Sparse Estimation of High-Dimensional Inverse Covariance Matrices with Explicit Eigenvalue Constraints

Firstly, this paper proposes a generalized log-determinant optimization model with the purpose of estimating the high-dimensional sparse inverse covariance matrices. Under the normality assumption, the zero components in the inverse covariance matrices represent the conditional independence between...

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Vydané v:Journal of the Operations Research Society of China (Internet) Ročník 9; číslo 3; s. 543 - 568
Hlavní autori: Xiao, Yun-Hai, Li, Pei-Li, Lu, Sha
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Beijing Operations Research Society of China 01.09.2021
Springer Nature B.V
Predmet:
Algorithms
Covariance matrix
Decomposition
Determinants
Discriminant analysis
Efficiency
Eigenvalues
Estimation
Euclidean space
Iterative methods
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Optimization models
Random variables
Synthetic data
Maximum likelihood estimation
Symmetric Gauss–Seidel iteration
65K05
Augmented Lagrangian function
90C46
Inverse covariance matrix
90C25
Non-smooth convex minimization
ISSN:2194-668X, 2194-6698
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Shrnutí:Firstly, this paper proposes a generalized log-determinant optimization model with the purpose of estimating the high-dimensional sparse inverse covariance matrices. Under the normality assumption, the zero components in the inverse covariance matrices represent the conditional independence between pairs of variables given all the other variables. The generalized model considered in this study, because of the setting of the eigenvalue bounded constraints, covers a large number of existing estimators as special cases. Secondly, rather than directly tracking the challenging optimization problem, this paper uses a couple of alternating direction methods of multipliers (ADMM) to solve its dual model where 5 separable structures are contained. The first implemented algorithm is based on a single Gauss–Seidel iteration, but it does not necessarily converge theoretically. In contrast, the second algorithm employs the symmetric Gauss–Seidel (sGS) based ADMM which is equivalent to the 2-block iterative scheme from the latest sGS decomposition theorem. Finally, we do numerical simulations using the synthetic data and the real data set which show that both algorithms are very effective in estimating high-dimensional sparse inverse covariance matrix.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2194-668X
2194-6698
DOI:10.1007/s40305-021-00351-y