Recovering Barab\'asi-Albert Parameters of Graphs through Disentanglement

TL;DR

This paper introduces a method to recover Barabási-Albert graph parameters by combining supervised learning with a GNN and Random Forest, and a variational autoencoder with an LSTM decoder, improving parameter inference for sequential graph models.

Contribution

It proposes a novel approach that replaces the decoder in a $eta$-VAE with an LSTM to better recover BA model parameters, integrating supervised learning and deep generative models.

Findings

Successfully recovers BA parameters using the combined GNN and VAE approach.

Improves parameter estimation accuracy for sequential graph models.

Demonstrates the effectiveness of the LSTM decoder in capturing BA graph properties.

Abstract

Classical graph modeling approaches such as Erd\H{o}s R\'{e}nyi (ER) random graphs or Barab\'asi-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 $\beta$-Variational Autoencoder ($\beta$-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 $\beta$-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 Forest Regressor, by minimizing the squared loss between the true generative parameters and the latent variables. Next, we train a $\beta$-VAE model, combining the GNN encoder from the first stage with an LSTM-based decoder with a customized loss.