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Uncovering latent structure in valued graphs: A variational approach

Mahendra Mariadassou, Stéphane Robin, Corinne Vacher

The Annals of Applied Statistics · 2010 · 219 citations · 44 references

Open access

TL;DR

Statistical analysis of valued graphs is increasingly common as network data grow, and latent structure detection is a key strategy, though existing methods mainly address binary graphs. The study proposes a model‑based strategy to uncover groups of nodes in valued graphs. The framework supports a broad class of parametric random graph models, incorporates covariates, and uses variational inference for approximate maximum‑likelihood estimation, demonstrated on host–parasite interaction networks. Simulation studies demonstrate that the estimation method performs well across a broad range of scenarios.

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.