  We study the problem of estimating from data, a sparse approximation to the
inverse covariance matrix. Estimating a sparsity constrained inverse covariance
matrix is a key component in Gaussian graphical model learning, but one that is
numerically very challenging. We address this challenge by developing a new
adaptive gradient-based method that carefully combines gradient information
with an adaptive step-scaling strategy, which results in a scalable, highly
competitive method. Our algorithm, like its predecessors, maximizes an
$\ell_1$-norm penalized log-likelihood and has the same per iteration
arithmetic complexity as the best methods in its class. Our experiments reveal
that our approach outperforms state-of-the-art competitors, often significantly
so, for large problems.
