The Annals of Applied Statistics

Uncovering latent structure in valued graphs: A variational approach

Mahendra Mariadassou, Stéphane Robin, and Corinne Vacher

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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.

Article information

Ann. Appl. Stat. Volume 4, Number 2 (2010), 715-742.

First available in Project Euclid: 3 August 2010

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Ecological networks host–parasite interactions latent structure mixture model random graph valued graph variational method


Mariadassou, Mahendra; Robin, Stéphane; Vacher, Corinne. Uncovering latent structure in valued graphs: A variational approach. Ann. Appl. Stat. 4 (2010), no. 2, 715--742. doi:10.1214/10-AOAS361.

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Supplemental materials

  • Supplementary material: Interaction network between tree and fungal species. This file contains: •The adjacency matrix of interactions between tree and fungal species. •The list of the tree species. •The list of the fungal species. •The matrix of genetic distances between tree species. •The matrix of geographical distances between tree species. •The matrix of taxonomic distances between fungal species. •The matrix of nutritional type of the fungal species.