A Model-Agnostic Graph Neural Network for Integrating Local and Global Information

Area of Science:

• Graph Neural Networks
• Machine Learning
• Network Analysis

Background:

• Existing Graph Neural Networks (GNNs) lack interpretability and struggle with learning multi-order representations.
• The black-box nature of current GNNs limits understanding of their results.
• There is a need for GNN frameworks that can provide interpretable insights and handle complex graph structures.

Purpose of the Study:

• To propose a novel Model-agnostic Graph Neural Network (MaGNet) framework.
• To address the limitations of interpretability and multi-order representation learning in GNNs.
• To extract knowledge from high-order neighbors and identify influential graph structures.

Main Methods:

• Developed a two-component MaGNet framework: an estimation model for latent representations and an interpretation model for influential structures.
• Established a generalization error bound for MaGNet using empirical Rademacher complexity.
• Demonstrated the framework's ability to represent layer-wise neighborhood mixing.

Main Results:

• MaGNet effectively integrates information of various orders and extracts knowledge from high-order neighbors.
• The framework provides meaningful and interpretable results by identifying influential compact graph structures.
• Comprehensive numerical studies on simulated data showed superior performance compared to state-of-the-art alternatives.

Conclusions:

• MaGNet offers a significant advancement in GNN interpretability and multi-order representation learning.
• The framework's effectiveness is validated through theoretical analysis and empirical studies.
• MaGNet shows promise for real-world applications, such as analyzing brain activity data for scientific discovery.