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The estimation of high dimensional precision matrices has been a centraltopic in statistical learning. However, as the number of parameters scalesquadratically with the dimension $p$, many state-of-the-art methods do notscale well to solve problems with a very large $p$. In this paper, we propose avery efficient algorithm for precision matrix estimation via penalizedquadratic loss functions. Under the high dimension low sample size setting, thecomputation complexity of our algorithm is linear in both the sample size andthe number of parameters. Such a computation complexity is in some senseoptimal, as it is the same as the complexity needed for computing the samplecovariance matrix. Numerical studies show that our algorithm is much moreefficient than other state-of-the-art methods when the dimension $p$ is verylarge.

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