  We focus on the problem of estimating the change in the dependency structures
of two $p$-dimensional Gaussian Graphical models (GGMs). Previous studies for
sparse change estimation in GGMs involve expensive and difficult non-smooth
optimization. We propose a novel method, DIFFEE for estimating DIFFerential
networks via an Elementary Estimator under a high-dimensional situation. DIFFEE
is solved through a faster and closed form solution that enables it to work in
large-scale settings. We conduct a rigorous statistical analysis showing that
surprisingly DIFFEE achieves the same asymptotic convergence rates as the
state-of-the-art estimators that are much more difficult to compute. Our
experimental results on multiple synthetic datasets and one real-world data
about brain connectivity show strong performance improvements over baselines,
as well as significant computational benefits.
