In many biological and ecological case studies, the empirical covariance matrix of the variables of interest
displays large blocks of uniform correlation. This suggests the existence of one or several unobserved (missing)
variables having a simultaneous influence on a series of observed ones, and that we observe a sample drawn
from a distribution where the unobserved variables have been marginalized out. The inference of underlying networks
is compromised in this context because marginalizing variables yields locally dense structures that challenge the
generally accepted assumption that biological networks are sparse. We present a procedure for inferring Gaussian
graphical models from an independent sample in the presence of unobserved variables. Our model is based on spanning trees
and the EM algorithm and accounts both for the influence of unobserved variables and the low density of the network.
We treat the graph structure and the unobserved nodes as latent variables and compute posterior probabilities of edge
appearance. We also compare our method to existing graph inference techniques on synthetic and flow cytometry data.