# A Robust Procedure For Gaussian Graphical Model Search From Microarray Data With p Larger Than n

Robert Castelo, Alberto Roverato.

Year: 2006, Volume: 7, Issue: 94, Pages: 2621−2650

#### Abstract

Learning of large-scale networks of interactions from microarray
data is an important and challenging problem in bioinformatics. A
widely used approach is to assume that the available data constitute
a random sample from a multivariate distribution belonging to a
Gaussian graphical model. As a consequence, the prime objects of
inference are *full-order partial correlations* which are
partial correlations between two variables given the remaining ones.
In the context of microarray data the number of variables exceed the
sample size and this precludes the application of traditional
structure learning procedures because a sampling version of
full-order partial correlations does not exist. In this paper we
consider *limited-order partial correlations*, these are
partial correlations computed on marginal distributions of
manageable size, and provide a set of rules that allow one to assess
the usefulness of these quantities to derive the independence
structure of the underlying Gaussian graphical model. Furthermore,
we introduce a novel structure learning procedure based on a
quantity, obtained from limited-order partial correlations, that we
call the *non-rejection rate*. The applicability and usefulness of
the procedure are demonstrated by both simulated and real data.