Learning latent variable Gaussian graphical model for biomolecular network with low sample complexity
type: Item
instance of: scholarly article
title: Learning latent variable Gaussian graphical model for biomolecular network with low sample complexity
zbMATH Open document ID: 1367.92047
DOI: 10.1155/2016/2078214
author: Quan Liu
author: Bo Yuan
author: Yan-Bo Wang
published in: Computational \& Mathematical Methods in Medicine
publication date: 2017-08-04T00:00:00Z
review text: Summary: Learning a Gaussian graphical model with latent variables is ill posed when there is insufficient sample complexity, thus having to be appropriately regularized. A common choice is convex \(\ell_1\) plus nuclear norm to regularize the searching process. However, the best estimator performance is not always achieved with these additive convex regularizations, especially when the sample complexity is low. In this paper, we consider a concave additive regularization which does not require the strong irrepresentable condition. We use concave regularization to correct the intrinsic estimation biases from Lasso and nuclear penalty as well. We establish the proximity operators for our concave regularizations, respectively, which induces sparsity and low rankness. In addition, we extend our method to also allow the decomposition of fused structure-sparsity plus low rankness, providing a powerful tool for models with temporal information. Specifically, we develop a nontrivial modified alternating direction method of multipliers with at least local convergence. Finally, we use both synthetic and real data to validate the excellence of our method. In the application of reconstructing two-stage cancer networks, ``the Warburg effect'' can be revealed directly.
Mathematics Subject Classification ID: 92C42
Mathematics Subject Classification ID: 62P10
zbMATH DE Number: 6756922
zbMATH Keywords: Gaussian graphical model
zbMATH Keywords: additive convex regularizations
zbMATH Keywords: sparsity
zbMATH Keywords: low rankness
Wikidata QID: Q37396771
describes a project that uses: GADMM
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/2078214
OpenAlex ID: W2536936056
cites work: Compressed sensing
cites work: Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
cites work: Robust principal component analysis?
cites work: Model Selection and Estimation in Regression with Grouped Variables
cites work: Latent variable graphical model selection via convex optimization
cites work: Network exploration via the adaptive LASSO and SCAD penalties
cites work: A general theory of concave regularization for high-dimensional sparse estimation problems
cites work: The sparsity and bias of the LASSO selection in high-dimensional linear regression
cites work: Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
cites work: Strong oracle optimality of folded concave penalized estimation
cites work: Sparsity and Smoothness Via the Fused Lasso
cites work: On first-order algorithms forl1/nuclear norm minimization
cites work: Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
cites work: Alternating Direction Methods for Latent Variable Gaussian Graphical Model Selection
cites work: On the \(O(1/n)\) convergence rate of the Douglas-Rachford alternating direction method
cites work: PARTIAL CORRELATION AND CONDITIONAL CORRELATION AS MEASURES OF CONDITIONAL INDEPENDENCE
cites work: Model selection and estimation in the Gaussian graphical model
cites work: High-dimensional covariance estimation by minimizing \(\ell _{1}\)-penalized log-determinant divergence
cites work: Sparse permutation invariant covariance estimation
cites work: Joint estimation of multiple graphical models
cites work: The Joint Graphical Lasso for Inverse Covariance Estimation Across Multiple Classes
cites work: A trace inequality of John von Neumann
cites work: Generalized alternating direction method of multipliers: new theoretical insights and applications
cites work: Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities
cites work: Local Shrinkage Rules, Lévy Processes and Regularized Regression
description: scientific article; zbMATH DE number 6756922