Precision Matrix Estimation in High Dimensional Gaussian Graphical Models with Faster Rates

We present a new estimator for precision matrix in high dimensional Gaussian graphical models. At the core of the proposed estimator is a collection of node-wise linear regression with nonconvex penalty. In contrast to existing estimators for Gaussian graphical models with O(s √ log d/n) estimation error bound in terms of spectral norm, where s is the maximum degree of a graph, the proposed estimator could attain O(s/ √ n+ √ log d/n) spectral norm based convergence rate in the best case, and it is no worse than exiting estimators in general. In addition, our proposed estimator enjoys the oracle property under a milder condition than existing estimators. We show through extensive experiments on both synthetic and real datasets that our estimator outperforms the state-of-the-art estimators.