TITLE:
Positive-Definite Sparse Precision Matrix Estimation
AUTHORS:
Lin Xia, Xudong Huang, Guanpeng Wang, Tao Wu
KEYWORDS:
Positive-Definiteness, Sparsity, D-Trace Loss, Accelerated Gradient Method
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.7 No.1,
January
23,
2017
ABSTRACT: The positive-definiteness and sparsity are the most important property of high-dimensional precision matrices. To better achieve those property, this paper uses a sparse lasso penalized D-trace loss under the positive-definiteness constraint to estimate high-dimensional precision matrices. This paper derives an efficient accelerated gradient method to solve the challenging optimization problem and establish its converges rate as . The numerical simulations illustrated our method have competitive advantage than other methods.