Ridge estimation for high-dimensional precision matrices

Package contains proper L2-penalized ML estimators for the precision matrix as well as supporting functions to employ these estimators in a (integrative or meta-analytic) graphical modeling setting.

Details

The main function of the package is ridgeP which enables archetypal and proper alternative ML ridge estimation of the precision matrix. The alternative ridge estimators can be found in van Wieringen and Peeters (2015) and encapsulate both target and non-target shrinkage for the multivariate normal precision matrix. The estimators are analytic and enable estimation in large \(p\) small \(n\) settings. Supporting functions to employ these estimators in a graphical modeling setting are also given. These supporting functions enable, a.o., the determination of the optimal value of the penalty parameter, the determination of the support of a shrunken precision estimate, as well as various visualization options.

The package has a modular setup. The core module (rags2ridges.R) contains the functionality stated above. The fused module (rags2ridgesFused.R) extends the functionality of the core module to the joint estimation of multiple precision matrices from (aggregated) high-dimensional data consisting of distinct classes. The result is a targeted fused ridge estimator that is of use when the precision matrices of the constituent classes are believed to chiefly share the same structure while potentially differing in a number of locations of interest. The fused module also contains supporting functions for integrative or meta-analytic Gaussian graphical modeling. The third module is the miscellaneous module (rags2RidgesMisc.R) which contains assorted hidden functions.

Function overview core module:

• Function for (proper) ridge estimation of the precision matrix

  • ridgeP

• Functions for penalty parameter selection

  • CNplot

  • optPenalty.aLOOCV

  • optPenalty.kCV

  • optPenalty.kCVauto

• Functions for loss/entropy/fit evaluation

  • evaluateSfit

  • KLdiv

  • loss

• Functions for block-independence testing

  • GGMblockNullPenalty

  • GGMblockTest

• Function for support determination

  • sparsify

• Functions for (network) visualization

  • edgeHeat

  • ridgePathS

  • Ugraph

• Functions for topology statistics

  • GGMmutualInfo

  • GGMnetworkStats

  • GGMpathStats

• Wrapper function

  • fullMontyS

• Support functions

  • adjacentMat

  • covML

  • covMLknown

  • default.target

  • evaluateS

  • pcor

  • symm

Function overview fused module:

• Function for targeted fused ridge estimation of multiple precision matrices

  • ridgeP.fused

• Function for fused penalty parameter selection

  • optPenalty.fused

• Functions for loss/entropy/fit evaluation

  • KLdiv.fused

  • NLL

• Function for testing the necessity of fusion

  • fused.test

• Function for support determination

  • sparsify.fused

• Functions for topology statistics

  • GGMnetworkStats.fused

  • GGMpathStats.fused

• Support functions

  • createS

  • default.penalty

  • default.target.fused

  • getKEGGPathway

  • isSymmetricPD

  • is.Xlist

  • kegg.target

  • plot.ptest

  • pooledS

  • print.optPenaltyFusedGrid

  • print.ptest

  • rmvnormal

Calls of interest to miscellaneous module:

• rags2ridges:::.TwoCents() ~~(Unsolicited advice)

• rags2ridges:::.Brooke() ~~(Endorsement)

• rags2ridges:::.JayZScore() ~~(The truth)

• rags2ridges:::.theHoff() ~~(Wish)

• rags2ridges:::.rags2logo() ~~(Warm welcome)

References

Peeters, C.F.W., Bilgrau, A.E., and van Wieringen, W.N. (2022). rags2ridges: A One-Stop-l2-Shop for Graphical Modeling of High-Dimensional Precision Matrices. Journal of Statistical Software, vol. 102(4): 1-32.

Bilgrau, A.E., Peeters, C.F.W., Eriksen, P.S., Boegsted, M., and van Wieringen, W.N. (2020). Targeted Fused Ridge Estimation of Inverse Covariance Matrices from Multiple High-Dimensional Data Classes. Journal of Machine Learning Research, 21(26): 1-52. Also available as arXiv:1509.07982v2 [stat.ME].

Peeters, C.F.W., van de Wiel, M.A., & van Wieringen, W.N. (2020). The Spectral Condition Number Plot for Regularization Parameter Evaluation. Computational Statistics, 35: 629-646. Also available as arXiv:1608.04123 [stat.CO].

van Wieringen, W.N. & Peeters, C.F.W. (2016). Ridge Estimation of Inverse Covariance Matrices from High-Dimensional Data. Computational Statistics & Data Analysis, vol. 103: 284-303. Also available as arXiv:1403.0904v3 [stat.ME].

van Wieringen, W.N. & Peeters, C.F.W. (2015). Application of a New Ridge Estimator of the Inverse Covariance Matrix to the Reconstruction of Gene-Gene Interaction Networks. In: di Serio, C., Lio, P., Nonis, A., and Tagliaferri, R. (Eds.) `Computational Intelligence Methods for Bioinformatics and Biostatistics'. Lecture Notes in Computer Science, vol. 8623. Springer, pp. 170-179.

Author

Carel F.W. Peeters, Anders Ellern Bilgrau, Wessel, N. van Wieringen
Maintainer: Carel F.W. Peeters <carel.peeters@wur.nl>