Slope Heuristic for Block-Diagonal Covariance Selection in High Dimensional Gaussian Graphical Models

Description

Block-diagonal covariance selection for high dimensional Gaussian graphical models. The selection procedure is based on the slope heuristics.

Details

The function main function of the package (performShock) performs block-diagonal covariance selection for high-dimensional Gaussian graphical models.

Author(s)

Emilie Devijver, Melina Gallopin

Maintainer: Melina Gallopin <melina.gallopin@gmail.com>

References

Devijver, E., Gallopin, M. (2015). Block-diagonal covariance selection for high dimensional Gaussian graphical models. Inria Research Report . Available at http://arxiv.org/abs/1511.04033.

Examples

## load data to test 
data(dataTest)

## dimension of the dataset expdata
n <- dim(dataTest)[1]
p <- dim(dataTest)[2]

## perform partition of variables selection
## based on the slope heuristic
resShock <- shockSelect(dataTest)


## verify that the two slope heuristic 
## calibrations give the same result
table(resShock$SHDJlabels == resShock$SHRRlabels)

## collect the labels of variables 
SHlabels  <- resShock$SHDJlabels

## SHadjaMat: adjacency matrix of the inferred network
## Shock network inference 
SHadjaMat<- diag(p)
for(itt in 1:length(unique(SHlabels))){  
  stepdata <- as.matrix(dataTest[,SHlabels==itt],nrow=dim(dataTest)[1])
  if(dim(stepdata)[2]>1){
    resNet <- networkInferenceGlassoBIC(stepdata)
    SHadjaMat[SHlabels==itt,SHlabels==itt] <- resNet$A
  }
}

Compute the log-likelihood of the model

Description

This function computes the log-likelihood of a multivariate Gaussian model with a block-diagonal covariance matrix.

Usage

computeLoglikeFromPartition(labels, expdata)

Arguments

Details

This function computes the log-likelihood of a multivariate Gaussian model with a block-diagonal covariance matrix described in the labels vector.

Value

Examples

## load data to test
 data(dataTest)
 
## threshold of absS matrix
myLABELS <- thresholdAbsSPath(dataTest)$partitionList

## compute loglikelihood 
logLikePath <- lapply(myLABELS, function(x) computeLoglikeFromPartition(x,dataTest))

Simulated data to test the R package

Description

This toy dataset as been simulated under a multivariate normal distribution with a block-diagonal covariance matrix and is used to test the method.

Usage

dataTest

Format

The dataset dataTest is a matrix.

Network inference using the glasso algorithm

Description

This function performs network inference using the glasso algorithm for several regularization parameters and selects a network based on the BIC of the model.

Usage

networkInferenceGlassoBIC(dataNet, nb.rho = 100)

Arguments

Value

References

https://cran.r-project.org/web/packages/glasso/glasso.pdf

Examples

## load data to test 
data(dataTest)

## perform network inference 
resNet <- networkInferenceGlassoBIC(dataTest)

Shock selection

Description

This function performs block-diagonal covariance selection for high-dimensional Gaussian graphical models.

Usage

shockSelect(expdata)

Arguments

Value

Examples

## load data to test 
data(dataTest)

## dimension of the dataset expdata
n <- dim(dataTest)[1]
p <- dim(dataTest)[2]

## perform partition of variables selection
## based on the slope heuristic
resShock <- shockSelect(dataTest)

Simulate a modular network

Description

This function simulates a modular network with p variables based on the partition of variables into blocks labels.

Usage

simulateBlockDiagNetwork(p, labels)

Arguments

Details

To simulate covariance matrices, we use the methodology detailed in Giraud, S. Huet, and N. Verzelen. Graph selection with GGMselect. 2009

http://fr.arxiv.org/abs/0907.0619 https://cran.r-project.org/package=GGMselect

Value

Examples

## number of variables
p <- 100
## number of blocks
K <- 15
## vector of partition into blocks
labels <- factor(rep(1:K, length.out=p))
## simulate network 
g <- simulateBlockDiagNetwork(p,labels)
        

Detect partitions of variables into blocks.

Description

This function returns a list of partitions of variables based on the sample covariance matrix for several levels of threshold.

Usage

thresholdAbsSPath(expdata)

Arguments

Value

Examples

## load data to test 
data(dataTest)

## detect partitions of variables into blocks based on the sample covariance matrix
partitions <- thresholdAbsSPath(dataTest)$partitionList