Growing Better Graphs With Latent-Variable Probabilistic Graph Grammars

TL;DR

This paper introduces latent-variable probabilistic graph grammars that, when trained with EM, generate graphs with properties closer to real-world networks and outperform existing models in generalization.

Contribution

It extends hyperedge replacement grammars with latent variables and demonstrates improved graph generation and generalization capabilities.

Findings

Latent-variable HRGs outperform existing models in likelihood on test graphs.

The method provides insights into the structure of real-world networks.

Latent variables improve the quality and generalization of generated graphs.

Abstract

Recent work in graph models has found that probabilistic hyperedge replacement grammars (HRGs) can be extracted from graphs and used to generate new random graphs with graph properties and substructures close to the original. In this paper, we show how to add latent variables to the model, trained using Expectation-Maximization, to generate still better graphs, that is, ones that generalize better to the test data. We evaluate the new method by separating training and test graphs, building the model on the former and measuring the likelihood of the latter, as a more stringent test of how well the model can generalize to new graphs. On this metric, we find that our latent-variable HRGs consistently outperform several existing graph models and provide interesting insights into the building blocks of real world networks.