Type: Package
Title: Multiscale Graphical Lasso
Version: 0.1.2
Description: Inference of Multiscale graphical models with neighborhood selection approach. The method is based on solving a convex optimization problem combining a Lasso and fused-group Lasso penalties. This allows to infer simultaneously a conditional independence graph and a clustering partition. The optimization is based on the Continuation with Nesterov smoothing in a Shrinkage-Thresholding Algorithm solver (Hadj-Selem et al. 2018) <doi:10.1109/TMI.2018.2829802> implemented in python.
License: MIT + file LICENSE
Imports: corpcor, ggplot2, ggrepel, gridExtra, Matrix, methods, R.utils, reticulate (≥ 1.25), rstudioapi
Suggests: knitr, mvtnorm, rmarkdown, testthat (≥ 3.0.0)
VignetteBuilder: knitr
ByteCompile: true
Config/reticulate: list( packages = list( list(package = "scipy", version = "1.7.1"), list(package = "numpy", version = "1.22.4"), list(package = "matplotlib"), list(package = "scikit-learn"), list(package = "six"), list(package = "pylearn-parsimony", version = "0.3.1", pip = TRUE) ) )
Encoding: UTF-8
RoxygenNote: 7.2.1
URL: https://desanou.github.io/mglasso/
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2022-09-05 22:06:02 UTC; doedm
Author: Edmond Sanou [aut, cre], Tung Le [ctb], Christophe Ambroise [ths], Geneviève Robin [ths]
Maintainer: Edmond Sanou <doedmond.sanou@univ-evry.fr>
Repository: CRAN
Date/Publication: 2022-09-08 13:12:55 UTC

Adjacency matrix

Description

Adjacency matrix

Usage

adj_mat(mat, sym_rule = "and")

Arguments

mat

matrix of regression coefficients

sym_rule

symmetrization rule, either AND or OR

Value

adjacency matrix

Initialize regression matrix

Description

Initialize regression matrix

Usage

beta_ols(X)

Arguments

X

data

Value

A zero-diagonal matrix of regression vectors.

Transform a matrix of regression coefficients to vector removing the diagonal

Description

Transform a matrix of regression coefficients to vector removing the diagonal

Usage

beta_to_vector(beta_mat)

Arguments

beta_mat

matrix of regressions vectors

Value

A numeric vector of all regression coefficients.

CONESTA solver.

Description

Solve the MGLasso optimization problem using CONESTA algorithm. Interface to the pylearn.parsimony python library.

Usage

conesta(
  X,
  lam1,
  lam2,
  beta_warm = c(0),
  type_ = "initial",
  W_ = NULL,
  mean_ = FALSE,
  max_iter_ = 10000,
  prec_ = 0.01
)

Arguments

X

Data matrix nxp.

lam1

Sparsity penalty.

lam2

Total variation penalty.

beta_warm

Warm initialization vector.

type_

Character scalar. By default set to initial version which doesn't use weights

W_

Weights matrix for total variation penalties.

mean_

Logical scalar. If TRUE weights the optimization function by the inverse of sample size.

max_iter_

Numeric scalar. Maximum number of iterations.

prec_

Numeric scalar. Tolerance for the stopping criterion (duality gap).

Details

COntinuation with NEsterov smoothing in a Shrinkage-Thresholding Algorithm (CONESTA, Hadj-Selem et al. 2018) doi:10.1109/TMI.2018.2829802 is an algorithm design for solving optimization problems including group-wise penalties. This function is an interface with the python solver. The MGLasso problem is first reformulated in a problem of the form

argmin 1/2 ||Y - \tilde{X} \tilde{\beta}||_2^2 + \lambda_1 ||\tilde{\beta}||_1 + \lambda_2 \sum_{i<j} ||\boldsymbol A_{ij} \tilde{\beta}||_2

where vector Y is the vectorized form of matrix X.

Value

Numeric matrix of size pxp. Line k of the matrix represents the coefficients obtained from the L1-L2 penalized regression of variable k on the others.

See Also

mglasso() for the MGLasso model estimation.

Examples

## Not run: # because of installation of external packages during checks
mglasso::install_pylearn_parsimony(envname = "rmglasso", method = "conda")
reticulate::use_condaenv("rmglasso", required = TRUE)
reticulate::py_config()
n = 30
K = 2
p = 4
rho = 0.85
blocs <- list()
for (j in 1:K) {
 bloc <- matrix(rho, nrow = p/K, ncol = p/K)
   for(i in 1:(p/K)) { bloc[i,i] <- 1 }
   blocs[[j]] <- bloc
   }

mat.covariance <- Matrix::bdiag(blocs)
mat.covariance
set.seed(11)
X <- mvtnorm::rmvnorm(n, mean = rep(0,p), sigma = as.matrix(mat.covariance))
X <- scale(X)
res <- conesta(X, 0.1, 0.1)

## End(Not run)

Mglasso cost function

Description

cost computes the cost function of Mglasso method.

Usage

cost(beta, x, lambda1 = 0, lambda2 = 0)

Arguments

beta

p by p numeric matrix. In rows, regression vectors coefficients after node-wise regression. diag(beta) = 0.

x

n by p numeric matrix. Data with variables in columns.

lambda1

numeric scalar. Lasso penalization parameter.

lambda2

numeric scalar. Fused-group Lasso penalization parameter.

Value

numeric scalar. The cost.

Compute distance matrix between regression vectors

Description

Compute distance matrix between regression vectors

Usage

dist_beta(beta, distance = "euclidean")

Arguments

beta

matrix of regression vectors

distance

euclidean or relative distance

Value

A numeric matrix of distances.

weighted sum/difference of two regression vectors

Description

fun_lines applies function fun to regression vectors while reordering the coefficients, such that the j-th coefficient in beta[j, ] is permuted with the i-th coefficient.

Usage

fun_lines(i, j, beta, fun = `-`, ni = 1, nj = 1)

Arguments

i

integer scalar. Index of the first vector.

j

integer scalar. Index of the second vector.

beta

p by p numeric matrix. In rows, regression vectors coefficients after node-wise regression. diag(beta) = 0.

fun

function. Applied on lines.

ni

integer scalar. Weight for vector i.

nj

integer scalar. Weight for vector j.

Value

numeric vector

Examples

beta <- matrix(round(rnorm(9),2), ncol = 3)
diag(beta) <- 0
beta
fun_lines(1, 2, beta)
fun_lines(2, 1, beta)

Plot the image of a matrix

Description

Plot the image of a matrix

Usage

image_sparse(matrix, main_ = "", sub_ = "", col_names = FALSE)

Arguments

matrix

matrix of regression coefficients

main_

title

sub_

subtitle

col_names

columns names

Value

No return value.

Install the python library pylearn-parsimony and other required libraries

Description

pylearn-parsimony contains the solver CONESTA used for the mglasso problem and is available on github at https://github.com/neurospin/pylearn-parsimony It is advised to use a python version ">=3.7,<3.10". Indeed, the latest version of scipy under which mglasso was developped is scipy 1.7.1 which is based on python ">=3.7,<3.10". In turn, this version of scipy can only be associated with a version of numpy ">=1.16.5,<1.23.0"

Usage

install_pylearn_parsimony(
  method = c("auto", "virtualenv", "conda"),
  conda = "auto",
  extra_pack = c("scipy == 1.7.1", "scikit-learn", "numpy == 1.22.4", "six",
    "matplotlib"),
  python_version = "3.8",
  restart_session = TRUE,
  envname = NULL,
  ...
)

Arguments

method

Installation method. By default, "auto" automatically finds a method that will work in the local environment. Change the default to force a specific installation method. Note that the "virtualenv" method is not available on Windows.

conda

The path to a conda executable. Use "auto" to allow reticulate to automatically find an appropriate conda binary. See Finding Conda and conda_binary() for more details.

extra_pack

Character vector. Extra-packages to be installed.

python_version

The requested Python version. Ignored when attempting to install with a Python virtual environment.

restart_session

Restart R session after installing (note this will only occur within RStudio)

envname

The name, or full path, of the environment in which Python packages are to be installed. When NULL (the default), the active environment as set by the RETICULATE_PYTHON_ENV variable will be used; if that is unset, then the r-reticulate environment will be used.

...

additionnal arguments passed to reticulate::py_install()

Value

No return value.

compute clusters partition from pairs of variables to merge

Description

compute clusters partition from pairs of variables to merge

Usage

merge_clusters(pairs_to_merge, clusters)

Arguments

pairs_to_merge

table of the indices of variables to be merge

clusters

numeric vector. By default 1:p where p is the number of variables

Value

A numeric vector.

Inference of Multiscale Gaussian Graphical Model.

Description

Cluster variables using L2 fusion penalty and simultaneously estimates a gaussian graphical model structure with the addition of L1 sparsity penalty.

Usage

mglasso(
  x,
  lambda1 = 0,
  fuse_thresh = 0.001,
  maxit = NULL,
  distance = c("euclidean", "relative"),
  lambda2_start = 1e-04,
  lambda2_factor = 1.5,
  precision = 0.01,
  weights_ = NULL,
  type = c("initial"),
  compact = TRUE,
  verbose = FALSE
)

Arguments

x

Numeric matrix (n x p). Multivariate normal sample with n independent observations.

lambda1

Positive numeric scalar. Lasso penalty.

fuse_thresh

Positive numeric scalar. Threshold for clusters fusion.

maxit

Integer scalar. Maximum number of iterations.

distance

Character. Distance between regression vectors with permutation on symmetric coefficients.

lambda2_start

Numeric scalar. Starting value for fused-group Lasso penalty (clustering penalty).

lambda2_factor

Numeric scalar. Step used to update fused-group Lasso penalty in a multiplicative way..

precision

Tolerance for the stopping criterion (duality gap).

weights_

Matrix of weights.

type

If "initial" use classical version of MGLasso without weights.

compact

Logical scalar. If TRUE, only save results when previous clusters are different from current.

verbose

Logical scalar. Print trace. Default value is FALSE.

Details

Estimates a gaussian graphical model structure while hierarchically grouping variables by optimizing a pseudo-likelihood function combining Lasso and fuse-group Lasso penalties. The problem is solved via the COntinuation with NEsterov smoothing in a Shrinkage-Thresholding Algorithm (Hadj-Selem et al. 2018). Varying the fusion penalty \lambda_2 in a multiplicative fashion allow to uncover a seemingly hierarchical clustering structure. For \lambda_2 = 0, the approach is theoretically equivalent to the Meinshausen-Bühlmann (2006) neighborhood selection as resuming to the optimization of pseudo-likelihood function with \ell_1 penalty (Rocha et al., 2008). The algorithm stops when all the variables have merged into one cluster. The criterion used to merge clusters is the \ell_2-norm distance between regression vectors.

For each iteration of the algorithm, the following function is optimized :

1/2 \sum_{i=1}^p || X^i - X^{\ i} \beta^i ||_2 ^2 + \lambda_1 \sum_{i = 1}^p || \beta^i ||_1 + \lambda_2 \sum_{i < j} || \beta^i - \tau_{ij}(\beta^j) ||_2.

where \beta^i is the vector of coefficients obtained after regression X^i on the others and \tau_{ij} is a permutation exchanging \beta_j^i with \beta_i^j.

Value

A list-like object of class mglasso is returned.

out

List of lists. Each element of the list corresponds to a clustering level. An element named levelk contains the regression matrix beta and clusters vector clusters for a clustering in k clusters. When compact = TRUE out has as many elements as the number of unique partitions. When set to FALSE, the function returns as many items as the the range of values taken by lambda2.

l1

the sparsity penalty lambda1 used in the problem solving.

See Also

conesta() for the problem solver, plot_mglasso() for plotting the output of mglasso.

Examples

## Not run: 
reticulate::use_condaenv("rmglasso", required = TRUE)
n = 50
K = 3
p = 9
rho = 0.85
blocs <- list()
for (j in 1:K) {
  bloc <- matrix(rho, nrow = p/K, ncol = p/K)
  for(i in 1:(p/K)) { bloc[i,i] <- 1 }
  blocs[[j]] <- bloc
}

mat.covariance <- Matrix::bdiag(blocs)
mat.covariance

set.seed(11)
X <- mvtnorm::rmvnorm(n, mean = rep(0,p), sigma = as.matrix(mat.covariance))
X <- scale(X)

res <- mglasso(X, 0.1, lambda2_start = 0.1)
res$out[[1]]$clusters
res$out[[1]]$beta

## End(Not run)

Plot MGLasso Clusterpath

Description

Plot MGLasso Clusterpath

Usage

plot_clusterpath(X, mglasso_res, colnames_ = NULL)

Arguments

X

numeric matrix

mglasso_res

object of class mglasso

colnames_

columns labels

Details

This function plot the clustering path of mglasso method on the 2 principal components axis of X. As the centroids matrices are not of the same dimension as X, we choose to plot the predicted X matrix path.

Value

no return value.

Plot mglasso function output.

Description

Plot the object returned by the mglasso function.

Usage

plot_mglasso(mglasso_, levels_ = NULL)

Arguments

mglasso_

Object of class mglasso.

levels_

Character vector. Selected levels for which estimated matrices will be plot. If NULL plot all levels.

Value

No return value.

Compute precision matrix from regression vectors

Description

Compute precision matrix from regression vectors

Usage

precision_to_regression(K)

Arguments

K

precision matrix

Value

A numeric matrix.

Apply symmetrization on estimated graph

Description

Apply symmetrization on estimated graph

Usage

symmetrize(mat, rule = "and")

Arguments

mat

graph or precision matrix

rule

"and" or "or" rule

Value

A numeric matrix.