Simulation of Gaussian graphical models

This repository contains the files for replicating the experiments described in the papers:

• Córdoba I., Varando G., Bielza C., Larrañaga P. A partial orthogonalization method for simulating covariance and concentration graph matrices. Proceedings of Machine Learning Research (PGM 2018), vol 72, pp. 61-72, 2018.
• Córdoba I., Varando G., Bielza C., Larrañaga P. Generating random Gaussian graphical models, arXiv:1909.01062, 2019.

The experiments are related with the analysis of four methods for sampling partial correlation matrices, possibly constrained by an undirected graph:

• The traditional diagonal dominance method, implemented in many software packages, and also in gmat::diagdom().
• Partial orthogonalization (Córdoba et al. 2018), implemented in gmat::port()
• Uniform sampling (Córdoba et al. 2019), implemented in gmat::chol_mh().
• Uniform sampling combined with partial orthogonalization (Córdoba et al. 2019), implemented in gmat::port_chol().

Main contents

• experiment_kramer.R and plot_kramer.R: execute the experiment of

 N. Krämer, J. Schäfer, and A.-L. Boulesteix. Regularized estimation of
 large-scale gene association networks using graphical Gaussian models.
 BMC Bioinformatics, 10(1):384, 2009,

whose results are included for comparison in Córdoba et al. (2018, 2019), and generate the corresponding figures.

• experiment_pgm.R and plot_pgm.R: execute the experiments and generate the figures in Córdoba et al. (2018), except for the Kramer et al. (2009) experiment.
• plot_ext.R: generate the figures in Córdoba et al. (2019).

The CRAN packages gmat and ggplot2 are required for all the experiments and plots, respectively. The generateds plots are stored in a directory plot_[experiment-name], where experiment-name may be pgm, ext or kramer, and which is newly created if it does not already exist.

Remarks on generating the figures in Córdoba et al. (2018)

Source first file experiment_pgm.R and then plot_pgm.R. This experiment is computationally intensive, and requires the dplyr R package for generating the plots.

Note that because gmat::port() and gmat::diagdom() have been modified since the publication of Córdoba et al. (2018), some of its original graphics have been affected. In particular:

• The results for the average off-diagonal/diagonal ratio statistic R has changed: matrices obtained with the partial orthogonalization method are more well conditioned, but their behaviour regarding R is more similar to those with dominant diagonal, although somewhat mitigated.
• Now the condition numbers and execution time for gmat::port() are lower.
• The results for the Kramer experiment with diagonally dominant matrices are slightly different since now the independent and identically distributed original random entries are generated with a Gaussian instead of a uniform distribution.

Remarks on reproducing the Kramer et al. (2009) experiment

Source the file experiment_kramer.R and then plot_kramer.R. This experiment is computationally intensive, and requires additional R packages to be executed: doParallel, foreach, parcor, corpcor, MASS and reshape2.

The performance statistics are calculated by the function in performance.pcor.R, which is a modification of parcor::performance.pcor:

• It solves a bug by calling GeneNet::network.test.edges() instead of GeneNet::ggm.test.edges(), which does not exist in the newest version of GeneNet.
• Variables ppv and tpr are correctly initialized to 1 instead of -Inf.