  We consider a graphical model where a multivariate normal vector is
associated with each node of the underlying graph and estimate the graphical
structure. We minimize a loss function obtained by regressing the vector at
each node on those at the remaining ones under a group penalty. We show that
the proposed estimator can be computed by a fast convex optimization algorithm.
We show that as the sample size increases, the estimated regression
coefficients and the correct graphical structure are correctly estimated with
probability tending to one. By extensive simulations, we show the superiority
of the proposed method over comparable procedures. We apply the technique on
two real datasets. The first one is to identify gene and protein networks
showing up in cancer cell lines, and the second one is to reveal the
connections among different industries in the US.
