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

TL;DR

This paper introduces GraphSHAP-IQ, an efficient method for exact computation of Shapley Interactions in GNNs, enabling better interpretability of node contributions and interactions with reduced complexity.

Contribution

The paper presents GraphSHAP-IQ, a novel approach that computes any-order Shapley Interactions exactly in GNNs, leveraging graph structure to reduce computational complexity.

Findings

GraphSHAP-IQ significantly reduces complexity of SI computation.

Exact SIs can be efficiently computed for GNNs with message passing.

Visualization of SIs on real-world networks demonstrates interpretability.

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.