Alternating Direction Methods for Latent Variable Gaussian Graphical Model Selection

Ma, Shiqian; Xue, Lingzhou; Zou, Hui

doi:10.1162/neco_a_00379

Cited by 72 publications

(71 citation statements)

References 62 publications

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“…Assuming that the gene expression levels follow a multivariate normal distribution, the conditional independence can be recovered by estimating the support of the inverse covariance matrix of the expression data. One approach is to estimate the inverse covariance matrix directly using penalized maximum likelihood approaches [Cai, Liu and Luo (2011), Cai, Liu and Zhou (2012), Friedman, Hastie and Tibshirani (2008), Ma, Xue and Zou (2013)]. Alternatively, the neighborhood selection method is based on sparse regression techniques to select the pairs of genes with nonzero partial correlations.…”

Section: Background and Datamentioning

confidence: 99%

Network assisted analysis to reveal the genetic basis of autism

2015

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While studies show that autism is highly heritable, the nature of the genetic basis of this disorder remains illusive. Based on the idea that highly correlated genes are functionally interrelated and more likely to affect risk, we develop a novel statistical tool to find more potentially autism risk genes by combining the genetic association scores with gene co-expression in specific brain regions and periods of development. The gene dependence network is estimated using a novel partial neighborhood selection (PNS) algorithm, where node specific properties are incorporated into network estimation for improved statistical and computational efficiency. Then we adopt a hidden Markov random field (HMRF) model to combine the estimated network and the genetic association scores in a systematic manner. The proposed modeling framework can be naturally extended to incorporate additional structural information concerning the dependence between genes. Using currently available genetic association data from whole exome sequencing studies and brain gene expression levels, the proposed algorithm successfully identified 333 genes that plausibly affect autism risk.

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Section: Background and Datamentioning

confidence: 99%

Network assisted analysis to reveal the genetic basis of autism

2015

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“…ADMM (1.6) has been revisited recently due to its success in the emerging applications of structured convex optimization problems arising from image processing, compressed sensing, machine learning, semidefinite programming and statistics etc. (see e.g., [5,27,29,30,32,34,47,54,56,58,60,62,64,66,70,71,73,75,78]). …”

Section: Alternating Direction Methods Of Multipliersmentioning

confidence: 99%

Alternating Proximal Gradient Method for Convex Minimization

2015

J Sci Comput

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In this paper, we apply the idea of alternating proximal gradient to solve separable convex minimization problems with three or more blocks of variables linked by some linear constraints. The method proposed in this paper is to firstly group the variables into two blocks, and then apply a proximal gradient based inexact alternating direction method of multipliers to solve the new formulation. The main computational effort in each iteration of the proposed method is to compute the proximal mappings of the involved convex functions. The global convergence result of the proposed method is established. We show that many interesting problems arising from machine learning, statistics, medical imaging and computer vision can be solved by the proposed method. Numerical results on problems such as latent variable graphical model selection, stable principal component pursuit and compressive principal component pursuit are presented.

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“…Especially, its special case of m = 2, which is the well-known alternating direction method of multipliers (ADMM) contributed in [22,23], received a revived interest and is widely used in the areas of variational inequalities [32], signal/image processing [8,10,24], statistical learning [5,13,36,41,52,54], etc. Compared with the well-developed ADMM, however, the most recent work of Chen et al [12] shows that the direct extension (1.2) of ADMM for m ≥ 3 is not necessarily convergent.…”

Section: Augmented-lagrangian-based Splitting Methodsmentioning

confidence: 99%

A distributed Douglas-Rachford splitting method for multi-block convex minimization problems

Han

2015

Adv Comput Math

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A customized Douglas-Rachford splitting method (DRSM) was recently proposed to solve two-block separable convex optimization problems with linear constraints and simple abstract constraints. The algorithm has advantage over the well-known alternating direction method of multipliers (ADMM), the dual application of DRSM to the two-block convex minimization problem, in the sense that the subproblems can have larger opportunity of possessing closed-form solutions since they are unconstrained. In this paper, we further study along this way by considering the primal application of DRSM for the general case m ≥ 3, i.e., we consider the multi-block separable convex minimization problem with linear constraints where the objective function is separable into m individual convex functions without coupled variables. The resulting method fully exploits the separable structure and enjoys decoupled subproblems which can be solved simultaneously. Both the exact and inexact versions of the new method are presented in a unified framework. Under mild conditions, we manage to prove the global convergence of the algorithm. Preliminary numerical experiments for extracting the background from corrupted surveillance video verify the encouraging efficiency of the new algorithm.Keywords Douglas-Rachford splitting method · Multi-block convex minimization problem · Alternating direction method of multipliers · Robust principal component analysis Mathematics Subject Classifications (2010) 90C25 · 65K10 · 94A08

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Alternating Direction Methods for Latent Variable Gaussian Graphical Model Selection

Cited by 72 publications

References 62 publications

Network assisted analysis to reveal the genetic basis of autism

Network assisted analysis to reveal the genetic basis of autism

Alternating Proximal Gradient Method for Convex Minimization

A distributed Douglas-Rachford splitting method for multi-block convex minimization problems

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