Rethinking and Extending the Probabilistic Inference Capacity of GNNs

Tuo Xu, Lei Zou

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Keywords: graph neural networks, expressiveness, approximate inference

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TL;DR: Discuss and extend GNNs' expressive power for probabilistic inference.

Abstract: Designing expressive Graph Neural Networks (GNNs) is an important topic in graph machine learning fields. Despite the existence of numerous approaches proposed to enhance GNNs based on Weisfeiler-Lehman (WL) tests, what GNNs can and cannot learn still lacks a deeper understanding. This paper adopts a fundamentally different approach to examine the expressive power of GNNs from a probabilistic perspective. By establishing connections between GNNs' predictions and the central inference problems of probabilistic graphical models (PGMs), we can analyze previous GNN variants with a novel hierarchical framework and gain new insights into their node-level and link-level behaviors. Additionally, we introduce novel methods that can provably enhance GNNs' ability to capture complex dependencies and make complex predictions. Experiments on both synthetic and real-world datasets demonstrate the effectiveness of our approaches.

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Primary Area: learning on graphs and other geometries & topologies

Submission Number: 9389