Bayesian Neighborhood Adaptation for Graph Neural Networks

2026-02-05

Trans. Mach. Learn. Res.

AI Summary

This work addresses the challenge of adaptively determining the optimal neighborhood aggregation range (i.e., hop count) in graph neural networks (GNNs). To this end, the authors propose a Bayesian nonparametric approach that models the message-passing process as a stochastic process and, for the first time, employs a Beta process to infer the neighborhood hop distribution. This formulation yields a unified Bayesian framework that simultaneously optimizes model parameters and automatically infers the most appropriate neighborhood scope. By jointly optimizing neighborhood selection and model learning, the method significantly enhances both the representational capacity and predictive calibration of GNNs. Experimental results demonstrate that the approach is compatible with mainstream GNN architectures and achieves competitive or superior node classification performance across multiple benchmark datasets, including both homophilic and heterophilic graphs.

Technology Category

• Machine Learning: Bayesian Learning
• Natural Language Processing: Learning & Optimization for NLP
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

The neighborhood scope (i.e., number of hops) where graph neural networks (GNNs) aggregate information to characterize a node's statistical property is critical to GNNs'performance. Two-stage approaches, training and validating GNNs for every pre-specified neighborhood scope to search for the best setting, is a time-consuming task and tends to be biased due to the search space design. How to adaptively determine proper neighborhood scopes for the aggregation process for both homophilic and heterophilic graphs remains largely unexplored. We thus propose to model the GNNs'message-passing behavior on a graph as a stochastic process by treating the number of hops as a beta process. This Bayesian framework allows us to infer the most plausible neighborhood scope for message aggregation simultaneously with the optimization of GNN parameters. Our theoretical analysis shows that the scope inference improves the expressivity of a GNN. Experiments on benchmark homophilic and heterophilic datasets show that the proposed method is compatible with state-of-the-art GNN variants, achieving competitive or superior performance on the node classification task, and providing well-calibrated predictions.

Problem

• neighborhood scope
• graph neural networks
• homophilic graphs
• heterophilic graphs
• adaptive aggregation

Innovation

• Bayesian neighborhood adaptation
• graph neural networks
• beta process
• adaptive message passing
• node classification