Package 'nethet'

Title:	A bioconductor package for high-dimensional exploration of biological network heterogeneity
Description:	Package nethet is an implementation of statistical solid methodology enabling the analysis of network heterogeneity from high-dimensional data. It combines several implementations of recent statistical innovations useful for estimation and comparison of networks in a heterogeneous, high-dimensional setting. In particular, we provide code for formal two-sample testing in Gaussian graphical models (differential network and GGM-GSA; Stadler and Mukherjee, 2013, 2014) and make a novel network-based clustering algorithm available (mixed graphical lasso, Stadler and Mukherjee, 2013).
Authors:	Nicolas Staedler, Frank Dondelinger
Maintainer:	Nicolas Staedler <[email protected]>, Frank Dondelinger <[email protected]>
License:	GPL-2
Version:	1.37.0
Built:	2024-07-02 05:07:01 UTC
Source:	https://github.com/bioc/nethet

Help Index

NetHet-package
Meinshausen p-value aggregation
bwprun_mixglasso
Differential Network
Differential Network for user specified data splits
Differential Regression (multi-split version).
Computation "split-asym" p-values.
Differential Regression (single-split version).
Create a plot showing the edges with the highest partial correlation in any cluster.
Export networks as a CSV table.
Generate sparse invcov with overlap
generate_inv_cov
Multi-split GGMGSA (parallelized computation)
Single-split GGMGSA
Irizarry approach for gene-set testing
Cross-validated glasso on heterogeneous dataset with grouping
Convert inverse covariance to partial correlation
Convert inverse covariance to partial correlation for several inverse covariance matrices collected in an array.
Log-likelihood-ratio statistics used in DiffNet
mixglasso
mixglasso_init
Plot two networks (GGMs)
Plotting function for object of class 'diffnet'
Plotting function for object of class 'diffregr'
Plotting function for object of class 'ggmgmsa'
Plot networks
Print function for object of class 'nethetsummmary'
Create a scatterplot showing correlation between specific nodes in the network for each pre-specified group.
AIC-tuned glasso with additional thresholding
BIC-tuned glasso with additional thresholding
Cross-validated glasso with additional thresholding
Cross-validated Lasso screening (lambda.1se-rule)
Cross-validated Lasso screening and upper bound on number of predictors.
Cross-validation lasso screening (lambda.min-rule)
Cross-validated Lasso screening and sqrt-truncation.
Cross-validated Lasso screening and additional truncation.
Simulate from mixture model.
sim_mix_networks
Summary function for object of class 'diffnet'
Summary function for object of class 'diffregr'
Summary function for object of class 'ggmgsa'
Summary function for object of class 'nethetclustering'

NetHet-package

Description

A bioconductor package for high-dimensional exploration of biological network heterogeneity

Details

Includes: *Network-based clustering (MixGLasso) *Differential network (DiffNet) *Differential regression (DiffRegr) *Gene-set analysis based on graphical models (GGMGSA) *Plotting functions for exploring network heterogeneity

References

St\"adler, N. and Mukherjee, S. (2013). Two-Sample Testing in High-Dimensional Models. Preprint http://arxiv.org/abs/1210.4584.

Meinshausen p-value aggregation

Description

Meinshausen p-value aggregation.

Usage

aggpval(pval, gamma.min = 0.05)
aggpval(pval, gamma.min = 0.05)

Arguments

`pval`	Vector of p-values.
`gamma.min`	See inf-quantile formula of Meinshausen et al 2009 (default=0.05).

Details

Inf-quantile formula for p-value aggregation presented in Meinshausen et al 2009.

Value

Aggregated p-value.

Author(s)

n.stadler

Examples

pval=runif(50)
aggpval(pval)
pval=runif(50)
aggpval(pval)

bwprun_mixglasso

Description

Mixglasso with backward pruning

Usage

bwprun_mixglasso(x, n.comp.min = 1, n.comp.max, lambda = sqrt(2 *
  nrow(x) * log(ncol(x)))/2, pen = "glasso.parcor",
  selection.crit = "mmdl", term = 10^{     -3 }, min.compsize = 5,
  init = "kmeans.hc", my.cl = NULL, modelname.hc = "VVV",
  nstart.kmeans = 1, iter.max.kmeans = 10, reinit.out = FALSE,
  reinit.in = FALSE, mer = TRUE, del = TRUE, ...)
bwprun_mixglasso(x, n.comp.min = 1, n.comp.max, lambda = sqrt(2 *
  nrow(x) * log(ncol(x)))/2, pen = "glasso.parcor",
  selection.crit = "mmdl", term = 10^{     -3 }, min.compsize = 5,
  init = "kmeans.hc", my.cl = NULL, modelname.hc = "VVV",
  nstart.kmeans = 1, iter.max.kmeans = 10, reinit.out = FALSE,
  reinit.in = FALSE, mer = TRUE, del = TRUE, ...)

Arguments

`x`	Input data matrix
`n.comp.min`	Minimum number of components. Take n.comp.min=1 !
`n.comp.max`	Maximum number of components
`lambda`	Regularization parameter. Default=sqrt(2nlog(p))/2
`pen`	Determines form of penalty: glasso.parcor (default), glasso.invcov, glasso.invcor
`selection.crit`	Selection criterion. Default='mmdl'
`term`	Termination criterion of EM algorithm. Default=10^-3
`min.compsize`	Stop EM if any(compsize)<min.compsize; Default=5
`init`	Initialization. Method used for initialization init='cl.init','r.means','random','kmeans','kmeans.hc','hc'. Default='kmeans.hc'
`my.cl`	Initial cluster assignments; need to be provided if init='cl.init' (otherwise this param is ignored). Default=NULL
`modelname.hc`	Model class used in hc. Default="VVV"
`nstart.kmeans`	Number of random starts in kmeans; default=1
`iter.max.kmeans`	Maximal number of iteration in kmeans; default=10
`reinit.out`	Re-initialization if compsize<min.compsize (at the start of algorithm) ?
`reinit.in`	Re-initialization if compsize<min.compsize (at the bwprun-loop level of algorithm) ?
`mer`	Merge closest comps for initialization
`del`	Delete smallest comp for initialization
`...`	Other arguments. See mixglasso_init

Details

This function runs mixglasso with various number of mixture components: It starts with a too large number of components and iterates towards solutions with smaller number of components by initializing using previous solutions.

Value

list consisting of

`selcrit`	Selcrit for all models with number of components between n.comp.min and n.comp.max
`res.init`	Initialization for all components
`comp.name`	List of names of components. Indicates which states where merged/deleted during backward pruning
`re.init.in`	Logical vector indicating whether re-initialization was performed or not
`fit.mixgl.selcrit`	Results for model with optimal number of components. List see mixglasso_init

Author(s)

n.stadler

Examples

##generate data
set.seed(1)
n <- 1000
n.comp <- 3
p <- 10

# Create different mean vectors
Mu <- matrix(0,p,n.comp)

nonzero.mean <- split(sample(1:p),rep(1:n.comp,length=p))
for(k in 1:n.comp){
  Mu[nonzero.mean[[k]],k] <- -2/sqrt(ceiling(p/n.comp))
}

sim <- sim_mix_networks(n, p, n.comp, Mu=Mu)

##run mixglasso

fit <-  bwprun_mixglasso(sim$data,n.comp=1,n.comp.max=5,selection.crit='bic')
plot(fit$selcrit,ylab='bic',xlab='Num.Comps',type='b')
##generate data
set.seed(1)
n <- 1000
n.comp <- 3
p <- 10

# Create different mean vectors
Mu <- matrix(0,p,n.comp)

nonzero.mean <- split(sample(1:p),rep(1:n.comp,length=p))
for(k in 1:n.comp){
  Mu[nonzero.mean[[k]],k] <- -2/sqrt(ceiling(p/n.comp))
}

sim <- sim_mix_networks(n, p, n.comp, Mu=Mu)

##run mixglasso

fit <-  bwprun_mixglasso(sim$data,n.comp=1,n.comp.max=5,selection.crit='bic')
plot(fit$selcrit,ylab='bic',xlab='Num.Comps',type='b')

Differential Network

Description

Differential Network

Usage

diffnet_multisplit(x1, x2, b.splits = 50, frac.split = 1/2,
  screen.meth = "screen_bic.glasso", include.mean = FALSE,
  gamma.min = 0.05, compute.evals = "est2.my.ev3",
  algorithm.mleggm = "glasso_rho0", method.compquadform = "imhof",
  acc = 1e-04, epsabs = 1e-10, epsrel = 1e-10, show.warn = FALSE,
  save.mle = FALSE, verbose = TRUE, mc.flag = FALSE,
  mc.set.seed = TRUE, mc.preschedule = TRUE,
  mc.cores = getOption("mc.cores", 2L), ...)
diffnet_multisplit(x1, x2, b.splits = 50, frac.split = 1/2,
  screen.meth = "screen_bic.glasso", include.mean = FALSE,
  gamma.min = 0.05, compute.evals = "est2.my.ev3",
  algorithm.mleggm = "glasso_rho0", method.compquadform = "imhof",
  acc = 1e-04, epsabs = 1e-10, epsrel = 1e-10, show.warn = FALSE,
  save.mle = FALSE, verbose = TRUE, mc.flag = FALSE,
  mc.set.seed = TRUE, mc.preschedule = TRUE,
  mc.cores = getOption("mc.cores", 2L), ...)

Arguments

`x1`	Data-matrix sample 1. You might need to center and scale your data-matrix.
`x2`	Data-matrix sample 1. You might need to center and scale your data-matrix.
`b.splits`	Number of splits (default=50).
`frac.split`	Fraction train-data (screening) / test-data (cleaning) (default=0.5).
`screen.meth`	Screening procedure. Options: 'screen_bic.glasso' (default), 'screen_cv.glasso', 'screen_shrink' (not recommended).
`include.mean`	Should sample specific means be included in hypothesis? Use include.mean=FALSE (default and recommended) which assumes mu1=mu2=0 and tests the hypothesis H0: Omega_1=Omega_2.
`gamma.min`	Tuning parameter in p-value aggregation of Meinshausen et al (2009). (Default=0.05).
`compute.evals`	Method to estimate the weights in the weighted-sum-of-chi2s distribution. The default and (currently) the only available option is the method 'est2.my.ev3'.
`algorithm.mleggm`	Algorithm to compute MLE of GGM. The algorithm 'glasso_rho' is the default and (currently) the only available option.
`method.compquadform`	Method to compute distribution function of weighted-sum-of-chi2s (default='imhof').
`acc`	See ?davies (default 1e-04).
`epsabs`	See ?imhof (default 1e-10).
`epsrel`	See ?imhof (default 1e-10).
`show.warn`	Should warnings be showed (default=FALSE)?
`save.mle`	If TRUE, MLEs (inverse covariance matrices for samples 1 and 2) are saved for all b.splits. The median aggregated inverse covariance matrix is provided in the output as 'medwi'. The default is save.mle=FALSE.
`verbose`	If TRUE, show output progress.
`mc.flag`	If `TRUE` use parallel execution for each b.splits via function `mclapply` of package `parallel`.
`mc.set.seed`	See mclapply. Default=TRUE
`mc.preschedule`	See mclapply. Default=TRUE
`mc.cores`	Number of cores to use in parallel execution. Defaults to mc.cores option if set, or 2 otherwise.
`...`	Additional arguments for screen.meth.

Details

Remark:

* If include.mean=FALSE, then x1 and x2 have mean zero and DiffNet tests the hypothesis H0: Omega_1=Omega_2. You might need to center x1 and x2. * If include.mean=TRUE, then DiffNet tests the hypothesis H0: mu_1=mu_2 & Omega_1=Omega_2 * However, we recommend to set include.mean=FALSE and to test equality of the means separately. * You might also want to scale x1 and x2, if you are only interested in differences due to (partial) correlations.

Value

list consisting of

`ms.pval`	p-values for all b.splits
`ss.pval`	single-split p-value
`medagg.pval`	median aggregated p-value
`meinshagg.pval`	meinshausen aggregated p-value (meinshausen et al 2009)
`teststat`	test statistics for b.splits
`weights.nulldistr`	estimated weights
`active.last`	active-sets obtained in last screening-step
`medwi`	median of inverse covariance matrices over b.splits
`sig.last`	constrained mle (covariance matrix) obtained in last cleaning-step
`wi.last`	constrained mle (inverse covariance matrix) obtained in last cleaning-step

Author(s)

n.stadler

Examples


############################################################
##This example illustrates the use of Differential Network##
############################################################


##set seed
set.seed(1)

##sample size and number of nodes
n <- 40
p <- 10

##specifiy sparse inverse covariance matrices
gen.net <- generate_2networks(p,graph='random',n.nz=rep(p,2),
                              n.nz.common=ceiling(p*0.8))
invcov1 <- gen.net[[1]]
invcov2 <- gen.net[[2]]
plot_2networks(invcov1,invcov2,label.pos=0,label.cex=0.7)

##get corresponding correlation matrices
cor1 <- cov2cor(solve(invcov1))
cor2 <- cov2cor(solve(invcov2))

##generate data under null hypothesis (both datasets have the same underlying
## network)
library('mvtnorm')
x1 <- rmvnorm(n,mean = rep(0,p), sigma = cor1)
x2 <- rmvnorm(n,mean = rep(0,p), sigma = cor1)

##run diffnet (under null hypothesis)
dn.null <- diffnet_multisplit(x1,x2,b.splits=1,verbose=FALSE)
dn.null$ss.pval#single-split p-value

##generate data under alternative hypothesis (datasets have different networks)
x1 <- rmvnorm(n,mean = rep(0,p), sigma = cor1)
x2 <- rmvnorm(n,mean = rep(0,p), sigma = cor2)

##run diffnet (under alternative hypothesis)
dn.altn <- diffnet_multisplit(x1,x2,b.splits=1,verbose=FALSE)
dn.altn$ss.pval#single-split p-value
dn.altn$medagg.pval#median aggregated p-value

##typically we would choose a larger number of splits
# dn.altn <- diffnet_multisplit(x1,x2,b.splits=10,verbose=FALSE)
# dn.altn$ms.pval#multi-split p-values
# dn.altn$medagg.pval#median aggregated p-value
# plot(dn.altn)#histogram of single-split p-values
############################################################
##This example illustrates the use of Differential Network##
############################################################


##set seed
set.seed(1)

##sample size and number of nodes
n <- 40
p <- 10

##specifiy sparse inverse covariance matrices
gen.net <- generate_2networks(p,graph='random',n.nz=rep(p,2),
                              n.nz.common=ceiling(p*0.8))
invcov1 <- gen.net[[1]]
invcov2 <- gen.net[[2]]
plot_2networks(invcov1,invcov2,label.pos=0,label.cex=0.7)

##get corresponding correlation matrices
cor1 <- cov2cor(solve(invcov1))
cor2 <- cov2cor(solve(invcov2))

##generate data under null hypothesis (both datasets have the same underlying
## network)
library('mvtnorm')
x1 <- rmvnorm(n,mean = rep(0,p), sigma = cor1)
x2 <- rmvnorm(n,mean = rep(0,p), sigma = cor1)

##run diffnet (under null hypothesis)
dn.null <- diffnet_multisplit(x1,x2,b.splits=1,verbose=FALSE)
dn.null$ss.pval#single-split p-value

##generate data under alternative hypothesis (datasets have different networks)
x1 <- rmvnorm(n,mean = rep(0,p), sigma = cor1)
x2 <- rmvnorm(n,mean = rep(0,p), sigma = cor2)

##run diffnet (under alternative hypothesis)
dn.altn <- diffnet_multisplit(x1,x2,b.splits=1,verbose=FALSE)
dn.altn$ss.pval#single-split p-value
dn.altn$medagg.pval#median aggregated p-value

##typically we would choose a larger number of splits
# dn.altn <- diffnet_multisplit(x1,x2,b.splits=10,verbose=FALSE)
# dn.altn$ms.pval#multi-split p-values
# dn.altn$medagg.pval#median aggregated p-value
# plot(dn.altn)#histogram of single-split p-values

Differential Network for user specified data splits

Description

Differential Network for user specified data splits

Usage

diffnet_singlesplit(x1, x2, split1, split2,
  screen.meth = "screen_bic.glasso", compute.evals = "est2.my.ev3",
  algorithm.mleggm = "glasso_rho0", include.mean = FALSE,
  method.compquadform = "imhof", acc = 1e-04, epsabs = 1e-10,
  epsrel = 1e-10, show.warn = FALSE, save.mle = FALSE, ...)
diffnet_singlesplit(x1, x2, split1, split2,
  screen.meth = "screen_bic.glasso", compute.evals = "est2.my.ev3",
  algorithm.mleggm = "glasso_rho0", include.mean = FALSE,
  method.compquadform = "imhof", acc = 1e-04, epsabs = 1e-10,
  epsrel = 1e-10, show.warn = FALSE, save.mle = FALSE, ...)

Arguments

`x1`	Data-matrix sample 1. You might need to center and scale your data-matrix.
`x2`	Data-matrix sample 2. You might need to center and scale your data-matrix.
`split1`	Samples (condition 1) used in screening step.
`split2`	Samples (condition 2) used in screening step.
`screen.meth`	Screening procedure. Options: 'screen_bic.glasso' (default), 'screen_cv.glasso', 'screen_shrink' (not recommended).
`compute.evals`	Method to estimate the weights in the weighted-sum-of-chi2s distribution. The default and (currently) the only available option is the method 'est2.my.ev3'.
`algorithm.mleggm`	Algorithm to compute MLE of GGM. The algorithm 'glasso_rho' is the default and (currently) the only available option.
`include.mean`	Should sample specific means be included in hypothesis? Use include.mean=FALSE (default and recommended) which assumes mu1=mu2=0 and tests the hypothesis H0: Omega_1=Omega_2.
`method.compquadform`	Method to compute distribution function of weighted-sum-of-chi2s (default='imhof').
`acc`	See ?davies (default 1e-04).
`epsabs`	See ?imhof (default 1e-10).
`epsrel`	See ?imhof (default 1e-10).
`show.warn`	Should warnings be showed (default=FALSE)?
`save.mle`	Should MLEs be in the output list (default=FALSE)?
`...`	Additional arguments for screen.meth.

Details

Remark:

Value

list consisting of

`pval.onesided`	p-value
`pval.twosided`	ignore this output
`teststat`	log-likelihood-ratio test statistic
`weights.nulldistr`	estimated weights
`active`	active-sets obtained in screening-step
`sig`	constrained mle (covariance) obtained in cleaning-step
`wi`	constrained mle (inverse covariance) obtained in cleaning-step
`mu`	mle (mean) obtained in cleaning-step

Author(s)

n.stadler

Examples


##set seed
set.seed(1)

##sample size and number of nodes
n <- 40
p <- 10

##specifiy sparse inverse covariance matrices
gen.net <- generate_2networks(p,graph='random',n.nz=rep(p,2),
                              n.nz.common=ceiling(p*0.8))
invcov1 <- gen.net[[1]]
invcov2 <- gen.net[[2]]
plot_2networks(invcov1,invcov2,label.pos=0,label.cex=0.7)

##get corresponding correlation matrices
cor1 <- cov2cor(solve(invcov1))
cor2 <- cov2cor(solve(invcov2))

##generate data under alternative hypothesis
library('mvtnorm')
x1 <- rmvnorm(n,mean = rep(0,p), sigma = cor1)
x2 <- rmvnorm(n,mean = rep(0,p), sigma = cor2)

##run diffnet
split1 <- sample(1:n,20)#samples for screening (condition 1)
split2 <- sample(1:n,20)#samples for screening (condition 2)
dn <- diffnet_singlesplit(x1,x2,split1,split2)
dn$pval.onesided#p-value
##set seed
set.seed(1)

##sample size and number of nodes
n <- 40
p <- 10

##specifiy sparse inverse covariance matrices
gen.net <- generate_2networks(p,graph='random',n.nz=rep(p,2),
                              n.nz.common=ceiling(p*0.8))
invcov1 <- gen.net[[1]]
invcov2 <- gen.net[[2]]
plot_2networks(invcov1,invcov2,label.pos=0,label.cex=0.7)

##get corresponding correlation matrices
cor1 <- cov2cor(solve(invcov1))
cor2 <- cov2cor(solve(invcov2))

##generate data under alternative hypothesis
library('mvtnorm')
x1 <- rmvnorm(n,mean = rep(0,p), sigma = cor1)
x2 <- rmvnorm(n,mean = rep(0,p), sigma = cor2)

##run diffnet
split1 <- sample(1:n,20)#samples for screening (condition 1)
split2 <- sample(1:n,20)#samples for screening (condition 2)
dn <- diffnet_singlesplit(x1,x2,split1,split2)
dn$pval.onesided#p-value

Differential Regression (multi-split version).

Description

Differential Regression (multi-split version).

Usage

diffregr_multisplit(y1, y2, x1, x2, b.splits = 50, frac.split = 1/2,
  screen.meth = "screen_cvtrunc.lasso", gamma.min = 0.05,
  compute.evals = "est2.my.ev3.diffregr",
  method.compquadform = "imhof", acc = 1e-04, epsabs = 1e-10,
  epsrel = 1e-10, show.warn = FALSE, n.perm = NULL,
  mc.flag = FALSE, mc.set.seed = TRUE, mc.preschedule = TRUE,
  mc.cores = getOption("mc.cores", 2L), ...)
diffregr_multisplit(y1, y2, x1, x2, b.splits = 50, frac.split = 1/2,
  screen.meth = "screen_cvtrunc.lasso", gamma.min = 0.05,
  compute.evals = "est2.my.ev3.diffregr",
  method.compquadform = "imhof", acc = 1e-04, epsabs = 1e-10,
  epsrel = 1e-10, show.warn = FALSE, n.perm = NULL,
  mc.flag = FALSE, mc.set.seed = TRUE, mc.preschedule = TRUE,
  mc.cores = getOption("mc.cores", 2L), ...)

Arguments

`y1`	Response vector condition 1.
`y2`	Response vector condition 2.
`x1`	Predictor matrix condition 1.
`x2`	Predictor matrix condition 2.
`b.splits`	Number of splits (default=50).
`frac.split`	Fraction train-data (screening) / test-data (cleaning) (default=0.5).
`screen.meth`	Screening method (default='screen_cvtrunc.lasso').
`gamma.min`	Tuning parameter in p-value aggregation of Meinshausen et al (2009) (default=0.05).
`compute.evals`	Method to estimate the weights in the weighted-sum-of-chi2s distribution. The default and (currently) the only available option is the method 'est2.my.ev3.diffregr'.
`method.compquadform`	Algorithm for computing distribution function of weighted-sum-of-chi2 (default='imhof').
`acc`	See ?davies (default=1e-4).
`epsabs`	See ?imhof (default=1e-10).
`epsrel`	See ?imhof (default=1e-10).
`show.warn`	Show warnings (default=FALSE)?
`n.perm`	Number of permutation for "split-perm" p-value. Default=NULL, which means that the asymptotic approximation is used.
`mc.flag`	If `TRUE` use parallel execution for each b.splits via function `mclapply` of package `parallel`.
`mc.set.seed`	See mclapply. Default=TRUE
`mc.preschedule`	See mclapply. Default=TRUE
`mc.cores`	Number of cores to use in parallel execution. Defaults to mc.cores option if set, or 2 otherwise.
`...`	Other arguments specific to screen.meth.

Details

Intercepts in regression models are assumed to be zero (mu1=mu2=0). You might need to center the input data prior to running Differential Regression.

Value

List consisting of

`ms.pval`	p-values for all b.splits
`ss.pval`	single-split p-value
`medagg.pval`	median aggregated p-value
`meinshagg.pval`	meinshausen aggregated p-value (meinshausen et al 2009)
`teststat`	test statistics for b.splits
`weights.nulldistr`	estimated weights
`active.last`	active-sets obtained in last screening-step
`beta.last`	constrained mle (regression coefficients) obtained in last cleaning-step

Author(s)

n.stadler

Examples

###############################################################
##This example illustrates the use of Differential Regression##
###############################################################

##set seed
set.seed(1)

## Number of predictors and sample size
p <- 100
n <- 80

## Predictor matrices
x1 <- matrix(rnorm(n*p),n,p)
x2 <- matrix(rnorm(n*p),n,p)

## Active-sets and regression coefficients
act1 <- sample(1:p,5)
act2 <- c(act1[1:3],sample(setdiff(1:p,act1),2))
beta1 <- beta2 <- rep(0,p)
beta1[act1] <- 0.5
beta2[act2] <- 0.5

## Response vectors under null-hypothesis
y1 <- x1%*%as.matrix(beta1)+rnorm(n,sd=1)
y2 <- x2%*%as.matrix(beta1)+rnorm(n,sd=1)

## Diffregr (asymptotic p-values)
fit.null <- diffregr_multisplit(y1,y2,x1,x2,b.splits=5)
fit.null$ms.pval#multi-split p-values
fit.null$medagg.pval#median aggregated p-values

## Response vectors under alternative-hypothesis
y1 <- x1%*%as.matrix(beta1)+rnorm(n,sd=1)
y2 <- x2%*%as.matrix(beta2)+rnorm(n,sd=1)

## Diffregr (asymptotic p-values)
fit.alt <- diffregr_multisplit(y1,y2,x1,x2,b.splits=5)
fit.alt$ms.pval
fit.alt$medagg.pval

## Diffregr (permutation-based p-values; 100 permutations)
fit.alt.perm <- diffregr_multisplit(y1,y2,x1,x2,b.splits=5,n.perm=100)
fit.alt.perm$ms.pval
fit.alt.perm$medagg.pval


###############################################################
##This example illustrates the use of Differential Regression##
###############################################################

##set seed
set.seed(1)

## Number of predictors and sample size
p <- 100
n <- 80

## Predictor matrices
x1 <- matrix(rnorm(n*p),n,p)
x2 <- matrix(rnorm(n*p),n,p)

## Active-sets and regression coefficients
act1 <- sample(1:p,5)
act2 <- c(act1[1:3],sample(setdiff(1:p,act1),2))
beta1 <- beta2 <- rep(0,p)
beta1[act1] <- 0.5
beta2[act2] <- 0.5

## Response vectors under null-hypothesis
y1 <- x1%*%as.matrix(beta1)+rnorm(n,sd=1)
y2 <- x2%*%as.matrix(beta1)+rnorm(n,sd=1)

## Diffregr (asymptotic p-values)
fit.null <- diffregr_multisplit(y1,y2,x1,x2,b.splits=5)
fit.null$ms.pval#multi-split p-values
fit.null$medagg.pval#median aggregated p-values

## Response vectors under alternative-hypothesis
y1 <- x1%*%as.matrix(beta1)+rnorm(n,sd=1)
y2 <- x2%*%as.matrix(beta2)+rnorm(n,sd=1)

## Diffregr (asymptotic p-values)
fit.alt <- diffregr_multisplit(y1,y2,x1,x2,b.splits=5)
fit.alt$ms.pval
fit.alt$medagg.pval

## Diffregr (permutation-based p-values; 100 permutations)
fit.alt.perm <- diffregr_multisplit(y1,y2,x1,x2,b.splits=5,n.perm=100)
fit.alt.perm$ms.pval
fit.alt.perm$medagg.pval

Computation "split-asym" p-values.

Description

Computation "split-asym"/"split-perm" p-values.

Usage

diffregr_pval(y1, y2, x1, x2, beta1, beta2, beta, act1, act2, act,
  compute.evals, method.compquadform, acc, epsabs, epsrel, show.warn,
  n.perm)
diffregr_pval(y1, y2, x1, x2, beta1, beta2, beta, act1, act2, act,
  compute.evals, method.compquadform, acc, epsabs, epsrel, show.warn,
  n.perm)

Arguments

`y1`	Response vector condition 1.
`y2`	Response vector condition 2.
`x1`	Predictor matrix condition 1.
`x2`	Predictor matrix condition 2.
`beta1`	Regression coefficients condition 1.
`beta2`	Regression coefficients condition 2.
`beta`	Pooled regression coefficients.
`act1`	Active-set condition 1.
`act2`	Active-set condition 2.
`act`	Pooled active-set.
`compute.evals`	Method for computation of weights.
`method.compquadform`	Method to compute distribution function of w-sum-of-chi2.
`acc`	See ?davies.
`epsabs`	See ?imhof.
`epsrel`	See ?imhof.
`show.warn`	Show warnings?
`n.perm`	Number of permutations.

Value

P-value, test statistic, estimated weights.

Author(s)

n.stadler

Differential Regression (single-split version).

Description

Differential Regression (single-split version).

Usage

diffregr_singlesplit(y1, y2, x1, x2, split1, split2,
  screen.meth = "screen_cvtrunc.lasso",
  compute.evals = "est2.my.ev3.diffregr",
  method.compquadform = "imhof", acc = 1e-04, epsabs = 1e-10,
  epsrel = 1e-10, show.warn = FALSE, n.perm = NULL, ...)
diffregr_singlesplit(y1, y2, x1, x2, split1, split2,
  screen.meth = "screen_cvtrunc.lasso",
  compute.evals = "est2.my.ev3.diffregr",
  method.compquadform = "imhof", acc = 1e-04, epsabs = 1e-10,
  epsrel = 1e-10, show.warn = FALSE, n.perm = NULL, ...)

Arguments

`y1`	Response vector condition 1.
`y2`	Response vector condition 2.
`x1`	Predictor matrix condition 1.
`x2`	Predictor matrix condition 2.
`split1`	Samples condition 1 used in screening-step.
`split2`	Samples condition 2 used in screening-step.
`screen.meth`	Screening method (default='screen_cvtrunc.lasso').
`compute.evals`	Method to estimate the weights in the weighted-sum-of-chi2s distribution. The default and (currently) the only available option is the method 'est2.my.ev3.diffregr'.
`method.compquadform`	Algorithm for computing distribution function of weighted-sum-of-chi2 (default='imhof').
`acc`	See ?davies (default=1e-4).
`epsabs`	See ?imhof (default=1e-10).
`epsrel`	See ?imhof (default=1e-10).
`show.warn`	Show warnings (default=FALSE)?
`n.perm`	Number of permutation for "split-perm" p-value (default=NULL).
`...`	Other arguments specific to screen.meth.

Details

Intercepts in regression models are assumed to be zero (mu1=mu2=0). You might need to center the input data prior to running Differential Regression.

Value

List consisting of

`pval.onesided`	"One-sided" p-value.
`pval.twosided`	"Two-sided" p-value. Ignore all "*.twosided results.
`teststat`	2 times Log-likelihood-ratio statistics
`weights.nulldistr`	Estimated weights of weighted-sum-of-chi2s.
`active`	List of active-sets obtained in screening step.
`beta`	Regression coefficients (MLE) obtaind in cleaning-step.

Author(s)

n.stadler

Examples


##set seed
set.seed(1)

##number of predictors / sample size
p <- 100
n <- 80

##predictor matrices
x1 <- matrix(rnorm(n*p),n,p)
x2 <- matrix(rnorm(n*p),n,p)

##active-sets and regression coefficients
act1 <- sample(1:p,5)
act2 <- c(act1[1:3],sample(setdiff(1:p,act1),2))
beta1 <- beta2 <- rep(0,p)
beta1[act1] <- 0.5
beta2[act2] <- 0.5

##response vectors 
y1 <- x1%*%as.matrix(beta1)+rnorm(n,sd=1)
y2 <- x2%*%as.matrix(beta2)+rnorm(n,sd=1)

##run diffregr
split1 <- sample(1:n,50)#samples for screening (condition 1)
split2 <- sample(1:n,50)#samples for screening (condition 2)
fit <- diffregr_singlesplit(y1,y2,x1,x2,split1,split2)
fit$pval.onesided#p-value


##set seed
set.seed(1)

##number of predictors / sample size
p <- 100
n <- 80

##predictor matrices
x1 <- matrix(rnorm(n*p),n,p)
x2 <- matrix(rnorm(n*p),n,p)

##active-sets and regression coefficients
act1 <- sample(1:p,5)
act2 <- c(act1[1:3],sample(setdiff(1:p,act1),2))
beta1 <- beta2 <- rep(0,p)
beta1[act1] <- 0.5
beta2[act2] <- 0.5

##response vectors 
y1 <- x1%*%as.matrix(beta1)+rnorm(n,sd=1)
y2 <- x2%*%as.matrix(beta2)+rnorm(n,sd=1)

##run diffregr
split1 <- sample(1:n,50)#samples for screening (condition 1)
split2 <- sample(1:n,50)#samples for screening (condition 2)
fit <- diffregr_singlesplit(y1,y2,x1,x2,split1,split2)
fit$pval.onesided#p-value

Create a plot showing the edges with the highest partial correlation in any cluster.

Description

This function takes the output of het_cv_glasso or mixglasso and creates a plot of the highest scoring edges along the y axis, where, the edge in each cluster is represented by a circle whose area is proportional to the smallest mean of the two nodes that make up the edge, and the position along the y axis shows the partial correlation of the edge.

Usage

dot_plot(net.clustering, p.corrs.thresh = 0.25, hard.limit = 50,
  display = TRUE, node.names = rownames(net.clustering$Mu),
  group.names = sort(unique(net.clustering$comp)),
  dot.size.range = c(3, 12))
dot_plot(net.clustering, p.corrs.thresh = 0.25, hard.limit = 50,
  display = TRUE, node.names = rownames(net.clustering$Mu),
  group.names = sort(unique(net.clustering$comp)),
  dot.size.range = c(3, 12))

Arguments

`net.clustering`	A network clustering object as returned by `het_cv_glasso` or `mixglasso`.
`p.corrs.thresh`	Cutoff for the partial correlations; only edges with absolute partial correlation > p.corrs.thresh (in any cluster) will be displayed.
`hard.limit`	Additional hard limit on the number of edges to display. If p.corrs.thresh results in more edges than hard.limit, only hard.limit edges with the highest partial correlation are returned.
`display`	If TRUE, print the plot to the current output device.
`node.names`	Names for the nodes in the network.
`group.names`	Names for the clusters or groups.
`dot.size.range`	Graphical parameter for scaling the size of the circles (dots) representing an edge in each cluster.

Value

Returns a ggplot2 object. If display=TRUE, additionally displays the plot.

Examples

n = 500
p = 10
s = 0.9
n.comp = 3

# Create different mean vectors
Mu = matrix(0,p,n.comp)

# Define non-zero means in each group (non-overlapping)
nonzero.mean = split(sample(1:p),rep(1:n.comp,length=p))

# Set non-zero means to fixed value
for(k in 1:n.comp){
	Mu[nonzero.mean[[k]],k] = -2/sqrt(ceiling(p/n.comp))
}

# Generate data
sim.result = sim_mix_networks(n, p, n.comp, s, Mu=Mu)
mixglasso.result = mixglasso(sim.result$data, n.comp=3)
mixglasso.clustering = mixglasso.result$models[[mixglasso.result$bic.opt]]

dot_plot(mixglasso.clustering, p.corrs.thresh=0.5)
n = 500
p = 10
s = 0.9
n.comp = 3

# Create different mean vectors
Mu = matrix(0,p,n.comp)

# Define non-zero means in each group (non-overlapping)
nonzero.mean = split(sample(1:p),rep(1:n.comp,length=p))

# Set non-zero means to fixed value
for(k in 1:n.comp){
	Mu[nonzero.mean[[k]],k] = -2/sqrt(ceiling(p/n.comp))
}

# Generate data
sim.result = sim_mix_networks(n, p, n.comp, s, Mu=Mu)
mixglasso.result = mixglasso(sim.result$data, n.comp=3)
mixglasso.clustering = mixglasso.result$models[[mixglasso.result$bic.opt]]

dot_plot(mixglasso.clustering, p.corrs.thresh=0.5)

Export networks as a CSV table.

Description

This function takes the output of het_cv_glasso or mixglasso and exports it as a text table in CSV format, where each entry in the table records an edge in one group and its partial correlation.

Usage

export_network(net.clustering, file = "network_table.csv",
  node.names = rownames(net.clustering$Mu),
  group.names = sort(unique(net.clustering$comp)),
  p.corrs.thresh = 0.2, ...)
export_network(net.clustering, file = "network_table.csv",
  node.names = rownames(net.clustering$Mu),
  group.names = sort(unique(net.clustering$comp)),
  p.corrs.thresh = 0.2, ...)

Arguments

`net.clustering`	A network clustering object as returned by `screen_cv.glasso` or `mixglasso`.
`file`	Filename to save the network table under.
`node.names`	Names for the nodes in the network. If NULL, names from net.clustering will be used.
`group.names`	Names for the clusters or groups. If NULL, names from net.clustering will be used (by default these are integets 1:numClusters).
`p.corrs.thresh`	Threshold applied to the absolute partial correlations. Edges that are below the threshold in all of the groups are not exported. Using a negative value will export all possible edges (including those with zero partial correlation).
`...`	Further parameters passed to write.csv.

Value

Function does not return anything.

Author(s)

Frank Dondelinger

Examples

n = 500
p = 10
s = 0.9
n.comp = 3

# Create different mean vectors
Mu = matrix(0,p,n.comp)

# Define non-zero means in each group (non-overlapping)
nonzero.mean = split(sample(1:p),rep(1:n.comp,length=p))

# Set non-zero means to fixed value
for(k in 1:n.comp){
	Mu[nonzero.mean[[k]],k] = -2/sqrt(ceiling(p/n.comp))
}

# Generate data
sim.result = sim_mix_networks(n, p, n.comp, s, Mu=Mu)
mixglasso.result = mixglasso(sim.result$data, n.comp=3)
mixglasso.clustering = mixglasso.result$models[[mixglasso.result$bic.opt]]

## Not run: 
# Save network in CSV format suitable for Cytoscape import
export_network(mixglasso.clustering, file='nethet_network.csv',
						 p.corrs.thresh=0.25, quote=FALSE)

## End(Not run)
n = 500
p = 10
s = 0.9
n.comp = 3

# Create different mean vectors
Mu = matrix(0,p,n.comp)

# Define non-zero means in each group (non-overlapping)
nonzero.mean = split(sample(1:p),rep(1:n.comp,length=p))

# Set non-zero means to fixed value
for(k in 1:n.comp){
	Mu[nonzero.mean[[k]],k] = -2/sqrt(ceiling(p/n.comp))
}

# Generate data
sim.result = sim_mix_networks(n, p, n.comp, s, Mu=Mu)
mixglasso.result = mixglasso(sim.result$data, n.comp=3)
mixglasso.clustering = mixglasso.result$models[[mixglasso.result$bic.opt]]

## Not run: 
# Save network in CSV format suitable for Cytoscape import
export_network(mixglasso.clustering, file='nethet_network.csv',
						 p.corrs.thresh=0.25, quote=FALSE)

## End(Not run)

Generate sparse invcov with overlap

Description

Generate two sparse inverse covariance matrices with overlap

Usage

generate_2networks(p, graph = "random", n.nz = rep(p, 2),
  n.nz.common = p, n.hub = 2, n.hub.diff = 1, magn.nz.diff = 0.8,
  magn.nz.common = 0.9, magn.diag = 0, emin = 0.1, verbose = FALSE)
generate_2networks(p, graph = "random", n.nz = rep(p, 2),
  n.nz.common = p, n.hub = 2, n.hub.diff = 1, magn.nz.diff = 0.8,
  magn.nz.common = 0.9, magn.diag = 0, emin = 0.1, verbose = FALSE)

Arguments

`p`	number of nodes
`graph`	'random' or 'hub'
`n.nz`	number of edges per graph (only for graph='random')
`n.nz.common`	number of edges incommon between graphs (only for graph='random')
`n.hub`	number of hubs (only for graph='hub')
`n.hub.diff`	number of different hubs
`magn.nz.diff`	default=0.9
`magn.nz.common`	default=0.9
`magn.diag`	default=0
`emin`	default=0.1 (see ?huge.generator)
`verbose`	If verbose=FALSE then tracing output is disabled.

Value

Two sparse inverse covariance matrices with overlap

Examples

n <- 70
p <- 30

## Specifiy sparse inverse covariance matrices,
## with number of edges in common equal to ~ 0.8*p
gen.net <- generate_2networks(p,graph='random',n.nz=rep(p,2),
                              n.nz.common=ceiling(p*0.8))

invcov1 <- gen.net[[1]]
invcov2 <- gen.net[[2]]

plot_2networks(invcov1,invcov2,label.pos=0,label.cex=0.7)
n <- 70
p <- 30

## Specifiy sparse inverse covariance matrices,
## with number of edges in common equal to ~ 0.8*p
gen.net <- generate_2networks(p,graph='random',n.nz=rep(p,2),
                              n.nz.common=ceiling(p*0.8))

invcov1 <- gen.net[[1]]
invcov2 <- gen.net[[2]]

plot_2networks(invcov1,invcov2,label.pos=0,label.cex=0.7)

generate_inv_cov

Description

Generate an inverse covariance matrix with a given sparsity and dimensionality

Usage

generate_inv_cov(p = 162, sparsity = 0.7)
generate_inv_cov(p = 162, sparsity = 0.7)

Arguments

`p`	Dimensionality of the matrix.
`sparsity`	Determined the proportion of non-zero off-diagonal entries.

Details

This function generates an inverse covariance matrix, with at most (1-sparsity)*p(p-1) non-zero off-diagonal entries, where the non-zero entries are sampled from a beta distribution.

Value

A p by p positive definite inverse covariance matrix.

Examples

generate_inv_cov(p=162)
generate_inv_cov(p=162)

Multi-split GGMGSA (parallelized computation)

Description

Multi-split GGMGSA (parallelized computation)

Usage

ggmgsa_multisplit(x1, x2, b.splits = 50, gene.sets, gene.names,
  gs.names = NULL, method.p.adjust = "fdr",
  order.adj.agg = "agg-adj", mc.flag = FALSE, mc.set.seed = TRUE,
  mc.preschedule = TRUE, mc.cores = getOption("mc.cores", 2L),
  verbose = TRUE, ...)
ggmgsa_multisplit(x1, x2, b.splits = 50, gene.sets, gene.names,
  gs.names = NULL, method.p.adjust = "fdr",
  order.adj.agg = "agg-adj", mc.flag = FALSE, mc.set.seed = TRUE,
  mc.preschedule = TRUE, mc.cores = getOption("mc.cores", 2L),
  verbose = TRUE, ...)

Arguments

`x1`	Expression matrix for condition 1 (mean zero is required).
`x2`	Expression matrix for condition 2 (mean zero is required).
`b.splits`	Number of random data splits (default=50).
`gene.sets`	List of gene-sets.
`gene.names`	Gene names. Each column in x1 (and x2) corresponds to a gene.
`gs.names`	Gene-set names (default=NULL).
`method.p.adjust`	Method for p-value adjustment (default='fdr').
`order.adj.agg`	Order of aggregation and adjustment of p-values. Options: 'agg-adj' (default), 'adj-agg'.
`mc.flag`	If `TRUE` use parallel execution for each b.splits via function `mclapply` of package `parallel`.
`mc.set.seed`	See mclapply. Default=TRUE
`mc.preschedule`	See mclapply. Default=TRUE
`mc.cores`	Number of cores to use in parallel execution. Defaults to mc.cores option if set, or 2 otherwise.
`verbose`	If TRUE, show output progess.
`...`	Other arguments (see diffnet_singlesplit).

Details

Computation can be parallelized over many data splits.

Value

List consisting of

`medagg.pval`	Median aggregated p-values
`meinshagg.pval`	Meinshausen aggregated p-values
`pval`	matrix of p-values before correction and adjustement, dim(pval)=(number of gene-sets)x(number of splits)
`teststatmed`	median aggregated test-statistic
`teststatmed.bic`	median aggregated bic-corrected test-statistic
`teststatmed.aic`	median aggregated aic-corrected test-statistic
`teststat`	matrix of test-statistics, dim(teststat)=(number of gene-sets)x(number of splits)
`rel.edgeinter`	normalized intersection of edges in condition 1 and 2
`df1`	degrees of freedom of GGM obtained from condition 1
`df2`	degrees of freedom of GGM obtained from condition 2
`df12`	degrees of freedom of GGM obtained from pooled data (condition 1 and 2)

Author(s)

n.stadler

Examples

#######################################################
##This example illustrates the use of GGMGSA         ##
#######################################################


## Generate networks
set.seed(1)
p <- 9#network with p nodes
n <- 40
hub.net <- generate_2networks(p,graph='hub',n.hub=3,n.hub.diff=1)#generate hub networks
invcov1 <- hub.net[[1]]
invcov2 <- hub.net[[2]]
plot_2networks(invcov1,invcov2,label.pos=0,label.cex=0.7)

## Generate data
library('mvtnorm')
x1 <- rmvnorm(n,mean = rep(0,p), sigma = cov2cor(solve(invcov1)))
x2 <- rmvnorm(n,mean = rep(0,p), sigma = cov2cor(solve(invcov2)))

## Run DiffNet
# fit.dn <- diffnet_multisplit(x1,x2,b.splits=2,verbose=FALSE)
# fit.dn$medagg.pval

## Identify hubs with 'gene-sets'
gene.names <- paste('G',1:p,sep='')
gsets <- split(gene.names,rep(1:3,each=3))

## Run GGM-GSA
fit.ggmgsa <- ggmgsa_multisplit(x1,x2,b.splits=2,gsets,gene.names,verbose=FALSE)
summary(fit.ggmgsa)
fit.ggmgsa$medagg.pval#median aggregated p-values
p.adjust(apply(fit.ggmgsa$pval,1,median),method='fdr')#or: first median aggregation,
                                                      #second fdr-correction






#######################################################
##This example illustrates the use of GGMGSA         ##
#######################################################


## Generate networks
set.seed(1)
p <- 9#network with p nodes
n <- 40
hub.net <- generate_2networks(p,graph='hub',n.hub=3,n.hub.diff=1)#generate hub networks
invcov1 <- hub.net[[1]]
invcov2 <- hub.net[[2]]
plot_2networks(invcov1,invcov2,label.pos=0,label.cex=0.7)

## Generate data
library('mvtnorm')
x1 <- rmvnorm(n,mean = rep(0,p), sigma = cov2cor(solve(invcov1)))
x2 <- rmvnorm(n,mean = rep(0,p), sigma = cov2cor(solve(invcov2)))

## Run DiffNet
# fit.dn <- diffnet_multisplit(x1,x2,b.splits=2,verbose=FALSE)
# fit.dn$medagg.pval

## Identify hubs with 'gene-sets'
gene.names <- paste('G',1:p,sep='')
gsets <- split(gene.names,rep(1:3,each=3))

## Run GGM-GSA
fit.ggmgsa <- ggmgsa_multisplit(x1,x2,b.splits=2,gsets,gene.names,verbose=FALSE)
summary(fit.ggmgsa)
fit.ggmgsa$medagg.pval#median aggregated p-values
p.adjust(apply(fit.ggmgsa$pval,1,median),method='fdr')#or: first median aggregation,
                                                      #second fdr-correction

Single-split GGMGSA

Description

Single-split GGMGSA

Usage

ggmgsa_singlesplit(x1, x2, gene.sets, gene.names,
  method.p.adjust = "fdr", verbose = TRUE, ...)
ggmgsa_singlesplit(x1, x2, gene.sets, gene.names,
  method.p.adjust = "fdr", verbose = TRUE, ...)

Arguments

`x1`	centered (scaled) data for condition 1
`x2`	centered (scaled) data for condition 2
`gene.sets`	List of gene-sets.
`gene.names`	Gene names. Each column in x1 (and x2) corresponds to a gene.
`method.p.adjust`	Method for p-value adjustment (default='fdr').
`verbose`	If TRUE, show output progess.
`...`	Other arguments (see diffnet_singlesplit).

Value

List of results.

Author(s)

n.stadler

Irizarry approach for gene-set testing

Description

Irizarry approach for gene-set testing

Usage

gsea.iriz(x1, x2, gene.sets, gene.names, gs.names = NULL,
  method.p.adjust = "fdr", alternative = "two-sided")
gsea.iriz(x1, x2, gene.sets, gene.names, gs.names = NULL,
  method.p.adjust = "fdr", alternative = "two-sided")

Arguments

`x1`	Expression matrix (condition 1)
`x2`	Expression matrix (condition 2)
`gene.sets`	List of gene-sets
`gene.names`	Gene names
`gs.names`	Gene-set names
`method.p.adjust`	Method for p-value adjustment (default='fdr')
`alternative`	Default='two-sided' (uses two-sided p-values).

Details

Implements the approach described in "Gene set enrichment analysis made simple" by Irizarry et al (2011). It tests for shift and/or change in scale of the distribution.

Value

List consisting of

`pval.shift`	p-values measuring shift
`pval.scale`	p-values measuring scale
`pval.combined`	combined p-values (minimum of pval.shift and pval.scale)

Author(s)

n.stadler

Examples

n <- 100
p <- 20
x1 <- matrix(rnorm(n*p),n,p)
x2 <- matrix(rnorm(n*p),n,p)
gene.names <- paste('G',1:p,sep='')
gsets <- split(gene.names,rep(1:4,each=5))
fit <- gsea.iriz(x1,x2,gsets,gene.names)
fit$pvals.combined

x2[,1:3] <- x2[,1:3]+0.5#variables 1-3 of first gene-set are upregulated
fit <- gsea.iriz(x1,x2,gsets,gene.names)
fit$pvals.combined
n <- 100
p <- 20
x1 <- matrix(rnorm(n*p),n,p)
x2 <- matrix(rnorm(n*p),n,p)
gene.names <- paste('G',1:p,sep='')
gsets <- split(gene.names,rep(1:4,each=5))
fit <- gsea.iriz(x1,x2,gsets,gene.names)
fit$pvals.combined

x2[,1:3] <- x2[,1:3]+0.5#variables 1-3 of first gene-set are upregulated
fit <- gsea.iriz(x1,x2,gsets,gene.names)
fit$pvals.combined

Cross-validated glasso on heterogeneous dataset with grouping

Description

Run glasso on a heterogeneous dataset to obtain networks (inverse covariance matrices) of the variables in the dataset for each pre-specified group of samples.

Usage

het_cv_glasso(data, grouping = rep(1, dim(data)[1]), mc.flag = FALSE,
  use.package = "huge", normalise = FALSE, verbose = FALSE, ...)
het_cv_glasso(data, grouping = rep(1, dim(data)[1]), mc.flag = FALSE,
  use.package = "huge", normalise = FALSE, verbose = FALSE, ...)

Arguments

`data`	The heterogenous network data. Needs to be a num.samples by dim.samples matrix or dataframe.
`grouping`	The grouping of samples; a vector of length num.samples, with num.groups unique elements.
`mc.flag`	Whether to use parallel processing via package mclapply to distribute the glasso estimation over different groups.
`use.package`	'glasso' for glasso package, or 'huge' for huge package (default)
`normalise`	If TRUE, normalise the columns of the data matrix before running glasso.
`verbose`	If TRUE, output progress.
`...`	Further parameters to be passed to `screen_cv.glasso`.

Details

This function runs the graphical lasso with cross-validation to determine the best parameter lambda for each group of samples. Note that this function defaults to using package huge (rather than package glasso) unless otherwise specified, as it tends to be more numerically stable.

Value

Returns a list with named elements 'Sig', 'SigInv', 'Mu', 'Sigma.diag', 'group.names' and 'var.names. The variables Sig and SigInv are arrays of size dim.samples by dim.samples by num.groups, where the first two dimensions contain the (inverse) covariance matrix for the network obtained by running glasso on group k. Variables Mu and Sigma.diag contain the mean and variance of the input data, and group.names and var.names contains the names for the groups and variables in the data (if specified as colnames of the input data matrix).

Examples

n = 100
p = 25

# Generate networks with random means and covariances. 
sim.result = sim_mix_networks(n, p, n.comp=3)

test.data = sim.result$data
test.labels = sim.result$comp

# Reconstruct networks for each component
networks = het_cv_glasso(data=test.data, grouping=test.labels) 
n = 100
p = 25

# Generate networks with random means and covariances. 
sim.result = sim_mix_networks(n, p, n.comp=3)

test.data = sim.result$data
test.labels = sim.result$comp

# Reconstruct networks for each component
networks = het_cv_glasso(data=test.data, grouping=test.labels)

Convert inverse covariance to partial correlation

Description

Convert inverse covariance to partial correlation

Usage

invcov2parcor(invcov)
invcov2parcor(invcov)

Arguments

invcov

Inverse covariance matrix

Value

The partial correlation matrix.

Examples

inv.cov = generate_inv_cov(p=25)
p.corr = invcov2parcor(inv.cov)
inv.cov = generate_inv_cov(p=25)
p.corr = invcov2parcor(inv.cov)

Convert inverse covariance to partial correlation for several inverse covariance matrices collected in an array.

Description

Convert inverse covariance to partial correlation for several inverse covariance matrices collected in an array.

Usage

invcov2parcor_array(invcov.array)
invcov2parcor_array(invcov.array)

Arguments

invcov.array

Array of inverse covariance matrices, of dimension numNodes by numNodes by numComps.

Value

Array of partial correlation matrices of dimension numNodes by numNodes by numComps

Examples

invcov.array = sapply(1:5, function(x) generate_inv_cov(p=25), simplify='array')
p.corr = invcov2parcor_array(invcov.array)
invcov.array = sapply(1:5, function(x) generate_inv_cov(p=25), simplify='array')
p.corr = invcov2parcor_array(invcov.array)

Log-likelihood-ratio statistics used in DiffNet

Description

Log-likelihood-ratio statistics used in Differential Network

Usage

logratio(x1, x2, x, sig1, sig2, sig, mu1, mu2, mu)
logratio(x1, x2, x, sig1, sig2, sig, mu1, mu2, mu)

Arguments

`x1`	data-matrix sample 1
`x2`	data-matrix sample 2
`x`	pooled data-matrix
`sig1`	covariance sample 1
`sig2`	covariance sample 2
`sig`	pooled covariance
`mu1`	mean sample 1
`mu2`	mean sample 2
`mu`	pooled mean

Value

Returns a list with named elements 'twiceLR', 'sig1', 'sig2', 'sig'. 'twiceLR' is twice the log-likelihood-ratio statistic.

Author(s)

n.stadler

Examples

x1=matrix(rnorm(100),50,2)
x2=matrix(rnorm(100),50,2)
logratio(x1,x2,rbind(x1,x2),diag(1,2),diag(1,2),diag(1,2),c(0,0),c(0,0),c(0,0))$twiceLR
x1=matrix(rnorm(100),50,2)
x2=matrix(rnorm(100),50,2)
logratio(x1,x2,rbind(x1,x2),diag(1,2),diag(1,2),diag(1,2),c(0,0),c(0,0),c(0,0))$twiceLR

mixglasso

Description

mixglasso

Usage

mixglasso(x, n.comp, lambda = sqrt(2 * nrow(x) * log(ncol(x)))/2,
  pen = "glasso.parcor", init = "kmeans.hc", my.cl = NULL,
  modelname.hc = "VVV", nstart.kmeans = 1, iter.max.kmeans = 10,
  term = 10^{     -3 }, min.compsize = 5, save.allfits = FALSE,
  filename = "mixglasso_fit.rda", mc.flag = FALSE,
  mc.set.seed = FALSE, mc.preschedule = FALSE,
  mc.cores = getOption("mc.cores", 2L), ...)
mixglasso(x, n.comp, lambda = sqrt(2 * nrow(x) * log(ncol(x)))/2,
  pen = "glasso.parcor", init = "kmeans.hc", my.cl = NULL,
  modelname.hc = "VVV", nstart.kmeans = 1, iter.max.kmeans = 10,
  term = 10^{     -3 }, min.compsize = 5, save.allfits = FALSE,
  filename = "mixglasso_fit.rda", mc.flag = FALSE,
  mc.set.seed = FALSE, mc.preschedule = FALSE,
  mc.cores = getOption("mc.cores", 2L), ...)

Arguments

`x`	Input data matrix
`n.comp`	Number of mixture components. If n.comp is a vector, `mixglasso` will estimate a model for each number of mixture components, and return a list of models, as well as their BIC and MMDL scores and the index of the best model according to each score.
`lambda`	Regularization parameter. Default=sqrt(2nlog(p))/2
`pen`	Determines form of penalty: glasso.parcor (default) to penalise the partial correlation matrix, glasso.invcov to penalise the inverse covariance matrix (this corresponds to classical graphical lasso), glasso.invcor to penalise the inverse correlation matrix.
`init`	Initialization. Method used for initialization init='cl.init','r.means','random','kmeans','kmeans.hc','hc'. Default='kmeans'
`my.cl`	Initial cluster assignments; need to be provided if init='cl.init' (otherwise this param is ignored). Default=NULL
`modelname.hc`	Model class used in hc. Default="VVV"
`nstart.kmeans`	Number of random starts in kmeans; default=1
`iter.max.kmeans`	Maximal number of iteration in kmeans; default=10
`term`	Termination criterion of EM algorithm. Default=10^-3
`min.compsize`	Stop EM if any(compsize)<min.compsize; Default=5
`save.allfits`	If TRUE, save output of mixglasso for all k's.
`filename`	If `save.allfits` is TRUE, output of mixglasso will be saved as `paste(filename, _fit.mixgl_k.rda, sep='')`.
`mc.flag`	If `TRUE` use parallel execution for each n.comp via function `mclapply` of package `parallel`.
`mc.set.seed`	See mclapply. Default=FALSE
`mc.preschedule`	See mclapply. Default=FALSE
`mc.cores`	Number of cores to use in parallel execution. Defaults to mc.cores option if set, or 2 otherwise.
`...`	Other arguments. See mixglasso_init

Details

Runs mixture of graphical lasso network clustering with one or several numbers of mixture components.

Value

A list with elements:

`models`	List with each element i containing an S3 object of class 'nethetclustering' that contains the result of fitting the mixture graphical lasso model with n.comps[i] components. See the documentation of mixglasso_ncomp_fixed for the description of this object.
`bic`	BIC for all fits.
`mmdl`	Minimum description length score for all fits.
`comp`	Component assignments for all fits.
`bix.opt`	Index of model with optimal BIC score.
`mmdl.opt`	Index of model with optimal MMDL score.

Author(s)

n.stadler

Examples



###########################################
##This an example of how to use MixGLasso##
###########################################

##generate data
set.seed(1)
n <- 1000
n.comp <- 3
p <- 10

# Create different mean vectors
Mu <- matrix(0,p,n.comp)

nonzero.mean <- split(sample(1:p),rep(1:n.comp,length=p))
for(k in 1:n.comp){
  Mu[nonzero.mean[[k]],k] <- -2/sqrt(ceiling(p/n.comp))
}

sim <- sim_mix_networks(n, p, n.comp, Mu=Mu)

##run mixglasso
set.seed(1)
fit1 <-  mixglasso(sim$data,n.comp=1:6)
fit1$bic
set.seed(1)
fit2 <-  mixglasso(sim$data,n.comp=6)
fit2$bic
set.seed(1)
fit3 <-  mixglasso(sim$data,n.comp=1:6,lambda=0)
set.seed(1)
fit4 <-  mixglasso(sim$data,n.comp=1:6,lambda=Inf)
#set.seed(1)
#fit5 <-  bwprun_mixglasso(sim$data,n.comp=1,n.comp.max=5,selection.crit='bic')
#plot(fit5$selcrit,ylab='bic',xlab='Num.Comps',type='b')

##compare bic
library('ggplot2')
plotting.frame <- 
  data.frame(BIC= c(fit1$bic, fit3$bic, fit4$bic), 
             Num.Comps=rep(1:6, 3), 
             Lambda=rep(c('Default', 
                          'Lambda = 0',
                          'Lambda = Inf'),
                        each=6))

p <- ggplot(plotting.frame) + 
	geom_line(aes(x=Num.Comps, y=BIC, colour=Lambda))

print(p)
###########################################
##This an example of how to use MixGLasso##
###########################################

##generate data
set.seed(1)
n <- 1000
n.comp <- 3
p <- 10

# Create different mean vectors
Mu <- matrix(0,p,n.comp)

nonzero.mean <- split(sample(1:p),rep(1:n.comp,length=p))
for(k in 1:n.comp){
  Mu[nonzero.mean[[k]],k] <- -2/sqrt(ceiling(p/n.comp))
}

sim <- sim_mix_networks(n, p, n.comp, Mu=Mu)

##run mixglasso
set.seed(1)
fit1 <-  mixglasso(sim$data,n.comp=1:6)
fit1$bic
set.seed(1)
fit2 <-  mixglasso(sim$data,n.comp=6)
fit2$bic
set.seed(1)
fit3 <-  mixglasso(sim$data,n.comp=1:6,lambda=0)
set.seed(1)
fit4 <-  mixglasso(sim$data,n.comp=1:6,lambda=Inf)
#set.seed(1)
#fit5 <-  bwprun_mixglasso(sim$data,n.comp=1,n.comp.max=5,selection.crit='bic')
#plot(fit5$selcrit,ylab='bic',xlab='Num.Comps',type='b')

##compare bic
library('ggplot2')
plotting.frame <- 
  data.frame(BIC= c(fit1$bic, fit3$bic, fit4$bic), 
             Num.Comps=rep(1:6, 3), 
             Lambda=rep(c('Default', 
                          'Lambda = 0',
                          'Lambda = Inf'),
                        each=6))

p <- ggplot(plotting.frame) + 
	geom_line(aes(x=Num.Comps, y=BIC, colour=Lambda))

print(p)

mixglasso_init

Description

mixglasso_init (initialization and lambda set by user)

Usage

mixglasso_init(x, n.comp, lambda, u.init, mix.prob.init, gamma = 0.5,
  pen = "glasso.parcor", penalize.diagonal = FALSE, term = 10^{    
  -3 }, miniter = 5, maxiter = 1000, min.compsize = 5,
  show.trace = FALSE)
mixglasso_init(x, n.comp, lambda, u.init, mix.prob.init, gamma = 0.5,
  pen = "glasso.parcor", penalize.diagonal = FALSE, term = 10^{    
  -3 }, miniter = 5, maxiter = 1000, min.compsize = 5,
  show.trace = FALSE)

Arguments

`x`	Input data matrix
`n.comp`	Number of mixture components
`lambda`	Regularization parameter
`u.init`	Initial responsibilities
`mix.prob.init`	Initial component probablities
`gamma`	Determines form of penalty
`pen`	Determines form of penalty: glasso.parcor (default), glasso.invcov, glasso.invcor
`penalize.diagonal`	Should the diagonal of the inverse covariance matrix be penalized ? Default=FALSE (recommended)
`term`	Termination criterion of EM algorithm. Default=10^-3
`miniter`	Minimal number of EM iteration before 'stop EM if any(compsize)<min.compsize' applies. Default=5
`maxiter`	Maximal number of EM iteration. Default=1000
`min.compsize`	Stop EM if any(compsize)<min.compsize; Default=5
`show.trace`	Should information during execution be printed ? Default=FALSE

Details

This function runs mixglasso; requires initialization (u.init,mix.prob.init)

Value

list consisting of

`mix.prob`	Component probabilities
`Mu`	Component specific mean vectors
`Sig`	Component specific covariance matrices
`SigInv`	Component specific inverse covariance matrices
`iter`	Number of EM iterations
`loglik`	Log-likelihood
`bic`	-loglik+log(n)*DF/2
`mmdl`	-loglik+penmmdl/2
`u`	Component responsibilities
`comp`	Component assignments
`compsize`	Size of components
`pi.comps`	Component probabilities
`warn`	Warnings during EM algorithm

Author(s)

n.stadler

Plot two networks (GGMs)

Description

Plot two networks (GGMs)

Usage

plot_2networks(invcov1, invcov2, node.label = paste("X", 1:nrow(invcov1),
  sep = ""), main = c("", ""), ...)
plot_2networks(invcov1, invcov2, node.label = paste("X", 1:nrow(invcov1),
  sep = ""), main = c("", ""), ...)

Arguments

`invcov1`	Inverse covariance matrix of GGM1.
`invcov2`	Inverse covariance matrix of GGM2.
`node.label`	Names of nodes.
`main`	Vector (two elements) with network names.
`...`	Other arguments (see plot.network).

Value

Figure with two panels (for each network).

Author(s)

nicolas

Examples

n <- 70
p <- 30

## Specifiy sparse inverse covariance matrices,
## with number of edges in common equal to ~ 0.8*p
gen.net <- generate_2networks(p,graph='random',n.nz=rep(p,2),
                              n.nz.common=ceiling(p*0.8))

invcov1 <- gen.net[[1]]
invcov2 <- gen.net[[2]]

plot_2networks(invcov1,invcov2,label.pos=0,label.cex=0.7)
n <- 70
p <- 30

## Specifiy sparse inverse covariance matrices,
## with number of edges in common equal to ~ 0.8*p
gen.net <- generate_2networks(p,graph='random',n.nz=rep(p,2),
                              n.nz.common=ceiling(p*0.8))

invcov1 <- gen.net[[1]]
invcov2 <- gen.net[[2]]

plot_2networks(invcov1,invcov2,label.pos=0,label.cex=0.7)

Plotting function for object of class 'diffnet'

Description

Plotting function for object of class 'diffnet'

Usage

## S3 method for class 'diffnet'
plot(x, ...)
## S3 method for class 'diffnet'
plot(x, ...)

Arguments

`x`	object of class 'diffnet'
`...`	Further arguments.

Value

Histogram over multi-split p-values.

Author(s)

nicolas

Plotting function for object of class 'diffregr'

Description

Plotting function for object of class 'diffregr'

Usage

## S3 method for class 'diffregr'
plot(x, ...)
## S3 method for class 'diffregr'
plot(x, ...)

Arguments

`x`	object of class 'diffregr'
`...`	Further arguments.

Value

Histogram over multi-split p-values.

Author(s)

nicolas

Plotting function for object of class 'ggmgmsa'

Description

Plotting function for object of class 'ggmgsa'

Usage

## S3 method for class 'ggmgsa'
plot(x, ...)
## S3 method for class 'ggmgsa'
plot(x, ...)

Arguments

`x`	object of class 'ggmgsa'
`...`	Further arguments.

Value

Boxplot of single-split p-values.

Author(s)

nicolas

Plot networks

Description

This function takes the output of screen_cv.glasso or mixglasso and creates a network plot using the network library.

Usage

## S3 method for class 'nethetclustering'
plot(x,
  node.names = rownames(net.clustering$Mu),
  group.names = sort(unique(net.clustering$comp)),
  p.corrs.thresh = 0.2, print.pdf = FALSE, pdf.filename = "networks",
  ...)
## S3 method for class 'nethetclustering'
plot(x,
  node.names = rownames(net.clustering$Mu),
  group.names = sort(unique(net.clustering$comp)),
  p.corrs.thresh = 0.2, print.pdf = FALSE, pdf.filename = "networks",
  ...)

Arguments

`x`	A network clustering object as returned by `screen_cv.glasso` or `mixglasso`.
`node.names`	Names for the nodes in the network. If NULL, names from net.clustering will be used.
`group.names`	Names for the clusters or groups. If NULL, names from net.clustering will be used (by default these are integets 1:numClusters).
`p.corrs.thresh`	Threshold applied to the absolute partial correlations. Edges that are below the threshold in all of the groups are not displayed.
`print.pdf`	If TRUE, save the output as a PDF file.
`pdf.filename`	If `print.pdf` is TRUE, specifies the file name of the output PDF file.
`...`	Further arguments

Value

Returns NULL and prints out the networks (or saves them to pdf if print.pdf is TRUE. The networks are displayed as a series of nComps+1 plots, where in the first plot edge widths are shown according to the maximum partial correlation of the edge over all groups. The following plots show the edges for each group. Positive partial correlation edges are shown in black, negative ones in blue. If an edge is below the threshold on the absolute partial correlation, it is displayed in gray or light blue respectively.

Print function for object of class 'nethetsummmary'

Description

Print function for object of class 'nethetsummary'

Usage

## S3 method for class 'nethetsummary'
print(x, ...)
## S3 method for class 'nethetsummary'
print(x, ...)

Arguments

`x`	object of class 'nethetsummary'
`...`	Other arguments

Value

Function does not return anything.

Author(s)

frankd

Create a scatterplot showing correlation between specific nodes in the network for each pre-specified group.

Description

This function takes the output of het_cv_glasso or mixglasso and creates a plot showing the correlation between specified node pairs in the network for all groups. The subplots for each node pair are arranged in a numPairs by numGroups grid. Partial correlations associated with each node pair are also displayed.

Usage

scatter_plot(net.clustering, data, node.pairs, display = TRUE,
  node.names = rownames(net.clustering$Mu),
  group.names = sort(unique(net.clustering$comp)), cex = 1)
scatter_plot(net.clustering, data, node.pairs, display = TRUE,
  node.names = rownames(net.clustering$Mu),
  group.names = sort(unique(net.clustering$comp)), cex = 1)

Arguments

`net.clustering`	A network clustering object as returned by `het_cv_glasso` or `mixglasso`.
`data`	Observed data for the nodes, a numObs by numNodes matrix. Note that nodes need to be in the same ordering as in node.names.
`node.pairs`	A matrix of size numPairs by 2, where each row contains a pair of nodes to display. If node.names is specified, names in node.pairs must correspond to elements of node.names.
`display`	If TRUE, print the plot to the current output device.
`node.names`	Names for the nodes in the network. If NULL, names from net.clustering will be used.
`group.names`	Names for the clusters or groups. If NULL, names from net.clustering will be used (by default these are integets 1:numClusters).
`cex`	Scale factor for text and symbols in plot.

Value

Returns a ggplot2 object. If display=TRUE, additionally displays the plot.

Examples

n = 500
p = 10
s = 0.9
n.comp = 3

# Create different mean vectors
Mu = matrix(0,p,n.comp)

# Define non-zero means in each group (non-overlapping)
nonzero.mean = split(sample(1:p),rep(1:n.comp,length=p))

# Set non-zero means to fixed value
for(k in 1:n.comp){
	Mu[nonzero.mean[[k]],k] = -2/sqrt(ceiling(p/n.comp))
}

# Generate data
sim.result = sim_mix_networks(n, p, n.comp, s, Mu=Mu)
mixglasso.result = mixglasso(sim.result$data, n.comp=3)
mixglasso.clustering = mixglasso.result$models[[mixglasso.result$bic.opt]]

# Specify edges
node.pairs = rbind(c(1,3), c(6,9),c(7,8))

# Create scatter plots of specified edges
scatter_plot(mixglasso.clustering, data=sim.result$data,
					 node.pairs=node.pairs)
n = 500
p = 10
s = 0.9
n.comp = 3

# Create different mean vectors
Mu = matrix(0,p,n.comp)

# Define non-zero means in each group (non-overlapping)
nonzero.mean = split(sample(1:p),rep(1:n.comp,length=p))

# Set non-zero means to fixed value
for(k in 1:n.comp){
	Mu[nonzero.mean[[k]],k] = -2/sqrt(ceiling(p/n.comp))
}

# Generate data
sim.result = sim_mix_networks(n, p, n.comp, s, Mu=Mu)
mixglasso.result = mixglasso(sim.result$data, n.comp=3)
mixglasso.clustering = mixglasso.result$models[[mixglasso.result$bic.opt]]

# Specify edges
node.pairs = rbind(c(1,3), c(6,9),c(7,8))

# Create scatter plots of specified edges
scatter_plot(mixglasso.clustering, data=sim.result$data,
					 node.pairs=node.pairs)

AIC-tuned glasso with additional thresholding

Description

AIC-tuned glasso with additional thresholding

Usage

screen_aic.glasso(x, include.mean = TRUE, length.lambda = 20,
  lambdamin.ratio = ifelse(ncol(x) > nrow(x), 0.01, 0.001),
  penalize.diagonal = FALSE, plot.it = FALSE,
  trunc.method = "linear.growth", trunc.k = 5, use.package = "huge",
  verbose = FALSE)
screen_aic.glasso(x, include.mean = TRUE, length.lambda = 20,
  lambdamin.ratio = ifelse(ncol(x) > nrow(x), 0.01, 0.001),
  penalize.diagonal = FALSE, plot.it = FALSE,
  trunc.method = "linear.growth", trunc.k = 5, use.package = "huge",
  verbose = FALSE)

Arguments

`x`	The input data. Needs to be a num.samples by dim.samples matrix.
`include.mean`	Include mean in likelihood. TRUE / FALSE (default).
`length.lambda`	Length of lambda path to consider (default=20).
`lambdamin.ratio`	Ratio lambda.min/lambda.max.
`penalize.diagonal`	If TRUE apply penalization to diagonal of inverse covariance as well. (default=FALSE)
`plot.it`	TRUE / FALSE (default)
`trunc.method`	None / linear.growth (default) / sqrt.growth
`trunc.k`	truncation constant, number of samples per predictor (default=5)
`use.package`	'glasso' or 'huge' (default).
`verbose`	If TRUE, output la.min, la.max and la.opt (default=FALSE).

Value

Returns a list with named elements 'rho.opt', 'wi', 'wi.orig'. Variable rho.opt is the optimal (scaled) penalization parameter (rho.opt=2*la.opt/n). The variables wi and wi.orig are matrices of size dim.samples by dim.samples containing the truncated and untruncated inverse covariance matrix.

Author(s)

n.stadler

Examples

n=50
p=5
x=matrix(rnorm(n*p),n,p)
wihat=screen_aic.glasso(x,length.lambda=5)$wi
n=50
p=5
x=matrix(rnorm(n*p),n,p)
wihat=screen_aic.glasso(x,length.lambda=5)$wi

BIC-tuned glasso with additional thresholding

Description

BIC-tuned glasso with additional thresholding

Usage

screen_bic.glasso(x, include.mean = TRUE, length.lambda = 20,
  lambdamin.ratio = ifelse(ncol(x) > nrow(x), 0.01, 0.001),
  penalize.diagonal = FALSE, plot.it = FALSE,
  trunc.method = "linear.growth", trunc.k = 5, use.package = "huge",
  verbose = FALSE)
screen_bic.glasso(x, include.mean = TRUE, length.lambda = 20,
  lambdamin.ratio = ifelse(ncol(x) > nrow(x), 0.01, 0.001),
  penalize.diagonal = FALSE, plot.it = FALSE,
  trunc.method = "linear.growth", trunc.k = 5, use.package = "huge",
  verbose = FALSE)

Arguments

`x`	The input data. Needs to be a num.samples by dim.samples matrix.
`include.mean`	Include mean in likelihood. TRUE / FALSE (default).
`length.lambda`	Length of lambda path to consider (default=20).
`lambdamin.ratio`	Ratio lambda.min/lambda.max.
`penalize.diagonal`	If TRUE apply penalization to diagonal of inverse covariance as well. (default=FALSE)
`plot.it`	TRUE / FALSE (default)
`trunc.method`	None / linear.growth (default) / sqrt.growth
`trunc.k`	truncation constant, number of samples per predictor (default=5)
`use.package`	'glasso' or 'huge' (default).
`verbose`	If TRUE, output la.min, la.max and la.opt (default=FALSE).

Value

Returns a list with named elements 'rho.opt', 'wi', 'wi.orig', Variable rho.opt is the optimal (scaled) penalization parameter (rho.opt=2*la.opt/n). The variables wi and wi.orig are matrices of size dim.samples by dim.samples containing the truncated and untruncated inverse covariance matrix.

Author(s)

n.stadler

Examples

n=50
p=5
x=matrix(rnorm(n*p),n,p)
wihat=screen_bic.glasso(x,length.lambda=5)$wi
n=50
p=5
x=matrix(rnorm(n*p),n,p)
wihat=screen_bic.glasso(x,length.lambda=5)$wi

Cross-validated glasso with additional thresholding

Description

Cross-validated glasso with additional thresholding

Usage

screen_cv.glasso(x, include.mean = FALSE, folds = min(10, dim(x)[1]),
  length.lambda = 20, lambdamin.ratio = ifelse(ncol(x) > nrow(x), 0.01,
  0.001), penalize.diagonal = FALSE, trunc.method = "linear.growth",
  trunc.k = 5, plot.it = FALSE, se = FALSE, use.package = "huge",
  verbose = FALSE)
screen_cv.glasso(x, include.mean = FALSE, folds = min(10, dim(x)[1]),
  length.lambda = 20, lambdamin.ratio = ifelse(ncol(x) > nrow(x), 0.01,
  0.001), penalize.diagonal = FALSE, trunc.method = "linear.growth",
  trunc.k = 5, plot.it = FALSE, se = FALSE, use.package = "huge",
  verbose = FALSE)

Arguments

`x`	The input data. Needs to be a num.samples by dim.samples matrix.
`include.mean`	Include mean in likelihood. TRUE / FALSE (default).
`folds`	Number of folds in the cross-validation (default=10).
`length.lambda`	Length of lambda path to consider (default=20).
`lambdamin.ratio`	Ratio lambda.min/lambda.max.
`penalize.diagonal`	If TRUE apply penalization to diagonal of inverse covariance as well. (default=FALSE)
`trunc.method`	None / linear.growth (default) / sqrt.growth
`trunc.k`	truncation constant, number of samples per predictor (default=5)
`plot.it`	TRUE / FALSE (default)
`se`	default=FALSE.
`use.package`	'glasso' or 'huge' (default).
`verbose`	If TRUE, output la.min, la.max and la.opt (default=FALSE).

Details

Run glasso on a single dataset, using cross-validation to estimate the penalty parameter lambda. Performs additional thresholding (optionally).

Value

Returns a list with named elements 'rho.opt', 'w', 'wi', 'wi.orig', 'mu'. Variable rho.opt is the optimal (scaled) penalization parameter (rho.opt=2*la.opt/n). Variable w is the estimated covariance matrix. The variables wi and wi.orig are matrices of size dim.samples by dim.samples containing the truncated and untruncated inverse covariance matrix. Variable mu is the mean of the input data.

Author(s)

n.stadler

Examples

n=50
p=5
x=matrix(rnorm(n*p),n,p)
wihat=screen_cv.glasso(x,folds=2)$wi
n=50
p=5
x=matrix(rnorm(n*p),n,p)
wihat=screen_cv.glasso(x,folds=2)$wi

Cross-validated Lasso screening (lambda.1se-rule)

Description

Cross-validated Lasso screening (lambda.1se-rule)

Usage

screen_cv1se.lasso(x, y)
screen_cv1se.lasso(x, y)

Arguments

`x`	Predictor matrix
`y`	Response vector

Value

Active-set

Author(s)

n.stadler

Examples

screen_cv1se.lasso(matrix(rnorm(5000),50,100),rnorm(50))
screen_cv1se.lasso(matrix(rnorm(5000),50,100),rnorm(50))

Cross-validated Lasso screening and upper bound on number of predictors.

Description

Cross-validated Lasso screening and upper bound on number of predictors

Usage

screen_cvfix.lasso(x, y, no.predictors = 10)
screen_cvfix.lasso(x, y, no.predictors = 10)

Arguments

`x`	Predictor matrix.
`y`	Response vector.
`no.predictors`	Upper bound on number of active predictors,

Details

Computes Lasso coefficients (cross-validation optimal lambda). Truncates smalles coefficients to zero such that there are no more than no.predictors non-zero coefficients

Value

Active-set.

Author(s)

n.stadler

Examples

screen_cvfix.lasso(matrix(rnorm(5000),50,100),rnorm(50))
screen_cvfix.lasso(matrix(rnorm(5000),50,100),rnorm(50))

Cross-validation lasso screening (lambda.min-rule)

Description

Cross-validated Lasso screening (lambda.min-rule)

Usage

screen_cvmin.lasso(x, y)
screen_cvmin.lasso(x, y)

Arguments

`x`	Predictor matrix
`y`	Response vector

Value

Active-set

Author(s)

n.stadler

Examples

screen_cvmin.lasso(matrix(rnorm(5000),50,100),rnorm(50))
screen_cvmin.lasso(matrix(rnorm(5000),50,100),rnorm(50))

Cross-validated Lasso screening and sqrt-truncation.

Description

Cross-validated Lasso screening and sqrt-truncation.

Usage

screen_cvsqrt.lasso(x, y)
screen_cvsqrt.lasso(x, y)

Arguments

`x`	Predictor matrix.
`y`	Response vector.

Details

Computes Lasso coefficients (cross-validation optimal lambda). Truncates smallest coefficients to zero, such that there are no more than sqrt(n) non-zero coefficients.

Value

Active-set.

Author(s)

n.stadler

Examples

screen_cvsqrt.lasso(matrix(rnorm(5000),50,100),rnorm(50))
screen_cvsqrt.lasso(matrix(rnorm(5000),50,100),rnorm(50))

Cross-validated Lasso screening and additional truncation.

Description

Cross-validated Lasso screening and additional truncation.

Usage

screen_cvtrunc.lasso(x, y, k.trunc = 5)
screen_cvtrunc.lasso(x, y, k.trunc = 5)

Arguments

`x`	Predictor matrix.
`y`	Response vector.
`k.trunc`	Truncation constant="number of samples per predictor" (default=5).

Details

Computes Lasso coefficients (cross-validation optimal lambda). Truncates smallest coefficients to zero, such that there are no more than n/k.trunc non-zero coefficients.

Value

Active-set.

Author(s)

n.stadler

Examples

screen_cvtrunc.lasso(matrix(rnorm(5000),50,100),rnorm(50))
screen_cvtrunc.lasso(matrix(rnorm(5000),50,100),rnorm(50))

Simulate from mixture model.

Description

Simulate from mixture model with multi-variate Gaussian or t-distributed components.

Usage

sim_mix(n, n.comp, mix.prob, Mu, Sig, dist = "norm", df = 2)
sim_mix(n, n.comp, mix.prob, Mu, Sig, dist = "norm", df = 2)

Arguments

`n`	sample size
`n.comp`	number of mixture components ("comps")
`mix.prob`	mixing probablities (need to sum to 1)
`Mu`	matrix of component-specific mean vectors
`Sig`	array of component-specific covariance matrices
`dist`	'norm' for Gaussian components, 't' for t-distributed components
`df`	degrees of freedom of the t-distribution (not used for Gaussian distribution), default=2

Value

a list consisting of:

`S`	component assignments
`X`	observed data matrix

Author(s)

n.stadler

Examples

n.comp = 4
p = 5 # dimensionality
Mu = matrix(rep(0, p), p, n.comp)
Sigma = array(diag(p), c(p, p, n.comp))
mix.prob = rep(0.25, n.comp)

sim_mix(100, n.comp, mix.prob, Mu, Sigma)
n.comp = 4
p = 5 # dimensionality
Mu = matrix(rep(0, p), p, n.comp)
Sigma = array(diag(p), c(p, p, n.comp))
mix.prob = rep(0.25, n.comp)

sim_mix(100, n.comp, mix.prob, Mu, Sigma)

sim_mix_networks

Description

Generate inverse covariances, means, mixing probabilities, and simulate data from resulting mixture model.

Usage

sim_mix_networks(n, p, n.comp, sparsity = 0.7, mix.prob = rep(1/n.comp,
  n.comp), Mu = NULL, Sig = NULL, ...)
sim_mix_networks(n, p, n.comp, sparsity = 0.7, mix.prob = rep(1/n.comp,
  n.comp), Mu = NULL, Sig = NULL, ...)

Arguments

`n`	Number of data points to simulate.
`p`	Dimensionality of the data.
`n.comp`	Number of components of the mixture model.
`sparsity`	Determines the proportion of non-zero off-diagonal entries.
`mix.prob`	Mixture probabilities for the components; defaults to uniform distribution.
`Mu`	Means for the mixture components, a p by n.comp matrix. If NULL, sampled from a standard Gaussian.
`Sig`	Covariances for the mixture components, a p by p by n.comp array. If NULL, generated using `generate_inv_cov`.
`...`	Further arguments passed to `sim_mix`.

Details

This function generates n.comp mean vectors from a standard Gaussian and n.comp covariance matrices, with at most (1-sparsity)*p(p-1)/2 non-zero off-diagonal entries, where the non-zero entries are sampled from a beta distribution. Then it uses sim_mix to simulate from a mixture model with these means and covariance matrices.

Means Mu and covariance matrices Sig can also be supplied by the user.

Value

A list with components: Mu Means of the mixture components. Sig Covariances of the mixture components. data Simulated data, a n by p matrix. S Component assignments, a vector of length n.

Examples

# Generate dataset with 100 samples of dimensionality 30, and 4 components
test.data = sim_mix_networks(n=100, p=30, n.comp=4)
# Generate dataset with 100 samples of dimensionality 30, and 4 components
test.data = sim_mix_networks(n=100, p=30, n.comp=4)

Summary function for object of class 'diffnet'

Description

Summary function for object of class 'diffnet'

Usage

## S3 method for class 'diffnet'
summary(object, ...)
## S3 method for class 'diffnet'
summary(object, ...)

Arguments

`object`	object of class 'diffnet'
`...`	Other arguments.

Value

aggregated p-values

Author(s)

nicolas

Summary function for object of class 'diffregr'

Description

Summary function for object of class 'diffregr'

Usage

## S3 method for class 'diffregr'
summary(object, ...)
## S3 method for class 'diffregr'
summary(object, ...)

Arguments

`object`	object of class 'diffregr
`...`	Other arguments

Value

aggregated p-values

Author(s)

nicolas

Summary function for object of class 'ggmgsa'

Description

Summary function for object of class 'ggmgsa'

Usage

## S3 method for class 'ggmgsa'
summary(object, ...)
## S3 method for class 'ggmgsa'
summary(object, ...)

Arguments

`object`	object of class 'ggmgsa'
`...`	Other arguments

Value

aggregated p-values

Author(s)

nicolas

Summary function for object of class 'nethetclustering'

Description

Summary function for object of class 'nethetclustering'

Usage

## S3 method for class 'nethetclustering'
summary(object, ...)
## S3 method for class 'nethetclustering'
summary(object, ...)

Arguments

`object`	object of class 'nethetclustering'
`...`	Other arguments

Value

Network statistics (a 'nethetsummary' object)

Author(s)

frankd