Partial Correlation Estimation by Joint Sparse Regression Models

By Jie Peng, Pei Wang, N. Zhou, Ji Zhu. Journal of the American Statistical Association, 2008

395 citations recorded by the source corpus.

This article features online supplementary material. In this article, we propose a computationally efficient approach—space (Sparse PArtial Correlation Estimation)—for selecting nonzero partial correlations under the high-dimension-low-sample-size setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting. We illustrate the performance of space by extensive simulation studies. It is shown that space performs well in both nonzero partial correlation selection and the identification of hub variables, and also outperforms two existing methods. We then apply space to a microarray breast cancer dataset and identify a set of hub genes that may provide important insights on genetic regulatory networks. Finally, we prove that, under a set of suitable assumptions, the proposed procedure is asymptotically consistent in terms of model selection and parameter estimation.

Subfields: Genetics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/31c88a88c9603ec32b237128dec6feeb5713a5d5

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Citations in the corpus

Regularized Multivariate Regression for Identifying Master Predictors with Application to Integrative Genomics Study of Breast Cancer (2008, methodology): “posed by Peng et al. (2008) and Friedman et al. (2008), which is a modification of the shooting algorithm proposed by Fu (1998) and also Friedman et al.”
Comparing Statistical Methods for Constructing Large Scale Gene Networks (2012, methodology): “The main contributions of this paper include: (1) The performance on constructing large scale GRNs is compared with a wide range of sample sizes and numbers of genes in the network; (2) The performance of identifying correct hub genes, which are likely to be the disease driver genes, is compared amo”
Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models (2010, methodology): “Other methods for estimating high dimensional graphs include (Liu, Laﬀerty and Wasserman, 2009; Meinshausen and B¨uhlmann, 2006; Peng et al. , 2009).”
Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes (2019, methodology): “Next, p × p precision matrices Ω l are generated for each E l based on the algorithm of Peng et al. (2009).”
Communication-Avoiding Parallel Sparse-Dense Matrix-Matrix Multiplication (2016, background): “Another application in statistical/machine learning is sparse inverse covariance selection (ICS) and related problems [8], [9], [10], [11], [12].”
NETS: Network estimation for time series (2019, positive): “As far as the estimation of c is concerned, we follow the two–step iterative procedure proposed in Peng et al. (2009): (i) Given an estimate of c, we estimate the θ parameter using nets. (ii) Given an estimate c and an estimate of θ we update the estimate of c. Notice, that cii is the reciprical of ”
Regularized rank-based estimation of high-dimensional nonparanormal graphical models (2012, neutral): “Peng et al. (2009) proposed the joint neighborhood lasso selection.”
ppcor: An R Package for a Fast Calculation to Semi-partial Correlation Coefficients (2015, methodology): “The R package space (Peng et al., 2009) can be used for sparse partial correlation estimation.”
Estimating time-varying networks (2008, methodology): “Peng et al. (2008) propose a different neighborhood selection procedure for the structure etimation in which they estimate all neighborhoods jointly.”
The joint graphical lasso for inverse covariance estimation across multiple classes (2011, methodology): “h a power law degree distribution. Power law degree distributions are thought to mimic the structure of biological networks (Chen & Sharp 2004) and are harder to estimate than simpler structures (Peng et al. 2009). Of the ten subnetworks, eight have the same structure and edge values in both cla”
High Dimensional Semiparametric Gaussian Copula Graphical Models. (2012, background): “The resulting estimator Ω̂ has been shown to have good theoretical properties (Lam and Fan, 2009; Peng et al., 2009; Ravikumar et al., 2009; Rothman et al., 2008).”
Estimation of functional connectivity in fMRI data using stability selection-based sparse partial correlation with elastic net penalty (2011, positive): “Also, Θ(m,n) is proportional to the regression coefficient of region n in the multiple regression of variable m on the rest of the regions (Hastie et al., 2009; Peng et al., 2009).”
Communication-Avoiding Optimization Methods for Distributed Massive-Scale Sparse Inverse Covariance Estimation (2017, methodology): “The work of [44] applies the “SPACE” estimator of [40], except augmented with an additional squared `2-norm penalty, to low-dimensional fMRI data; while certainly related to our approach, this method unfortunately suffers from all three of the aforementioned issues.”