GRAM: Scalable Generative Models for Graphs with Graph Attention Mechanism
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Graphs are ubiquitous real-world data structures, and generative models that can approximate distributions over graphs and derive samples from it have significant importance. There are several known challenges in graph generation tasks, and scalability handling large graphs and datasets is one of the most important for applications in a wide range of real-world domains. Although an increasing number of graph generative models have been proposed in the field of machine learning that have demonstrated impressive results in several tasks, scalability is still an unresolved problem owing to the complex generation process or difficulty in training parallelization. In this work, we first define scalability from three different perspectives: number of nodes, data, and node/edge labels, and then we propose GRAM, a generative model for real-world graphs that is scalable in all the three contexts, especially on training. We aim to achieve scalability by employing a novel graph attention mechanism, formulating the likelihood of graphs in a simple and general manner and utilizing the properties of real-world graphs such as community structure and sparseness of edges. Furthermore, we construct a non-domain-specific evaluation metric in node/edge-labeled graph generation tasks that combine a graph kernel and Maximum Mean Discrepancy. Our experiments on real-world graph datasets showed that our models can scale up to large graphs and datasets that baseline models had difficulty handling, and demonstrated results that were competitive with or superior than the baseline methods.
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