Scalable Generative Modeling of Weighted Graphs
This work addresses the need for scalable generative models for weighted graphs in domains like biology and social sciences, representing an incremental improvement over existing methods.
The authors tackled the problem of generating weighted graphs, which are common in fields like biology and social sciences, by developing an autoregressive model called BiGG-E that learns a joint distribution over graph topology and edge weights, achieving scalability with generation time of O((n + m) log n) and outperforming benchmarks in capturing distributions.
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 either designed for unweighted graphs and are not easily extended to weighted topologies or incorporate edge weights without consideration of a joint distribution with topology. 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 still exploiting sparsity to generate a weighted graph with $n$ nodes and $m$ edges in $O((n + m)\log n)$ 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.