Global Graph Counterfactual Explanation: A Subgraph Mapping Approach

TL;DR

The proposed GlobalGCE aims to identify a collection of subgraph mapping rules as counterfactual explanations for the target GNN, and designs a significant subgraph generator and a counterfactual subgraph autoencoder in the GlobalGCE, where the subgraphs and the rules can be effectively generated.

Abstract

Graph Neural Networks (GNNs) have been widely deployed in various real-world applications. However, most GNNs are black-box models that lack explanations. One strategy to explain GNNs is through counterfactual explanation, which aims to find minimum perturbations on input graphs that change the GNN predictions. Existing works on GNN counterfactual explanations primarily concentrate on the local-level perspective (i.e., generating counterfactuals for each individual graph), which suffers from information overload and lacks insights into the broader cross-graph relationships. To address such issues, we propose GlobalGCE, a novel global-level graph counterfactual explanation method. GlobalGCE aims to identify a collection of subgraph mapping rules as counterfactual explanations for the target GNN. According to these rules, substituting certain significant subgraphs with their counterfactual subgraphs will change the GNN prediction to the desired class for most graphs (i.e., maximum coverage). Methodologically, we design a significant subgraph generator and a counterfactual subgraph autoencoder in our GlobalGCE, where the subgraphs and the rules can be effectively generated. Extensive experiments demonstrate the superiority of our GlobalGCE compared to existing baselines. Our code can be found at https://anonymous.4open.science/r/GlobalGCE-92E8.

Figures (8)

• Figure 1: An illustration of GFE and GCE. (a) GFE. The graph is classified in the desired class because it contains a house motif, highlighted in blue. (b) GCE. Initially, the graph does not have a house motif and is classified as undesired. To minimally perturb the graph into the desired class, an edge (in yellow) is added, creating a house motif. The modified graph with the added edge is the counterfactual of the original graph.
• Figure 2: Comparison of global GCE provided by GCFExplainer huang2023global and our GlobalGCE. (a) displays ground-truth local GCEs for input graphs. In (b), the upper right shows GCFExplainer's output - a subset of counterfactuals (in this case, only one), while the lower right depicts a subgraph mapping rule as the global GCE generated by our approach. The global counterfactual rule involves changing subgraphs from the left box area to the right. This rule is not observable from the GCFExplainer output but is evident in our approach that generates subgraph mapping.
• Figure 3: Illustration of the usefulness of the proposed "comprehensibility" metric. (a) shows that original input graph. (b) and (c) are two of its valid counterfactuals, they have the same proximity of 0.25, but different comprehensibility 1 and 5 respectively. (b) is apparantly more human-comprehensive, which we can interpret as "removing house motif may alther the GNN prediction label for a graph." However, the graph edits for (c) is too scatter that human cannot conclude any GCE rule from the comparision of original input graph (a) and its counterfactual (c).
• Figure 4: A overview of our GlobalGCE framework. Initially, we identify significant subgraphs from $\mathcal{G}$ based on their diversity and frequency. Then, with a counterfactual subgraph autoencoder, we generate CSMs allowing all types of graph editions. In the final step, the model selects the most representative CSMs according to their coverage.
• Figure 5: Effectiveness of the GlobalGCE's two components (shadowed bars represent the original GlobalGCE framework). Here, ENZY. means ENZYMES, and PROT. means PROTEINS. We conduct experiments for GlobalGCE-NA and GlobalGCE-NS with counterfactual rules budget $k=30$, $k=10$, and $k=20$ for each dataset respectively. (a) presents the coverage comparison of GlobalGCE and GlobalGCE-NA; (b) presents the coverage comparison of GlobalGCE and GlobelGCE-NS.

Theorems & Definitions (3)

• Definition 1
• proof
• proof