Scalable Generative Modeling of Weighted Graphs

Weighted graphs are ubiquitous throughout biology, chemistry, and the social sciences, motivating the development of generative models for abstract weighted graph data using deep neural networks. However, most current deep generative models are designed for unweighted graphs and cannot be easily extended to weighted topologies. Among those that do incorporate edge weights, few consider a joint distribution with the topology of the graph. Furthermore, learning a distribution over weighted graphs must account for complex nonlocal dependencies between both the edges of the graph and corresponding weights of each edge. We develop an autoregressive model BiGG-E, a nontrivial extension of the BiGG model, that learns a joint distribution over weighted graphs while exploiting sparsity to generate a weighted graph with $n$ nodes and $m$ edges in $O\left(\right(n+m\left)logn\right)$ time. Simulation studies and experiments on a variety of benchmark datasets demonstrate that BiGG-E best captures distributions over weighted graphs while remaining scalable and computationally efficient.