Iterative reconstruction of high-dimensional Gaussian Graphical Models based on a new method to estimate partial correlations under constraints.

In the context of Gaussian Graphical Models (GGMs) with
high-dimensional small sample data, we present a simple procedure,
called PACOSE - standing for PArtial COrrelation SElection - to
estimate partial correlations under the constraint that some of
them are strictly zero. This method can also be extended to
covariance selection. If the goal is to estimate a GGM, our new
procedure can be applied to re-estimate the partial correlations
after a first graph has been estimated in the hope to improve the
estimation of non-zero coefficients. This iterated version of
PACOSE is called iPACOSE. In a simulation study, we compare PACOSE
to existing methods and show that the re-estimated partial
correlation coefficients may be closer to the real values in
important cases. Plus, we show on simulated and real data that
iPACOSE shows very interesting properties with regards to
sensitivity, positive predictive value and stability.