  We introduce the Poisson Log-Normal Graphical Model for count data, and
present a normality transformation for data arising from this distribution. The
model and transformation are feasible for high-throughput microRNA (miRNA)
sequencing data and directly account for known overdispersion relationships
present in this data set. The model allows for network dependencies to be
modeled, and we provide an algorithm which utilizes a one-step EM based result
in order to allow for a provable increase in performance in determining the
network structure. The model is shown to provide an increase in performance in
simulation settings over a range of network structures. The model is applied to
high-throughput miRNA sequencing data from patients with breast cancer from The
Cancer Genome Atlas (TCGA). By selecting the most highly connected miRNA
molecules in the fitted network we find that nearly all of them are known to be
involved in the regulation of breast cancer.
