  Large-scale precision matrix estimation is of fundamental importance yet
challenging in many contemporary applications for recovering Gaussian graphical
models. In this paper, we suggest a new approach of innovated scalable
efficient estimation (ISEE) for estimating large precision matrix. Motivated by
the innovated transformation, we convert the original problem into that of
large covariance matrix estimation. The suggested method combines the strengths
of recent advances in high-dimensional sparse modeling and large covariance
matrix estimation. Compared to existing approaches, our method is scalable and
can deal with much larger precision matrices with simple tuning. Under mild
regularity conditions, we establish that this procedure can recover the
underlying graphical structure with significant probability and provide
efficient estimation of link strengths. Both computational and theoretical
advantages of the procedure are evidenced through simulation and real data
examples.
