  We present a technique to characterize differentially expressed genes in
terms of their position in a high-dimensional co-expression network. The set-up
of Gaussian graphical models is used to construct representations of the
co-expression network in such a way that redundancy and the propagation of
spurious information along the network are avoided. The proposed inference
procedure is based on the minimization of the Bayesian Information Criterion
(BIC) in the class of decomposable graphical models. This class of models can
be used to represent complex relationships and has suitable properties that
allow to make effective inference in problems with high degree of complexity
(e.g. several thousands of genes) and small number of observations (e.g.
10-100) as typically occurs in high throughput gene expression studies. Taking
advantage of the internal structure of decomposable graphical models, we
construct a compact representation of the co-expression network that allows to
identify the regions with high concentration of differentially expressed genes.
It is argued that differentially expressed genes located in highly
interconnected regions of the co-expression network are less informative than
differentially expressed genes located in less interconnected regions. Based on
that idea, a measure of uncertainty that resembles the notion of relative
entropy is proposed. Our methods are illustrated with three publically
available data sets on microarray experiments (the larger involving more than
50,000 genes and 64 patients) and a short simulation study.
