Alternating Direction Method for Covariance Selection Models

Authors:
Xiaoming Yuan
Affiliations:
Department of Mathematics, Hong Kong Baptist University, Hong Kong, China
Venue:
Journal of Scientific Computing
Year:
2012

Citing 15
Cited 4

Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
Determinant Maximization with Linear Matrix Inequality Constraints

SIAM Journal on Matrix Analysis and Applications
A variable-penalty alternating directions method for convex optimization

Mathematical Programming: Series A and B
A Weak-to-Strong Convergence Principle for Fejé-Monotone Methods in Hilbert Spaces

Mathematics of Operations Research
Alternating Projection-Proximal Methods for Convex Programming and Variational Inequalities

SIAM Journal on Optimization
Smooth minimization of non-smooth functions

Mathematical Programming: Series A and B
Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data

The Journal of Machine Learning Research
A descent method for structured monotone variational inequalities

Optimization Methods & Software
First-Order Methods for Sparse Covariance Selection

SIAM Journal on Matrix Analysis and Applications
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images

SIAM Review
Smooth Optimization Approach for Sparse Covariance Selection

SIAM Journal on Optimization
Solving Constrained Total-variation Image Restoration and Reconstruction Problems via Alternating Direction Methods

SIAM Journal on Scientific Computing
Solving Log-Determinant Optimization Problems by a Newton-CG Primal Proximal Point Algorithm

SIAM Journal on Optimization
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing

SIAM Journal on Scientific Computing
Some convergence properties of a method of multipliers for linearly constrained monotone variational inequalities

Operations Research Letters

An alternating direction method for finding Dantzig selectors

Computational Statistics & Data Analysis
An ADM-based splitting method for separable convex programming

Computational Optimization and Applications
Alternating direction methods for latent variable gaussian graphical model selection

Neural Computation
A proximal parallel splitting method for minimizing sum of convex functions with linear constraints

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

The covariance selection problem captures many applications in various fields, and it has been well studied in the literature. Recently, an l 1-norm penalized log-likelihood model has been developed for the covariance selection problem, and this novel model is capable of completing the model selection and parameter estimation simultaneously. With the rapidly increasing magnitude of data, it is urged to consider efficient numerical algorithms for large-scale cases of the l 1-norm penalized log-likelihood model. For this purpose, this paper develops the alternating direction method (ADM). Some preliminary numerical results show that the ADM approach is very efficient for large-scale cases of the l 1-norm penalized log-likelihood model.