Uncovering latent structure in valued graphs: A variational approach

TL;DR

This paper introduces a variational approach for uncovering latent structures in valued graphs, enabling analysis of complex network data with covariates and demonstrating effectiveness through simulations and ecological applications.

Contribution

It presents a novel model-based method using variational tools for latent group detection in valued graphs, adaptable to various parametric models and including covariates.

Findings

Method performs well across diverse scenarios

Effective in analyzing ecological host-parasite networks

Provides approximate maximum likelihood estimation

Abstract

As more and more network-structured data sets are available, the statistical analysis of valued graphs has become common place. Looking for a latent structure is one of the many strategies used to better understand the behavior of a network. Several methods already exist for the binary case. We present a model-based strategy to uncover groups of nodes in valued graphs. This framework can be used for a wide span of parametric random graphs models and allows to include covariates. Variational tools allow us to achieve approximate maximum likelihood estimation of the parameters of these models. We provide a simulation study showing that our estimation method performs well over a broad range of situations. We apply this method to analyze host--parasite interaction networks in forest ecosystems.