Scalable Generative Modeling of Weighted Graphs

TL;DR

This paper introduces BiGG-E, a scalable autoregressive deep learning model that effectively captures the joint distribution of weighted graphs, outperforming existing models in efficiency and accuracy.

Contribution

The paper presents BiGG-E, a novel autoregressive model for weighted graphs that efficiently learns joint distributions while leveraging sparsity for scalability.

Findings

BiGG-E accurately models weighted graph distributions.

BiGG-E is computationally efficient, scaling to large graphs.

Experimental results outperform existing models on benchmarks.

Abstract

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.