Incomplete graphical model inference via latent tree aggregation

Abstract

Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical cases, not all variables involved in the network have been observed, and the samples are actually drawn from a distribution where some variables have been marginalized out. This challenges the sparsity assumption commonly made in graphical model inference, since marginalization yields locally dense structures, even when the original network is sparse. We present a procedure for inferring Gaussian graphical models when some variables are unobserved, that accounts both for the influence of missing variables and the low density of the original network. Our model is based on the aggregation of spanning trees, and the estimation procedure on the Expectation-Maximization algorithm. We treat the graph structure and the unobserved nodes as missing variables and compute posterior probabilities of edge appearance. To provide a complete methodology, we also propose several model selection criteria to estimate the number of missing nodes. A simulation study and an illustration flow cytometry data reveal that our method has favorable edge detection properties compared to existing graph inference techniques. The methods are implemented in an R package.

Tree‐based inference of species interaction networks from abundance data

“…Another extension may therefore be to detect ignored covariates or missing species. To this purpose EMtree could probably be combined with the approach developed by Robin, Ambroise, and Robin (2019) to identify missing actors.…”

“…Another extension may therefore be to detect ignored covariates or missing species. To this purpose EMtree could probably be combined with the approach developed by Robin et al (2018) to identify missing actors. Lastly, networks comparison is a wide and interesting question and tools lack to check which edges are shared by a set of networks.…”

Accounting for Missing Actors in Interaction Network Inference from Abundance Data

“…Our main goal is to infer the dependency structure of the complete latent vectors, that is to estimate the elements of the matrices T and the edges weights β. The latent dependency structure is similar to this considered by Robin et al (2019), but the inference strategy much differs, because of the additional hidden layer.…”

Accounting for missing actors in interaction network inference from abundance data

“…Missing actors could obviously not be identified from a regular PLN model, without restriction on the precision matrix Ω, as only the marginal precision matrix of the U Oi could be recovered. Still, to ensure identifiability we impose the same restriction as Robin et al (2019) that missing latent variables are not connected with each other (the block corresponding to U H × U H is diagonal in each Ω T ).…”

“…Our main goal is to infer the dependency structure of the complete latent vectors, that is to estimate the elements of the matrices Ω T and the edges weights β. The latent dependency structure is similar to this considered by Robin et al (2019), but the inference strategy much differs, because of the additional hidden layer.…”