explainability for graphs by providing realistic, actionable counterfactuals that maintain proximity to the data distribution and model decision boundaries.

Abstract

Counterfactual explanations have emerged as a powerful tool to unveil the opaque decision-making processes of graph neural networks (GNNs). However, existing techniques primarily focus on edge modifications, often overlooking the crucial role of node feature perturbations in shaping model predictions. To address this limitation, we propose COMBINEX, a novel GNN explainer that generates counterfactual explanations for both node and graph classification tasks. Unlike prior methods, which treat structural and feature-based changes independently, COMBINEX optimally balances modifications to edges and node features by jointly optimizing these perturbations. This unified approach ensures minimal yet effective changes required to flip a model's prediction, resulting in realistic and interpretable counterfactuals. Additionally, COMBINEX seamlessly handles both continuous and discrete node features, enhancing its versatility across diverse datasets and GNN architectures. Extensive experiments on real-world datasets and various GNN architectures demonstrate the effectiveness and robustness of our approach over existing baselines.

COMBINEX: A Unified Counterfactual Explainer for Graph Neural Networks via Node Feature and Structural Perturbations

TL;DR

COMBINEX introduces a unified counterfactual explainer for Graph Neural Networks that jointly optimizes node feature and graph-structure perturbations to flip predictions with minimal changes. By using differentiable perturbation matrices and a tunable trade-off parameter α, the method balances topology and feature modifications and supports both discrete and continuous features. Empirical results across node and graph classification tasks demonstrate strong validity, competitive fidelity, and sparsity, outperforming several baselines while offering improved scalability via an edge-weight sparsification technique. The approach is versatile across multiple GNN architectures and datasets, with flexible α-scheduling policies enabling adaptation to dataset characteristics. This work advances explainability for graphs by providing realistic, actionable counterfactuals that maintain proximity to the data distribution and model decision boundaries.

Abstract

Counterfactual explanations have emerged as a powerful tool to unveil the opaque decision-making processes of graph neural networks (GNNs). However, existing techniques primarily focus on edge modifications, often overlooking the crucial role of node feature perturbations in shaping model predictions. To address this limitation, we propose COMBINEX, a novel GNN explainer that generates counterfactual explanations for both node and graph classification tasks. Unlike prior methods, which treat structural and feature-based changes independently, COMBINEX optimally balances modifications to edges and node features by jointly optimizing these perturbations. This unified approach ensures minimal yet effective changes required to flip a model's prediction, resulting in realistic and interpretable counterfactuals. Additionally, COMBINEX seamlessly handles both continuous and discrete node features, enhancing its versatility across diverse datasets and GNN architectures. Extensive experiments on real-world datasets and various GNN architectures demonstrate the effectiveness and robustness of our approach over existing baselines.

Paper Structure

This paper contains 31 sections, 3 theorems, 4 equations, 1 figure, 22 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background
  4. Proposed Method
  5. Problem Formulation
  6. The COMBINEX Algorithm
  7. Computational Complexity Analysis
  8. Experiments
  9. Results
  10. The Impact of the Scheduling Policy $\alpha$
  11. Feasibility of our Method
  12. Conclusion and Future Work
  13. Appendix
  14. Edge Nullification Theorem for ChebConv
  15. Edge Nullification Theorem for GraphConv
  16. ...and 16 more sections

Key Result

Theorem 6.1

[Equivalence of Edge Weight Nullification and Adjacency Matrix Edge Removal in GCNs] Let $G = (V, E)$ be a graph with $n$ nodes and $m$ edges. Let $\mathbf{X} \in \mathbb{R}^{n \times d}$ be the node feature matrix, where each node has a feature vector of dimension $d$. Consider a GCNConv layer para

Figures (1)

  • Figure 1: Comparison of two approaches for generating counterfactual explanations in Graph Neural Networks (GNNs): CF-GNNExplainer vs. COMBINEX. CF-GNNExplainer (top) modifies the graph structure by perturbing the adjacency matrix through edge removal. COMBINEX (bottom) takes a unified approach, balancing both node feature and structural perturbations to find optimal counterfactual explanations.

Theorems & Definitions (3)

  • Theorem 6.1
  • Theorem A.1
  • Theorem A.2