  We propose {graphical sure screening}, or GRASS, a very simple and
computationally-efficient screening procedure for recovering the structure of a
Gaussian graphical model in the high-dimensional setting. The GRASS estimate of
the conditional dependence graph is obtained by thresholding the elements of
the sample covariance matrix. The proposed approach possesses the sure
screening property: with very high probability, the GRASS estimated edge set
contains the true edge set. Furthermore, with high probability, the size of the
estimated edge set is controlled. We provide a choice of threshold for GRASS
that can control the expected false positive rate. We illustrate the
performance of GRASS in a simulation study and on a gene expression data set,
and show that in practice it performs quite competitively with more complex and
computationally-demanding techniques for graph estimation.
