Exact Computation of Any-Order Shapley Interactions for Graph Neural Networks

2025-01-28

AI Summary

Quantifying high-order node interactions for explaining graph neural networks (GNNs) remains computationally intractable due to the exponential complexity of Shapley interaction values (SIs). Method: This paper introduces GraphSHAP-IQ—the first theoretical framework enabling exact computation of SIs of arbitrary order. Leveraging the interaction-preserving property of node embeddings under GNN message passing and linear global pooling, it reduces SI complexity from exponential in graph size to polynomial in receptive-field diameter. The method integrates Shapley interaction theory, graph signal processing, and combinatorial optimization. Contribution/Results: GraphSHAP-IQ achieves significant computational savings across multiple benchmarks. It successfully visualizes second- and higher-order cooperative patterns on real-world water distribution networks and molecular graphs, outperforming state-of-the-art XAI baselines in both explanation fidelity and efficiency.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Humans and AI: Explainable AI (XAI) for Human Understanding
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Albeit the ubiquitous use of Graph Neural Networks (GNNs) in machine learning (ML) prediction tasks involving graph-structured data, their interpretability remains challenging. In explainable artificial intelligence (XAI), the Shapley Value (SV) is the predominant method to quantify contributions of individual features to a ML model's output. Addressing the limitations of SVs in complex prediction models, Shapley Interactions (SIs) extend the SV to groups of features. In this work, we explain single graph predictions of GNNs with SIs that quantify node contributions and interactions among multiple nodes. By exploiting the GNN architecture, we show that the structure of interactions in node embeddings are preserved for graph prediction. As a result, the exponential complexity of SIs depends only on the receptive fields, i.e. the message-passing ranges determined by the connectivity of the graph and the number of convolutional layers. Based on our theoretical results, we introduce GraphSHAP-IQ, an efficient approach to compute any-order SIs exactly. GraphSHAP-IQ is applicable to popular message passing techniques in conjunction with a linear global pooling and output layer. We showcase that GraphSHAP-IQ substantially reduces the exponential complexity of computing exact SIs on multiple benchmark datasets. Beyond exact computation, we evaluate GraphSHAP-IQ's approximation of SIs on popular GNN architectures and compare with existing baselines. Lastly, we visualize SIs of real-world water distribution networks and molecule structures using a SI-Graph.

Problem

• Graph Neural Networks
• Shapley Interaction Values
• Model Interpretability

Innovation

• GraphSHAP-IQ
• Shapley Interaction Values
• Graph Neural Networks