Estimation of variances and covariances for high‐dimensional data: a selective review

Tong, Tiejun; Wang, Cheng; Wang, Yuedong

doi:10.1002/wics.1308

Cited by 23 publications

(17 citation statements)

References 90 publications

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“…Books and reviews dedicated to covariance and precision matrix estimation and graphical models are presented by Hastie et al, Pourahmadi, Tong et al, and Fan et al…”

Section: Discussionmentioning

confidence: 99%

Estimation of covariance and precision matrix, network structure, and a view toward systems biology

Kuismin

Sillanpää

2017

WIREs Computational Stats

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Covariance matrix and its inverse, known as the precision matrix, have many applications in multivariate analysis because their elements can exhibit the variance, correlation, covariance, and conditional independence between variables. The practice of estimating the precision matrix directly without involving any matrix inversion has obtained significant attention in the literature. We review the methods that have been implemented in R and their R packages, particularly when there are more variables than data samples and discuss ideas behind them. We describe how sparse precision matrix estimation methods can be used to infer network structure. Finally, we discuss methods that are suitable for gene coexpression network construction.

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“…Books and reviews dedicated to covariance and precision matrix estimation and graphical models are presented by Hastie et al, Pourahmadi, Tong et al, and Fan et al…”

Section: Discussionmentioning

confidence: 99%

Estimation of covariance and precision matrix, network structure, and a view toward systems biology

Kuismin

Sillanpää

2017

WIREs Computational Stats

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“…m ≈ n or m > n). In such situations this standard covariance matrix estimate is known to perform poorly (see Tong et al, 2014). To remedy this, we regularize the standard estimate using the approach developed in Schäfer and Strimmer (2005) and Opgen-Rhein and Strimmer (2007) which is implemented in the R package corpcor (see also Strimmer, 2008).…”

Section: Parameter Estimationmentioning

confidence: 99%

qtQDA: quantile transformed quadratic discriminant analysis for high-dimensional RNA-seq data

Koçhan

Tütüncü

Smyth

et al. 2019

Preprint

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Classification on the basis of gene expression data derived from RNA-seq promises to become an important part of modern medicine. We propose a new classification method based on a model where the data is marginally negative binomial but dependent, thereby incorporating the dependence known to be present between measurements from different genes. The method, called qtQDA, works by first performing a quantile transformation (qt) then applying Gaussian Quadratic Discriminant Analysis (QDA) using regularized covariance matrix estimates. We show that qtQDA has excellent performance when applied to real data sets and has advantages over some existing approaches. An R package implementing the method is also available.

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“…Despite use of the state of the art MCMC techniques, MCMC-EM might still converge to poor local minima solutions and result in sub-optimal performance [70], [71], [72]. Particularly, performance may be poorer for under-determined problems.…”

Section: ) Markov Chain Monte Carlo Em (Mcmc-em)mentioning

confidence: 99%

“…This prevents the spurious off-diagonal values inΣ from affecting the next cycle of MCMC samples and improves future estimates ofγ. • We incorporate the shrinkage estimation idea presented in [72], [74] and regularizeΣ as a convex sum of the empiricalΣ and a target matrix T such that,…”

Section: ) Markov Chain Monte Carlo Em (Mcmc-em)mentioning

confidence: 99%

Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem

Nalci

Fedorov

Al-Shoukairi

et al. 2018

IEEE Trans. Signal Process.

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In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares (S-NNLS) problem. We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R-GSM) to model the sparsity enforcing prior distribution for the solution. The R-GSM prior encompasses a variety of heavy-tailed densities such as the rectified Laplacian and rectified Studentt distributions with a proper choice of the mixing density. We utilize the hierarchical representation induced by the R-GSM prior and develop an evidence maximization framework based on the Expectation-Maximization (EM) algorithm. Using the EM based method, we estimate the hyper-parameters and obtain a point estimate for the solution. We refer to the proposed method as rectified sparse Bayesian learning (R-SBL). We provide four R-SBL variants that offer a range of options for computational complexity and the quality of the E-step computation. These methods include the Markov chain Monte Carlo EM, linear minimum mean-square-error estimation, approximate message passing and a diagonal approximation. Using numerical experiments, we show that the proposed R-SBL method outperforms existing S-NNLS solvers in terms of both signal and support recovery performance, and is also very robust against the structure of the design matrix.

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Estimation of variances and covariances for high‐dimensional data: a selective review

Cited by 23 publications

References 90 publications

Estimation of covariance and precision matrix, network structure, and a view toward systems biology

Estimation of covariance and precision matrix, network structure, and a view toward systems biology

qtQDA: quantile transformed quadratic discriminant analysis for high-dimensional RNA-seq data

Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem

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