iPACOSE: an iterative algorithm for the estimation of gene regulation networks

In the context of Gaussian Graphical Models (GGMs) with high- dimensional small sample data, we present a simple procedure to esti- mate partial correlations under the constraint that some of them are strictly zero. This method can also be extended to covariance selection. If the goal is to estimate a GGM, our new procedure can be applied to re-estimate the partial correlations after a first graph has been esti- mated in the hope to improve the estimation of non-zero coefficients. In a simulation study, we compare our new covariance selection procedure to existing methods and show that the re-estimated partial correlation coefficients may be closer to the real values in important cases

Iterative reconstruction of high-dimensional Gaussian Graphical Models based on a new method to estimate partial correlations under constraints.

In the context of Gaussian Graphical Models (GGMs) with high-dimensional small sample data, we present a simple procedure, called PACOSE - standing for PArtial COrrelation SElection - to estimate partial correlations under the constraint that some of them are strictly zero. This method can also be extended to covariance selection. If the goal is to estimate a GGM, our new procedure can be applied to re-estimate the partial correlations after a first graph has been estimated in the hope to improve the estimation of non-zero coefficients. This iterated version of PACOSE is called iPACOSE. In a simulation study, we compare PACOSE to existing methods and show that the re-estimated partial correlation coefficients may be closer to the real values in important cases. Plus, we show on simulated and real data that iPACOSE shows very interesting properties with regards to sensitivity, positive predictive value and stability

On Nonregularized Estimation of Psychological Networks.

An important goal for psychological science is developing methods to characterize relationships between variables. Customary approaches use structural equation models to connect latent factors to a number of observed measurements, or test causal hypotheses between observed variables. More recently, regularized partial correlation networks have been proposed as an alternative approach for characterizing relationships among variables through off-diagonal elements in the precision matrix. While the graphical Lasso (glasso) has emerged as the default network estimation method, it was optimized in fields outside of psychology with very different needs, such as high dimensional data where the number of variables (p) exceeds the number of observations (n). In this article, we describe the glasso method in the context of the fields where it was developed, and then we demonstrate that the advantages of regularization diminish in settings where psychological networks are often fitted ( p≪n ). We first show that improved properties of the precision matrix, such as eigenvalue estimation, and predictive accuracy with cross-validation are not always appreciable. We then introduce nonregularized methods based on multiple regression and a nonparametric bootstrap strategy, after which we characterize performance with extensive simulations. Our results demonstrate that the nonregularized methods can be used to reduce the false-positive rate, compared to glasso, and they appear to provide consistent performance across sparsity levels, sample composition (p/n), and partial correlation size. We end by reviewing recent findings in the statistics literature that suggest alternative methods often have superior performance than glasso, as well as suggesting areas for future research in psychology. The nonregularized methods have been implemented in the R package GGMnonreg

A comparative study of Gaussian Graphical Model approaches for genomic data

The inference of networks of dependencies by Gaussian Graphical models on high-throughput data is an open issue in modern molecular biology. In this paper we provide a comparative study of three methods to obtain small sample and high dimension estimates of partial correlation coefficients: the Moore-Penrose pseudoinverse (PINV), residual correlation (RCM) and covariance-regularized method $(\ell_{2C})$. We first compare them on simulated datasets and we find that PINV is less stable in terms of AUC performance when the number of variables changes. The two regularized methods have comparable performances but $\ell_{2C}$ is much faster than RCM. Finally, we present the results of an application of $\ell_{2C}$ for the inference of a gene network for isoprenoid biosynthesis pathways in Arabidopsis thaliana.Comment: 7 pages, 1 figure, RevTex4, version to appear in the proceedings of 1st International Workshop on Pattern Recognition, Proteomics, Structural Biology and Bioinformatics: PR PS BB 2011, Ravenna, Italy, 13 September 201

Ridge Estimation of Inverse Covariance Matrices from High-Dimensional Data

We study ridge estimation of the precision matrix in the high-dimensional setting where the number of variables is large relative to the sample size. We first review two archetypal ridge estimators and note that their utilized penalties do not coincide with common ridge penalties. Subsequently, starting from a common ridge penalty, analytic expressions are derived for two alternative ridge estimators of the precision matrix. The alternative estimators are compared to the archetypes with regard to eigenvalue shrinkage and risk. The alternatives are also compared to the graphical lasso within the context of graphical modeling. The comparisons may give reason to prefer the proposed alternative estimators