Nothing
R/gpregeFunctions.R
In robin: ROBustness in Network
Defines functions
.gprege
#AGPL-3 License
.gprege <- function(data, inputs, gpregeOptions) {
## GPREGE Gaussian process ranking and estimation of gene expression time-series.
## FORMAT
## DESC Fit two GPs with the an RBF (+ noise diagonal) kernel on each
## profile. One GP kernel is initialised wih a short lengthscale
## hyperparameter, signal variance as the observed variance and a zero noise
## variance. It is optimised via scaled conjugate gradients (netlab). The
## other GP has fixed hyperparameters with a zero inverse-width, zero signal
## variance and noise variance as the observed variance. The log-ratio of
## marginal likelihoods of the two hypotheses acts as a score of
## differential expression for the profile. Comparison via ROC curves is
## performed against BATS (Angelini et.al, 2007).
## See Kalaitzis & Lawrence (2011) for a detailed discussion of the
## ranking algorithm and dataset used.
## ARG data : The matrix of gene expression profiles; one profile per row.
## ARG inputs : Inputs to the GP.
## ARG gpregeOptions$explore: (LOGICAL) Operate in a user interactive mode.
## Used for examining individual gene expression profiles.
## ARG gpregeOptions$labels : Contains flags that specify whether the
## corresponding profile comes from a differentially expressed gene
## (usually from a ground truth).
## ARG gpregeOptions$indexRange : Range of indices of profiles on which the
## function should operate. Useful for selective exploration of specific
## profiles, e.g. only genes marked as differentially expressed in a ground
## truth list.
## ARG gpregeOptions$interpolatedT : New timepoints to interpolate for each
## profile, based on the estimated function values.
## ARG gpregeOptions$iters : The number of iterations for scaled-conjugate
## gradients (SCG) optimisation.
## ARG gpregeOptions$display : Display gradient and LML information on each
## SCG iteration.
## ARG gpregeOptions$inithypers : The matrix of hyperparameter
## configurations as its rows:
## [inverse-lengthscale percent-signal-variance percent-noise-variance]
## The first row corresponds to a (practically constant) function
## with a very large lengthscale. Such a function will account for 0 percent
## of the observed variance in the expression profile (hence 0 for signal)
## and explain it as noise (hence 1 for noise). Subsequent rows
## (initialisations for SCG optimisation) correspond to functions of various
## lengthscales that explain all the observed variance as signal. A
## reasonable lengthscale would be roughly in line with the time-point
## sampling intervals.
## ARG gpregeOptions$exhaustPlotRes : The search resolution. Used for
## interactive mode (explore == 1).
## ARG gpregeOptions$exhaustPlotLevels : # Exhaustive plot contour levels.
## Used for interactive mode (explore == 1).
## ARG gpregeOptions$exhaustPlotMaxWidth : maximum lengthscale to search
## for. Used for interactive mode (explore == 1).
## RETURN gpregeOutput$signalvar : The vertical lengthscales of the
## optimised RBF kernel for each profile.
## RETURN gpregeOutput$noisevar : Same, for the noise hyperparameter.
## RETURN gpregeOutput$width : Same, for the horizontal lengthscales of the RBF.
## RETURN gpregeOutput$LMLs : Log-marginal likelihood of the GP for each profile.
## RETURN gpregeOutput$interpolatedData : extended dataset with interpolated values.
## RETURN gpregeOutput$rankingScores : the ranking scores based on the
## log-ratio of marginal likelihoods.
##
## USAGE: gpregeOutput <- gprege(exprs_tp63_RMA, seq(0,240,by=20), gpregeOptions)
##
## SEEALSO : gpOptions, gpCreate, gpExpandParam, gpOptimise, gpExtractParam,
## gpLogLikelihood, gpPosteriorMeanVar
##
## COPYRIGHT: Alfredo A. Kalaitzis, 2010, 2011
##
## GPREGE
##
if (missing(data))
stop('Missing data.')
if (missing(inputs)) {
stop('Missing inputs.')
}
if (is.null(gpregeOptions$indexRange)) {
gpregeOptions$indexRange <- 1:dim(data)[1]
}
n = length(gpregeOptions$indexRange)
if (is.null(gpregeOptions$explore)) {
gpregeOptions$explore <- FALSE
} else {
if ((gpregeOptions$explore) && is.null(gpregeOptions$exhaustPlotRes)) {
gpregeOptions$exhaustPlotRes <- 20
}
if ((gpregeOptions$explore) && is.null(gpregeOptions$exhaustPlotMaxWidth)) {
gpregeOptions$exhaustPlotMaxWidth <- 30
}
}
if (is.null(gpregeOptions$iters)) {
gpregeOptions$iters <- 100
}
if (is.null(gpregeOptions$display)) {
gpregeOptions$display <- FALSE
}
gpregeOutput <- list()
if (!is.null(gpregeOptions$interpolatedT)) {
interpolate <- TRUE
newLength = dim(data)[2] + length(gpregeOptions$interpolatedT)
gpregeOutput$interpolatedData <- matrix(0,newLength, n)
} else {
interpolate <- FALSE
}
if (is.null(gpregeOptions$inithypers)) {
gpregeOptions$inithypers <- matrix( c(1/1000, 0, 1, 1/8, 0.999, 1e-3), ncol=3, byrow=TRUE)
}
npsets <- dim(gpregeOptions$inithypers)[1] ## Number of hparams sets.
if (is.null(gpregeOptions$labels)) {
gpregeOptions$labels <- rep(0,n)
}
options <- .gpOptions() ## Set up model.
options$kern$comp <- list("rbf","white")
x <- inputs
xstar <- matrix(seq(min(x)-(2*(max(x)-min(x))/100), max(x)+((max(x)-min(x))/100), length=100), ncol=1)
models <- list() ## Allocate space for vectors.
loghypers <- matrix(0, 3, npsets)
LMLs <- matrix(0, n, npsets)
signalvar <- matrix(0, n, 1); noisevar <- matrix(0, n, 1); width <- matrix(0, n, 1)
## Remove mean across timepoints. Dataset should not be standardized; Must
## look to the signal variance in the context of all signal variances.
data <- t(as.matrix(scale(t(data), scale=FALSE)))
datamax <- max(data); datamin <- min(data) ## Data min/max for plotting limits.
if (gpregeOptions$explore) {
# graphics.off()
# dev.new(width=5,height=12);
# plot.new() ## Close all devices, open new device, new plot.
# dev.new(width=5,height=5);
# plot.new();
# dev.new(width=5,height=5);
# plot.new()
}
for (ix in 1:n) {
i <- gpregeOptions$indexRange[ix]
y <- matrix(data[i,], ncol=1) ## Column vector.
if (sum(is.nan(y)) > (length(y)/2)) {
cat('Majority of points in profile are NaN.\n')
next
}
options$isMissingData <- any(is.nan(y))
options$isSpherical <- !any(is.nan(y))
stdy = sd(c(y[!is.nan(y)])) ## Profile variance.
## Hyperparameters: inverse-lengthscale, signal-variance, noise-variance.
## Use 1e-3 instead of 0, or R might coerse them into NaN.
# inithypers = t(2 * log(gpregeOptions$inithypers %*% diag(c(1, stdy, stdy))))
inithypers = t( log( gpregeOptions$inithypers %*% diag(c(1, stdy^2, stdy^2)) ) )
# lles = c(1000,8,20)
# inithypers = matrix(2*log(c(1e-3, 1e-3, stdy # 1/1.0 (stdy*1e-3) (stdy*0.999)
# , 1/8.0, (stdy*0.999), (stdy*1e-3)
# , 1/20.0, (stdy*0.999), (stdy*1e-3)
# )), nrow=3)
if (gpregeOptions$explore) {
# dev.set(2)
pdf(file=paste('gpPlot',ix,'.pdf',sep=''), paper="special", width=6, height=4*npsets)
close.screen(all.screens = TRUE)
split.screen(c(dim(inithypers)[2],1)) ## Reset any existing sub-figures setup.
#nf = layout(matrix(c(1:dim(inithypers)[2]), 1:dim(inithypers)[2], 1)); layout.show(nf)
}
## Optimise GP log likelihoods.
for (h in 1:npsets) {
models[[h]] <- .gpCreate(dim(x)[2], dim(y)[2], x, y, options)
models[[h]] <- .gpExpandParam(models[[h]], inithypers[, h]) ## This forces kernel computation.
if (h != 1) {
models[[h]] <- .gpOptimise(models[[h]], gpregeOptions$display, gpregeOptions$iters)
loghypers[, h] <- .gpExtractParam(models[[h]], only.values=FALSE)
}
LMLs[ix, h] <- .gpLogLikelihood(models[[h]]) ## GP log-marginal likelihood for model h.
if (gpregeOptions$explore) { ## Plot the regression...
screen(h); erase.screen(h) ## ...in sub-figure #h. Clear screen.
.gpPlot(models[[h]], xstar, col='blue', xlim=range(xstar), ylim=c(datamin, datamax),
title=paste("Init. length-scale = ", as.character(1/exp(inithypers[1,h]/2)), sep=""),
xlab='time(mins)', ylab=bquote(paste(log[2]~expression~(centred))))
}
}
## Save maximum log-marginal likelihood and respective hyper-parameters.
maxLML <- max(LMLs[ix, ]); mi <- which.max(LMLs[ix, ])
bestLoghypers <- loghypers[, mi]
width[ix] <- 1/exp(bestLoghypers[1]/2)
signalvar[ix] <- exp(bestLoghypers[2]/2)
noisevar[ix] <- exp(bestLoghypers[3]/2)
if (interpolate) {
meanVar <- .gpPosteriorMeanVar(models[[mi]], gpregeOptions$interpolatedT, varsigma.return=TRUE)
mu <- meanVar$mu; S <- meanVar$varsigma
## Add noise sampled from a Gaussian distribution with zero
## mean and variance equal to the predictive variance on new inputs.
mu <- mu + matrix(rnorm(length(mu)), ncol=1) * noisevar[ix]
gpregeOutput$interpolatedData[, ix] <- c(y, mu)
sortedInputs = sort(c(x, gpregeOutput$interpolatedT))
idx = sortedInputs$ix #sortedInputs = sortedInputs$x
gpregeOutput$interpolatedData[, ix] = gpregeOutput$interpolatedData[idx, ix] ## Order by augmented inputs.
}
if (gpregeOptions$explore) {
if (interpolate) {
points(gpregeOutput$interpolatedT, mu, pch = 4, cex = .5, lwd=2, col = 'blue')
}
cat('\n========================================================\n')
cat(' Profile ', as.character(i), '\t\t\t\tLabel: ', as.character(as.numeric(gpregeOptions$labels[i])))
cat('\n========================================================\n')
cat(sprintf('%-20s %-20s %s\n', 'Length-scale', 'Signal', 'Noise'))
cat(sprintf('% -20.5f % -20.5f % .5f\n\n', width[ix], signalvar[ix], noisevar[ix]))
cat(sprintf('%-20s %-20s %s\n', 'Init.le', 'LML', 'Best'))
best = replace(rep("",npsets), which(LMLs[ix,]==maxLML), " <--")
for (j in 1:npsets) {
cat(sprintf('% -20.0f % -20.8f %s\n', 1/exp(inithypers[1,j]/2), LMLs[ix, j], best[j], '\n', sep='\t\t'))
}
cat(sprintf('\n%-20s %-20s\n','Total st.dev.','Estim.sig + noise'))
cat(sprintf('% -20f % -20f\n\n', sd(c(y)), sum(exp(bestLoghypers[2:3]/2))))
## We express the profile-ranking metric through a log-ratio of marginal likelihoods.
cat('Log-ratio (max(LML[2:end]) - LML[1])\n ',max(LMLs[ix,2:npsets])-LMLs[ix,1],'\n')
# dev.copy(pdf, file = paste('gpPlot',ix,'.pdf', sep=''))
# dev.set(3)
dev.off()
pdf(file=paste('exhaustivePlot',ix,'.pdf',sep=''), paper="special", width=6, height=6)
C = .exhaustivePlot(y, x, xstar, options, gpregeOptions$exhaustPlotMaxWidth, gpregeOptions$exhaustPlotRes, gpregeOptions$exhaustPlotLevels)
dev.off()
# dev.copy(pdf, file = paste('exhaustivePlot',ix,'.pdf', sep=''))
readline(prompt='ENTER to continue')
} else{
cat(' Profile ', as.character(i), '\n')
}
}
gpregeOutput$signalvar <- signalvar
gpregeOutput$noisevar <- noisevar
gpregeOutput$width <- width
gpregeOutput$LMLs <- LMLs
gpregeOutput$rankingScores = apply(as.matrix(LMLs[,2:npsets]),1,max) - LMLs[,1]
return(gpregeOutput)
}
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Defines functions .gprege
#AGPL-3 License
.gprege <- function(data, inputs, gpregeOptions) {
## GPREGE Gaussian process ranking and estimation of gene expression time-series.
## FORMAT
## DESC Fit two GPs with the an RBF (+ noise diagonal) kernel on each
## profile. One GP kernel is initialised wih a short lengthscale
## hyperparameter, signal variance as the observed variance and a zero noise
## variance. It is optimised via scaled conjugate gradients (netlab). The
## other GP has fixed hyperparameters with a zero inverse-width, zero signal
## variance and noise variance as the observed variance. The log-ratio of
## marginal likelihoods of the two hypotheses acts as a score of
## differential expression for the profile. Comparison via ROC curves is
## performed against BATS (Angelini et.al, 2007).
## See Kalaitzis & Lawrence (2011) for a detailed discussion of the
## ranking algorithm and dataset used.
## ARG data : The matrix of gene expression profiles; one profile per row.
## ARG inputs : Inputs to the GP.
## ARG gpregeOptions$explore: (LOGICAL) Operate in a user interactive mode.
## Used for examining individual gene expression profiles.
## ARG gpregeOptions$labels : Contains flags that specify whether the
## corresponding profile comes from a differentially expressed gene
## (usually from a ground truth).
## ARG gpregeOptions$indexRange : Range of indices of profiles on which the
## function should operate. Useful for selective exploration of specific
## profiles, e.g. only genes marked as differentially expressed in a ground
## truth list.
## ARG gpregeOptions$interpolatedT : New timepoints to interpolate for each
## profile, based on the estimated function values.
## ARG gpregeOptions$iters : The number of iterations for scaled-conjugate
## gradients (SCG) optimisation.
## ARG gpregeOptions$display : Display gradient and LML information on each
## SCG iteration.
## ARG gpregeOptions$inithypers : The matrix of hyperparameter
## configurations as its rows:
## [inverse-lengthscale percent-signal-variance percent-noise-variance]
## The first row corresponds to a (practically constant) function
## with a very large lengthscale. Such a function will account for 0 percent
## of the observed variance in the expression profile (hence 0 for signal)
## and explain it as noise (hence 1 for noise). Subsequent rows
## (initialisations for SCG optimisation) correspond to functions of various
## lengthscales that explain all the observed variance as signal. A
## reasonable lengthscale would be roughly in line with the time-point
## sampling intervals.
## ARG gpregeOptions$exhaustPlotRes : The search resolution. Used for
## interactive mode (explore == 1).
## ARG gpregeOptions$exhaustPlotLevels : # Exhaustive plot contour levels.
## Used for interactive mode (explore == 1).
## ARG gpregeOptions$exhaustPlotMaxWidth : maximum lengthscale to search
## for. Used for interactive mode (explore == 1).
## RETURN gpregeOutput$signalvar : The vertical lengthscales of the
## optimised RBF kernel for each profile.
## RETURN gpregeOutput$noisevar : Same, for the noise hyperparameter.
## RETURN gpregeOutput$width : Same, for the horizontal lengthscales of the RBF.
## RETURN gpregeOutput$LMLs : Log-marginal likelihood of the GP for each profile.
## RETURN gpregeOutput$interpolatedData : extended dataset with interpolated values.
## RETURN gpregeOutput$rankingScores : the ranking scores based on the
## log-ratio of marginal likelihoods.
##
## USAGE: gpregeOutput <- gprege(exprs_tp63_RMA, seq(0,240,by=20), gpregeOptions)
##
## SEEALSO : gpOptions, gpCreate, gpExpandParam, gpOptimise, gpExtractParam,
## gpLogLikelihood, gpPosteriorMeanVar
##
## COPYRIGHT: Alfredo A. Kalaitzis, 2010, 2011
##
## GPREGE
##
if (missing(data))
stop('Missing data.')
if (missing(inputs)) {
stop('Missing inputs.')
}
if (is.null(gpregeOptions$indexRange)) {
gpregeOptions$indexRange <- 1:dim(data)[1]
}
n = length(gpregeOptions$indexRange)
if (is.null(gpregeOptions$explore)) {
gpregeOptions$explore <- FALSE
} else {
if ((gpregeOptions$explore) && is.null(gpregeOptions$exhaustPlotRes)) {
gpregeOptions$exhaustPlotRes <- 20
}
if ((gpregeOptions$explore) && is.null(gpregeOptions$exhaustPlotMaxWidth)) {
gpregeOptions$exhaustPlotMaxWidth <- 30
}
}
if (is.null(gpregeOptions$iters)) {
gpregeOptions$iters <- 100
}
if (is.null(gpregeOptions$display)) {
gpregeOptions$display <- FALSE
}
gpregeOutput <- list()
if (!is.null(gpregeOptions$interpolatedT)) {
interpolate <- TRUE
newLength = dim(data)[2] + length(gpregeOptions$interpolatedT)
gpregeOutput$interpolatedData <- matrix(0,newLength, n)
} else {
interpolate <- FALSE
}
if (is.null(gpregeOptions$inithypers)) {
gpregeOptions$inithypers <- matrix( c(1/1000, 0, 1, 1/8, 0.999, 1e-3), ncol=3, byrow=TRUE)
}
npsets <- dim(gpregeOptions$inithypers)[1] ## Number of hparams sets.
if (is.null(gpregeOptions$labels)) {
gpregeOptions$labels <- rep(0,n)
}
options <- .gpOptions() ## Set up model.
options$kern$comp <- list("rbf","white")
x <- inputs
xstar <- matrix(seq(min(x)-(2*(max(x)-min(x))/100), max(x)+((max(x)-min(x))/100), length=100), ncol=1)
models <- list() ## Allocate space for vectors.
loghypers <- matrix(0, 3, npsets)
LMLs <- matrix(0, n, npsets)
signalvar <- matrix(0, n, 1); noisevar <- matrix(0, n, 1); width <- matrix(0, n, 1)
## Remove mean across timepoints. Dataset should not be standardized; Must
## look to the signal variance in the context of all signal variances.
data <- t(as.matrix(scale(t(data), scale=FALSE)))
datamax <- max(data); datamin <- min(data) ## Data min/max for plotting limits.
if (gpregeOptions$explore) {
# graphics.off()
# dev.new(width=5,height=12);
# plot.new() ## Close all devices, open new device, new plot.
# dev.new(width=5,height=5);
# plot.new();
# dev.new(width=5,height=5);
# plot.new()
}
for (ix in 1:n) {
i <- gpregeOptions$indexRange[ix]
y <- matrix(data[i,], ncol=1) ## Column vector.
if (sum(is.nan(y)) > (length(y)/2)) {
cat('Majority of points in profile are NaN.\n')
next
}
options$isMissingData <- any(is.nan(y))
options$isSpherical <- !any(is.nan(y))
stdy = sd(c(y[!is.nan(y)])) ## Profile variance.
## Hyperparameters: inverse-lengthscale, signal-variance, noise-variance.
## Use 1e-3 instead of 0, or R might coerse them into NaN.
# inithypers = t(2 * log(gpregeOptions$inithypers %*% diag(c(1, stdy, stdy))))
inithypers = t( log( gpregeOptions$inithypers %*% diag(c(1, stdy^2, stdy^2)) ) )
# lles = c(1000,8,20)
# inithypers = matrix(2*log(c(1e-3, 1e-3, stdy # 1/1.0 (stdy*1e-3) (stdy*0.999)
# , 1/8.0, (stdy*0.999), (stdy*1e-3)
# , 1/20.0, (stdy*0.999), (stdy*1e-3)
# )), nrow=3)
if (gpregeOptions$explore) {
# dev.set(2)
pdf(file=paste('gpPlot',ix,'.pdf',sep=''), paper="special", width=6, height=4*npsets)
close.screen(all.screens = TRUE)
split.screen(c(dim(inithypers)[2],1)) ## Reset any existing sub-figures setup.
#nf = layout(matrix(c(1:dim(inithypers)[2]), 1:dim(inithypers)[2], 1)); layout.show(nf)
}
## Optimise GP log likelihoods.
for (h in 1:npsets) {
models[[h]] <- .gpCreate(dim(x)[2], dim(y)[2], x, y, options)
models[[h]] <- .gpExpandParam(models[[h]], inithypers[, h]) ## This forces kernel computation.
if (h != 1) {
models[[h]] <- .gpOptimise(models[[h]], gpregeOptions$display, gpregeOptions$iters)
loghypers[, h] <- .gpExtractParam(models[[h]], only.values=FALSE)
}
LMLs[ix, h] <- .gpLogLikelihood(models[[h]]) ## GP log-marginal likelihood for model h.
if (gpregeOptions$explore) { ## Plot the regression...
screen(h); erase.screen(h) ## ...in sub-figure #h. Clear screen.
.gpPlot(models[[h]], xstar, col='blue', xlim=range(xstar), ylim=c(datamin, datamax),
title=paste("Init. length-scale = ", as.character(1/exp(inithypers[1,h]/2)), sep=""),
xlab='time(mins)', ylab=bquote(paste(log[2]~expression~(centred))))
}
}
## Save maximum log-marginal likelihood and respective hyper-parameters.
maxLML <- max(LMLs[ix, ]); mi <- which.max(LMLs[ix, ])
bestLoghypers <- loghypers[, mi]
width[ix] <- 1/exp(bestLoghypers[1]/2)
signalvar[ix] <- exp(bestLoghypers[2]/2)
noisevar[ix] <- exp(bestLoghypers[3]/2)
if (interpolate) {
meanVar <- .gpPosteriorMeanVar(models[[mi]], gpregeOptions$interpolatedT, varsigma.return=TRUE)
mu <- meanVar$mu; S <- meanVar$varsigma
## Add noise sampled from a Gaussian distribution with zero
## mean and variance equal to the predictive variance on new inputs.
mu <- mu + matrix(rnorm(length(mu)), ncol=1) * noisevar[ix]
gpregeOutput$interpolatedData[, ix] <- c(y, mu)
sortedInputs = sort(c(x, gpregeOutput$interpolatedT))
idx = sortedInputs$ix #sortedInputs = sortedInputs$x
gpregeOutput$interpolatedData[, ix] = gpregeOutput$interpolatedData[idx, ix] ## Order by augmented inputs.
}
if (gpregeOptions$explore) {
if (interpolate) {
points(gpregeOutput$interpolatedT, mu, pch = 4, cex = .5, lwd=2, col = 'blue')
}
cat('\n========================================================\n')
cat(' Profile ', as.character(i), '\t\t\t\tLabel: ', as.character(as.numeric(gpregeOptions$labels[i])))
cat('\n========================================================\n')
cat(sprintf('%-20s %-20s %s\n', 'Length-scale', 'Signal', 'Noise'))
cat(sprintf('% -20.5f % -20.5f % .5f\n\n', width[ix], signalvar[ix], noisevar[ix]))
cat(sprintf('%-20s %-20s %s\n', 'Init.le', 'LML', 'Best'))
best = replace(rep("",npsets), which(LMLs[ix,]==maxLML), " <--")
for (j in 1:npsets) {
cat(sprintf('% -20.0f % -20.8f %s\n', 1/exp(inithypers[1,j]/2), LMLs[ix, j], best[j], '\n', sep='\t\t'))
}
cat(sprintf('\n%-20s %-20s\n','Total st.dev.','Estim.sig + noise'))
cat(sprintf('% -20f % -20f\n\n', sd(c(y)), sum(exp(bestLoghypers[2:3]/2))))
## We express the profile-ranking metric through a log-ratio of marginal likelihoods.
cat('Log-ratio (max(LML[2:end]) - LML[1])\n ',max(LMLs[ix,2:npsets])-LMLs[ix,1],'\n')
# dev.copy(pdf, file = paste('gpPlot',ix,'.pdf', sep=''))
# dev.set(3)
dev.off()
pdf(file=paste('exhaustivePlot',ix,'.pdf',sep=''), paper="special", width=6, height=6)
C = .exhaustivePlot(y, x, xstar, options, gpregeOptions$exhaustPlotMaxWidth, gpregeOptions$exhaustPlotRes, gpregeOptions$exhaustPlotLevels)
dev.off()
# dev.copy(pdf, file = paste('exhaustivePlot',ix,'.pdf', sep=''))
readline(prompt='ENTER to continue')
} else{
cat(' Profile ', as.character(i), '\n')
}
}
gpregeOutput$signalvar <- signalvar
gpregeOutput$noisevar <- noisevar
gpregeOutput$width <- width
gpregeOutput$LMLs <- LMLs
gpregeOutput$rankingScores = apply(as.matrix(LMLs[,2:npsets]),1,max) - LMLs[,1]
return(gpregeOutput)
}
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