Recovering Barabási-Albert Parameters of Graphs through Disentanglement

Cristina Guzmán, Daphna Keidar, Tristan Meynier, Andreas Opedal, Niklas Stoehr

Keywords: disentanglement, disentangled graph representations, graph neural networks, graph generation, Barabási-Albert

TL;DR: Recovering the generative parameters of the Barabási-Albert sequential graph generator model with beta-VAEs and graph neural networks.

Abstract: Classical graph modeling approaches such as Erdős-Rényi (ER) random graphs or Barabási-Albert (BA) graphs, here referred to as stylized models, aim to reproduce properties of real-world graphs in an interpretable way. While useful, graph generation with stylized models requires domain knowledge and iterative trial and error simulation. Previous work by Stoehr et al. (2019) addresses these issues by learning the generation process from graph data, using a disentanglement-focused deep autoencoding framework, more specifically, a β-Variational Autoencoder (β-VAE). While they successfully recover the generative parameters of ER graphs through the model’s latent variables, their model performs badly on sequentially generated graphs such as BA graphs, due to their oversimplified decoder. We focus on recovering the generative parameters of BA graphs by replacing their β-VAE decoder with a sequential one. We first learn the generative BA parameters in a supervised fashion using a Graph Neural Network (GNN) and a Random ForestRegressor, by minimizing the squared loss between the true generative parameters and the latent variables. Next, we train a β-VAE model, combining the GNN encoder from the first stage with an LSTM-based decoder with a customized loss.