Type: Package
Title: Mixed Neighbourhood Selection
Version: 1.0
Date: 2015-12-06
Author: Ricardo Pio Monti, Christoforos Anagnostopoulos and Giovanni Montana
Maintainer: Ricardo Pio Monti <ricardo.monti08@gmail.com>
Depends: igraph, MASS, glmnet, mvtnorm, parallel, R (≥ 2.10.1)
Imports: doParallel
Description: An implementation of the mixed neighbourhood selection (MNS) algorithm. The MNS algorithm can be used to estimate multiple related precision matrices. In particular, the motivation behind this work was driven by the need to understand functional connectivity networks across multiple subjects. This package also contains an implementation of a novel algorithm through which to simulate multiple related precision matrices which exhibit properties frequently reported in neuroimaging analysis.
License: GPL-2
Packaged: 2015-12-08 11:51:56 UTC; ricardo
NeedsCompilation: no
Repository: CRAN
Date/Publication: 2015-12-08 14:53:44

Mixed Neighbourhood Selection package

Description

An R package for estimating multiple, related grapical models using the Mixed Neighbourhood Selection algorithm. This package also includes two algorithm through which to simulate multiple, related graphical models which demonstrate some of the properties reported through empirical studies of functional connectivity networks.

Details

Package: MNS
Type: Package
Version: 1.0
Date: 2015-10-14
License: GPL-2

Author(s)

Ricardo Pio Monti

References

Monti, R., Anagnostopolus, C., Montana, G. "Inferring brain connectivity networks from functional MRI data via mixed neighbourhood selection", arXiv, 2015

See Also

MNS, cv.MNS, plot.MNS, gen.Network

Examples

set.seed(1)
N=4
Net = gen.Network(method = "cohort", p = 10, 
                       Nsub = N, sparsity = .2, 
                       REsize = 20, REprob = .5,
                       REnoise = 1, Nobs = 10)
## Not run: 
# plot simulated networks:
plot(Net, view="pop")

# run MNS algorithm:
mns = MNS(dat = Net$Data, lambda_pop = .1, lambda_random = .1, parallel = TRUE)

# plot results from MNS algorithm:
plot(mns) # plot population network
plot(mns, view="var") # plot variance network
plot(mns, view="sub") # plot subject networks (note red edges here are variable edges!)

## End(Not run)

Mixed Neighbourhood Selection

Description

Estimate multiple related graphical models using the mixed neighbourhood selection (MNS) algorithm.

Usage

MNS(dat, lambda_pop, lambda_random, 
    parallel = FALSE, cores = NULL, 
    max_iter = 100, tol = 1e-05)

Arguments

dat

List where each entry corresponds to the time series observations for each subject

lambda_pop

Regularization parameter applied to fixed effects components. See details below for more information

lambda_random

Regularization parameter applied to the standard deviations of random effect effects. See details below for more information

parallel

Indicate whether model fit should be done in parallel. Default is FALSE

cores

If fit in parallel, indicate how many cores should be used

max_iter

Maximum number of iterations in EM algorithm. See details below for more information

tol

Convergence tolerance in EM algorithm

Details

The MNS algorithm is an extension of neighbourhood selection to the scenario where the objective is to learn multiple related Gaussian graphical models. For further details see Monti et al. (2015).

Value

PresPop

Population connectivity matrix - encodes the sparse support structure of population precision

PresRE

Network of highly variable edges - encodes the sparse support structure of highly variable edges

PresBLUP

Array containing predicted subject specific deviations from population connectivity.

it

Iterations to fit MNS model (one per node)

Author(s)

Ricardo Pio monti

References

Monti, R., Anagnostopolus, C., Montana, G. "Inferring brain connectivity networks from functional MRI data via mixed neighbourhood selection", arXiv, 2015

See Also

cv.MNS, plot.MNS

Examples

set.seed(1)
N=4
Net = gen.Network(method = "cohort", p = 10, 
                       Nsub = N, sparsity = .2, 
                       REsize = 20, REprob = .5,
                       REnoise = 1, Nobs = 10)
## Not run: 
mns = MNS(dat = Net$Data, lambda_pop = .1, lambda_random = .1, parallel = TRUE)
# plot results:
plot(mns) # plot population network
plot(mns, view="var") # plot variance network
plot(mns, view="sub") # plot subject networks (note red edges here are variable edges!)


## End(Not run)

Select regularization parameters via cross-validation

Description

Select regularization parameters via K-fold cross-validation

Usage

cv.MNS(dat, l1range, alpharange, 
    K = 5, parallel = FALSE, 
    cores = NULL, verbose = FALSE)

Arguments

dat

List where each entry corresponds to the time series observations for each subject

l1range

Vector of candidate regularization parameters. See details below

alpharange

Vector of candidate weighting parameters. See details below.

K

Number of cross-validation folds

parallel

Indicate whether model fit should be done in parallel. Default is FALSE

cores

If fit in parallel, indicate how many units/cores should be used

verbose

Print progress. Only available for non-parallel implementation

Details

Select regularization parameters via cross-validation. In the interest of simplicity we re-parameterize penalty as an elastic net penalty:

\lambda * \alpha || \beta||_1 + \lambda * (1-\alpha) || \sigma||_1

Thus \lambda is the regularization parameter (specified by the l1range argument) and \alpha is the weighting parameter (specified by the alpharange argument).

Value

l1

selected regularization parameter

alpha

selected weighting parameter

CV

grid of cross-validation error for each pair of regularization parameters

Author(s)

Ricardo Pio Monti

References

Arlot, S., and Alain C. "A survey of cross-validation procedures for model selection." Statistics surveys 4 (2010): 40-79.

Monti, R., Anagnostopolus, C., Montana, G. "Inferring brain connectivity networks from functional MRI data via mixed neighbourhood selection", arXiv, 2015

See Also

MNS

Examples

set.seed(1)
Dat = gen.Network(p = 10, Nsub = 5, 
 sparsity = .2, REsize=10, REprob=.5, 
 REnoise = 1, Nobs=20)
## Not run: 
CVs = cv.MNS(dat = Dat, l1range = seq(.1, .5, length.out=10),
 alpharange = seq(.2, .8, length.out = 5), 
 parallel = FALSE, verbose = TRUE)

## End(Not run)

Simulate random networks for a population of subjects

Description

Implementations of two methods through which to simulation multiple related networks. The first simulates networks from a three-class population described in Danaher et al. (2014). The second simulates networks according to method proposed in Monti et al. (2015). For further details see the package vignette.

Usage

gen.Network(method = "cohort", p,
    Nobs, Nsub, sparsity,
    REsize, REprob, REnoise)

Arguments

method

Network simulation method. One of either "Danaher" for the three-class method of Danaher et al. (2014) or "cohort" for the cohort method described in Monti et al. (2015)

p

Number of nodes in network (i.e., this will be dimensionality of the resulting precision matrices)

Nobs

Number of observations per subject (assumed constant across subjects). If this is missing then only the precision matrices will be returned (i.e., random data is not simulated)

Nsub

Number of subjects for which to simulate networks. Note that this is set to 3 if method="Danaher"

sparsity

Sparsity level of precision matrices

REsize

Number of random effects edges to add to each subject (only for method="cohort")

REprob

Probability with which a random edge added to each subject (only for method="cohort")

REnoise

Variability of random edges (only for method="cohort")

Details

See package vignette for further details. Alternatively see Danaher et al. (2014) or Monti et al. (2015)

Value

Networks

List containing simulated netowrks where ith entry is the ith random network for the ith subject

Data

List where ith entry is simulated data for ith subject

PopNet

Population precision matrix (only if method="cohort")

RanNet

Sparse support for random edges (only if method="cohort")

Author(s)

Ricardo Pio Monti

References

Danaher, P., Wang, P. , and Witten, D. "The joint graphical lasso for inverse covariance estimation across multiple classes." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 76.2 (2014): 373-397.

Monti, R., Anagnostopolus, C., Montana, G. "Inferring brain connectivity networks from functional MRI data via mixed neighbourhood selection", arXiv, 2015

See Also

MNS, cv.MNS, plot.MNS

Examples

# generate data according to cohort model of Monti et al. (2015)
set.seed(1)
Dat = gen.Network(p = 10, Nsub = 5, 
 sparsity = .2, REsize=10, REprob=.5, 
 REnoise = 1, Nobs=20)

## Not run: 
# plot simulated networks:
plot(Net, view="pop")

## End(Not run)

Plotting function for MNS objects

Description

Plotting function for MNS objects. This function implements plotting for either population networks, high variable networks or subject-specific networks.

Usage

  ## S3 method for class 'MNS'
plot(x, view="pop", subID=NULL, ...)

Arguments

x

MNS object

view

Plotting view. This argument defines which networks are plotted. Three options are "pop": plot population network, "var": plot network of variable edges, "sub": plot subject-specific networks

subID

If view="sub", subID indicates which subjects networks should be plotted.

...

Additional arguments to pass to plot function

Details

Plotting function for MNS objects. Can be used to plot simulated networks or results obtained from running MNS algorithm. Note that if networks are simulated using the "Danaher" method then only subject-specific networks can be plotted (i.e., we require view="sub")

Author(s)

Ricardo Pio monti

References

Monti, R., Anagnostopolus, C., Montana, G. "Inferring brain connectivity networks from functional MRI data via mixed neighbourhood selection", arXiv, 2015

See Also

MNS, gen.Network

Examples

set.seed(1)
N=4
Net = gen.Network(method = "cohort", p = 10, 
                       Nsub = N, sparsity = .2, 
                       REsize = 20, REprob = .5,
                       REnoise = 1, Nobs = 10)
## Not run: 
# can plot simulated networks:
plot.MNS(Net, view="pop")

# can also plot results from MNS algorithm:
mns = MNS(dat = Net$Data, lambda_pop = .1, lambda_random = .1, parallel = TRUE)
plot.MNS(mns) # plot population network
plot.MNS(mns, view="var") # plot variance network
plot.MNS(mns, view="sub") # plot subject networks (note red edges here are variable edges!)

## End(Not run)