• 论文 •

1. 首都师范大学数学科学学院,北京  100048
• 出版日期:2021-02-25 发布日期:2021-04-19

WANG Guanpeng, TIAN Wan,HU Tao. ADMM Algorithmic Regularization Paths for High-Dimensional\\ Sparse Precision Matrix Estimation[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(2): 557-565.

ADMM Algorithmic Regularization Paths for High-Dimensional\\ Sparse Precision Matrix Estimation

WANG Guanpeng, TIAN Wan ,HU Tao

1. School of Mathematics Science, Capital Normal University, Beijing 100048
• Online:2021-02-25 Published:2021-04-19

This paper considers high-dimensional sparse precision matrix in which the number of predictors $p$ exceeds the sample size $n$. High-dimensional sparse precision matrix estimation has become more and more popular in the recently years, but we focus on computing regularization paths, or solving the optimization problem over the full range of regularization parameters. We first benefit from a precision matrix estimator which is defined as the minimizer of the Lasso under a positive-definiteness constraint. Then we aim to use the alternating direction method of multipliers (ADMM) algorithmic regularization path for sparse precision matrix to quickly approximate the sequence of sparse models associated with regularization paths for the purposes of statistical model selection. Numerical results show that our method can quickly outline the sequence of sparse models, and this approach not only overcomes the computing time issue, but also easies implementation and explores the model space at a fine resolution.

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