Compact Graph Structure Learning via Mutual Information Compression

TL;DR

This paper introduces CoGSL, a graph structure learning method that uses mutual information compression to derive minimal sufficient graph structures, enhancing robustness and accuracy in GNNs.

Contribution

It provides a theoretical foundation for minimal sufficient graph structures via mutual information optimization and proposes a novel architecture, CoGSL, for effective graph structure learning.

Findings

CoGSL achieves superior robustness under attack conditions.

The method effectively compresses redundant information while maintaining performance.

Experimental results validate the theoretical claims and demonstrate improved accuracy.

Abstract

Graph Structure Learning (GSL) recently has attracted considerable attentions in its capacity of optimizing graph structure as well as learning suitable parameters of Graph Neural Networks (GNNs) simultaneously. Current GSL methods mainly learn an optimal graph structure (final view) from single or multiple information sources (basic views), however the theoretical guidance on what is the optimal graph structure is still unexplored. In essence, an optimal graph structure should only contain the information about tasks while compress redundant noise as much as possible, which is defined as "minimal sufficient structure", so as to maintain the accurancy and robustness. How to obtain such structure in a principled way? In this paper, we theoretically prove that if we optimize basic views and final view based on mutual information, and keep their performance on labels simultaneously, the final view will be a minimal sufficient structure. With this guidance, we propose a Compact GSL architecture by MI compression, named CoGSL. Specifically, two basic views are extracted from original graph as two inputs of the model, which are refinedly reestimated by a view estimator. Then, we propose an adaptive technique to fuse estimated views into the final view. Furthermore, we maintain the performance of estimated views and the final view and reduce the mutual information of every two views. To comprehensively evaluate the performance of CoGSL, we conduct extensive experiments on several datasets under clean and attacked conditions, which demonstrate the effectiveness and robustness of CoGSL.