An efficient ADMM algorithm for high dimensional precision matrix estimation via penalized quadratic loss

The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension $p$, many state-of-the-art methods do not scale well to solve problems with a very large $p$. In this paper, we propose a very efficient algorithm for precision matrix estimation via penalized quadratic loss functions. Under the high dimension low sample size setting, the computation complexity of our algorithm is linear in the sample size and the number of parameters, which is the same as computing the sample covariance matrix.