Compact Graph Structure Learning via Mutual Information Compression
This provides a principled theoretical foundation for graph structure learning, addressing a key bottleneck in graph neural networks for applications like social network analysis and recommendation systems.
The paper tackles the problem of determining the optimal graph structure for Graph Neural Networks by theoretically proving that minimizing mutual information between views while maintaining label performance yields a minimal sufficient structure, and proposes CoGSL which achieves state-of-the-art results with up to 3.2% accuracy improvement on attacked datasets.
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.