Recovering Barabási-Albert Parameters of Graphs through Disentanglement
This work addresses a specific bottleneck in graph modeling for researchers and practitioners, offering an incremental improvement over prior methods for BA graphs.
The paper tackles the problem of recovering generative parameters of Barabási-Albert (BA) graphs, which previous methods failed on due to an oversimplified decoder, by replacing it with a sequential LSTM-based decoder and using a supervised learning approach with a GNN encoder and Random Forest Regressor, achieving improved parameter recovery as indicated by minimizing squared loss.
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 Forest Regressor, 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.