COMRECGC: Global Graph Counterfactual Explainer through Common Recourse

TL;DR

This work addresses explainability for graph neural networks by formalizing the problem of global counterfactual explanations through common recourse. It introduces ComRecGC, a method that combines graph embeddings, a multi-head vertex reinforced random walk, and clustering to identify a compact set of recourses that can turn any 'reject' graph into an 'accept' graph, maximizing coverage with a limited recourse budget. The authors prove FCR is $NP$-hard and provide approximation guarantees under certain conditions, and show FC is more challenging, motivating the proposed heuristic approach. Empirically, ComRecGC achieves higher coverage and competitive cost across four real-world datasets and offers explanations that are comparable or superior to global counterfactual explanations, highlighting its practical potential for domains such as drug discovery and computational biology.

Abstract

Graph neural networks (GNNs) have been widely used in various domains such as social networks, molecular biology, or recommendation systems. Concurrently, different explanations methods of GNNs have arisen to complement its black-box nature. Explanations of the GNNs' predictions can be categorized into two types--factual and counterfactual. Given a GNN trained on binary classification into ''accept'' and ''reject'' classes, a global counterfactual explanation consists in generating a small set of ''accept'' graphs relevant to all of the input ''reject'' graphs. The transformation of a ''reject'' graph into an ''accept'' graph is called a recourse. A common recourse explanation is a small set of recourse, from which every ''reject'' graph can be turned into an ''accept'' graph. Although local counterfactual explanations have been studied extensively, the problem of finding common recourse for global counterfactual explanation remains unexplored, particularly for GNNs. In this paper, we formalize the common recourse explanation problem, and design an effective algorithm, COMRECGC, to solve it. We benchmark our algorithm against strong baselines on four different real-world graphs datasets and demonstrate the superior performance of COMRECGC against the competitors. We also compare the common recourse explanations to the graph counterfactual explanation, showing that common recourse explanations are either comparable or superior, making them worth considering for applications such as drug discovery or computational biology.

Figures (4)

• Figure 1: Common Recourse on Mutagenicity: Removing an NO$_2$ complex. On the left two mutagenetic molecules from the input, on the right two resulting non-mutagenetic molecules.
• Figure 2: Common Recourse coverage and cost comparison between ComRecGC and baselines for the FC problem where $\Delta = 0.02, T = |\mathbb{G}|$ and $R=1$ to $100$ common recourse.
• Figure 3: Common Recourse on the Mutagenicity dataset: removing two Hydrogen and one Carbon, on the left two mutagenetic input graphs, on the right two non-mutagenetic graphs.
• Figure 4: Common Recourse on the Mutagenicity dataset: removing one Nitrogen, one Hydrogen, adding one Oxygen and one Carbon, on the left two mutagenetic input graphs, on the right two non-mutagenetic graphs.

Theorems & Definitions (7)

• Theorem 1
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