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Title: An efficient ADMM algorithm for high dimensional precision matrix estimation via penalized quadratic loss
Authors: Wang, C
Jiang, B 
Issue Date: Feb-2020
Source: Computational statistics and data analysis, Feb. 2020, v. 142, 106812
Abstract: 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 both the sample size and the number of parameters. Such a computation complexity is in some sense optimal, as it is the same as the complexity needed for computing the sample covariance matrix. Numerical studies show that our algorithm is much more efficient than other state-of-the-art methods when the dimension p is very large.
Keywords: ADMM
High dimension
Penalized quadratic loss
Precision matrix
Publisher: Elsevier
Journal: Computational statistics and data analysis 
EISSN: 0167-9473
DOI: 10.1016/j.csda.2019.106812
Rights: © 2019 Elsevier B.V. All rights reserved.
© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
The following publication Wang, C., & Jiang, B. (2020). An efficient ADMM algorithm for high dimensional precision matrix estimation via penalized quadratic loss. Computational Statistics & Data Analysis, 142, 106812 is available at https://doi.org/10.1016/j.csda.2019.106812
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