Maximum boundary size of the resulting qp-graphs

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Description

Calculates and plots the size of the largest vertex boundary as function of the non-rejection rate.

Usage

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qpBoundary(nrrMatrix, n=NA, threshold.lim=c(0,1), breaks=5, vertexSubset=NULL,
           plot=TRUE, qpBoundaryOutput=NULL, density.digits=0, logscale.bdsize=FALSE,
           titlebd="Maximum boundary size as function of threshold", verbose=FALSE)

Arguments

nrrMatrix

matrix of non-rejection rates.

n

number of observations from where the non-rejection rates were estimated.

threshold.lim

range of threshold values on the non-rejection rate.

breaks

either a number of threshold bins or a vector of threshold breakpoints.

vertexSubset

subset of vertices for which their maximum boundary size is calculated with respect to all other vertices.

plot

logical; if TRUE makes a plot of the result; if FALSE it does not.

qpBoundaryOutput

output from a previous call to qpBoundary. This allows one to plot the result changing some of the plotting parameters without having to do the calculation again.

density.digits

number of digits in the reported graph densities.

logscale.bdsize

logical; if TRUE then the scale for the maximum boundary size is logarithmic which is useful when working with more than 1000 variables; FALSE otherwise (default).

titlebd

main title to be shown in the plot.

verbose

show progress on calculations.

Details

The maximum boundary is calculated as the largest degree among all vertices of a given qp-graph.

Value

A list with the maximum boundary size and graph density as function of threshold, the threshold on the non-rejection rate that provides a maximum boundary size strictly smaller than the sample size n and the resulting maximum boundary size.

Author(s)

R. Castelo and A. Roverato

References

Castelo, R. and Roverato, A. A robust procedure for Gaussian graphical model search from microarray data with p larger than n. J. Mach. Learn. Res., 7:2621-2650, 2006.

See Also

qpHTF qpGraphDensity

Examples

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require(mvtnorm)

nVar <- 50  ## number of variables
maxCon <- 5 ## maximum connectivity per variable
nObs <- 30  ## number of observations to simulate

set.seed(123)

A <- qpRndGraph(p=nVar, d=maxCon)
Sigma <- qpG2Sigma(A, rho=0.5)
X <- rmvnorm(nObs, sigma=as.matrix(Sigma))

## the higher the q the less complex the qp-graph

nrr.estimates <- qpNrr(X, q=1, verbose=FALSE)

qpBoundary(nrr.estimates, plot=FALSE)

nrr.estimates <- qpNrr(X, q=5, verbose=FALSE)

qpBoundary(nrr.estimates, plot=FALSE)

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