Optimal Transport-Based Supervised Graph Summarization

Graph summarization is the problem of producing smaller graph representations of an input graph dataset, in such a way that the smaller ``compressed'' graphs capture relevant structural information for downstream tasks. One graph summarization method, recently proposed in Garg & Jaakkola (2019), formulates an optimal transport-based framework that allows prior information about node, edge, and attribute importance to be incorporated into the graph summarization process. We extend the optimal transport framework to a supervised graph summarization setting, wherein we seek to preserve relevant information about a class label. We first formulate the problem in terms of maximizing the mutual information between the summarized graph and the class label. We then propose a method that incorporates mutual information estimates between random variables associated with sample graphs and class labels into the optimal transport compression framework from Garg & Jaakkola (2019). We empirically show performance improvements over the previous work by Garg & Jaakkola (2019), in terms of classification and compression on synthetic and real datasets. We then theoretically show limitations of the optimal transport approach: e.g., that it fails to satisfy a certain desirable information monotonicity property.