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Iterative Reconstruction of High-Dimensional Gaussian Graphical Models Based on a New Method to Estimate Partial Correlations under Constraints

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  • Vincent Guillemot
  • Andreas Bender
  • Anne-Laure Boulesteix

Abstract

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.

Suggested Citation

  • Vincent Guillemot & Andreas Bender & Anne-Laure Boulesteix, 2013. "Iterative Reconstruction of High-Dimensional Gaussian Graphical Models Based on a New Method to Estimate Partial Correlations under Constraints," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-10, April.
    • Handle: RePEc:plo:pone00:0060536
    DOI: 10.1371/journal.pone.0060536
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    1. Daniela M. Witten & Robert Tibshirani, 2009. "Covariance‐regularized regression and classification for high dimensional problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 615-636, June.
    2. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
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