Package 'mglasso'

Title:	Multiscale Graphical Lasso
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.
Authors:	Edmond Sanou [aut, cre], Tung Le [ctb], Christophe Ambroise [ths], Geneviève Robin [ths]
Maintainer:	Edmond Sanou <[email protected]>
License:	MIT + file LICENSE
Version:	0.1.3
Built:	2025-03-10 05:51:35 UTC
Source:	https://github.com/desanou/mglasso

Help Index

Adjacency matrix
Init Beta 1 matrix
Init Beta via OLS
vectorize beta matrix
return precision matrix
cah_glasso
CONESTA solver.
CONESTA solver for numerical experiments.
cost function
distances Beta
Mean error from classical regression
Formula from Huge paper
TO DO: Fill upper triangular matrix then sum up with the transpose to have full matrix
doesn't work when dealing with matrix where diagonal of zero should be adjusted
extracts meta-variables indices
weighted sum/difference of two regression vectors
Plot ROC curve and calculate AUC
compute range of number of clusters from ROC outputs take in parameter an object from reorder_mglasso_roc_calculations
Title
Neighborhood selection estimate
Plot the image of a matrix
Install the python library pylearn-parsimony and other required libraries
lagrangian function
Check first estimate coeffs with glm
mean of randomly simulated precision matrices in the same configuration
Merge Beta Different types of merging and their effect
compute clusters partition from pairs of variables to merge
Merge labels
merge clusters from table
Merge X
Inference of Multiscale Gaussian Graphical Model.
neighbor_select
One simulation configuration
compute TPR, FPR, SHD given estimated and true precision matrices
get performances from list of estimations
Plot MGLasso Clusterpath
fonction qui affiche les matrices d'adjacence à chaque niveau de la hiérarchie à automatiser utiliser niveau de legende commune
Compute precision matrix from regression vectors
pareil pour les clusters ACP dimensions ?
EBIC
K-fold cross validation neghborhood lasso selection
K-fold cross validation mglasso
Finds the optimal number of clusters using slope heuristic
stability selection mglasso
stability selection mglasso II stars way
def sequences for lambda1s and lambda2s not sure if max of lambda1 s still the same as in the lasso case. But if find better equivalence will update this part
simulate data with given graph structure
symmetrize matrix of regression vectors pxp

Init Beta 1 matrix

Description

Init Beta 1 matrix

Usage

beta_idty(p)

beta_idty(p)
beta_idty(p)

beta_idty(p)

Init Beta via OLS

Description

Init Beta via OLS

Initialize regression matrix

Usage

beta_ols(X)

beta_ols(X)

beta_ols(X)
beta_ols(X)

beta_ols(X)

beta_ols(X)

Arguments

X

data

Value

A zero-diagonal matrix of regression vectors.

vectorize beta matrix

Description

vectorize beta matrix

Transform a matrix of regression coefficients to vector removing the diagonal

Usage

beta_to_vector(beta_mat)

beta_to_vector(beta_mat)

beta_to_vector(beta_mat)
beta_to_vector(beta_mat)

beta_to_vector(beta_mat)

beta_to_vector(beta_mat)

Arguments

beta_mat

matrix of regressions vectors

Value

A numeric vector of all regression coefficients.

return precision matrix

Description

return precision matrix

Usage

bloc_diag(n_vars, connectivity_mat, prop_clusters, rho)
bloc_diag(n_vars, connectivity_mat, prop_clusters, rho)

cah_glasso

Description

cah_glasso

Usage

cah_glasso(num_clusters, data, lam1, hclust_obj)
cah_glasso(num_clusters, data, lam1, hclust_obj)

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
)
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.

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)
## 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)

CONESTA solver for numerical experiments.

Description

CONESTA solver for numerical experiments.

Usage

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

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_rwrapper(X, 0.1, 0.1)

## End(Not run)
## 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_rwrapper(X, 0.1, 0.1)

## End(Not run)

cost function

Description

cost computes the cost function of Mglasso method.

Usage

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

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

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

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

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.

distances Beta

Description

distances Beta

Compute distance matrix between regression vectors

Usage

dist_beta(beta, distance = "euclidean")

dist_beta(beta, distance = "euclidean")
dist_beta(beta, distance = "euclidean")

dist_beta(beta, distance = "euclidean")

Arguments

`beta`	matrix of regression vectors
`distance`	euclidean or relative distance

Value

A numeric matrix of distances.

Mean error from classical regression

Description

Mean error from classical regression

Usage

error(Theta, X)
error(Theta, X)

Formula from Huge paper

Description

Formula from Huge paper

Usage

error_huge(Theta, X)
error_huge(Theta, X)

TO DO: Fill upper triangular matrix then sum up with the transpose to have full matrix

Description

TO DO: Fill upper triangular matrix then sum up with the transpose to have full matrix

Usage

expand_beta(beta_level, clusters)
expand_beta(beta_level, clusters)

doesn't work when dealing with matrix where diagonal of zero should be adjusted

Description

doesn't work when dealing with matrix where diagonal of zero should be adjusted

Usage

expand_beta_deprecated(beta_level, clusters)
expand_beta_deprecated(beta_level, clusters)

extracts meta-variables indices

Description

extracts meta-variables indices

Usage

extract_meta(full_graph = NULL, clusters)
extract_meta(full_graph = NULL, clusters)

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

Plot ROC curve and calculate AUC

Description

Plot ROC curve and calculate AUC

Usage

get_auc(omega_hat_list, omega, to = to_)
get_auc(omega_hat_list, omega, to = to_)

Arguments

type

Classical ROC curve tpr = f(FPR) or TPR = f(precision) adjusted version. Compute AUC and partial AUC

compute range of number of clusters from ROC outputs take in parameter an object from reorder_mglasso_roc_calculations

Description

compute range of number of clusters from ROC outputs take in parameter an object from reorder_mglasso_roc_calculations

Usage

get_range_nclusters(out, thresh_fuse = 1e-06, p = 40)
get_range_nclusters(out, thresh_fuse = 1e-06, p = 40)

Title

Description

Title

Usage

ggplot_roc(
  omega_hat_list,
  omega,
  type = c("classical", "precision_recall"),
  main = NULL
)
ggplot_roc(
  omega_hat_list,
  omega,
  type = c("classical", "precision_recall"),
  main = NULL
)

Arguments

main

Neighborhood selection estimate

Description

Neighborhood selection estimate

Usage

graph_estimate(rho, X)
graph_estimate(rho, X)

Plot the image of a matrix

Description

Plot the image of a matrix

Usage

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

lagrangian function

Description

Beta and X must have the same number of variables

Usage

lagrangian(Beta, X, lambda1 = 0, lambda2 = 0)

lagrangian(Beta, X, lambda1 = 0, lambda2 = 0)
lagrangian(Beta, X, lambda1 = 0, lambda2 = 0)

lagrangian(Beta, X, lambda1 = 0, lambda2 = 0)

Arguments

`Beta`	numeric matrix. In rows, regression vectors coefficients following of node-wise regression. diag(Beta) = 0
`X`	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 lagrangian

Examples


## Generation of K block partitions
n = 50
K = 3
p = 6
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 <- bdiag(blocs)
set.seed(11)
X <- rmvnorm(n, mean = rep(0,p), sigma = as.matrix(mat.covariance))
X <- scale(X)

## Initialization for Beta
Beta1 <- matrix(0, nrow = p, ncol = p)
for(i in 1:p){
  Beta1[i,-i] <- solve(t(X[,-i])%*%X[,-i]) %*% t(X[,-i]) %*% X[,i]
  }
lagrangian(Beta, X, 0, 0)

## Generation of K block partitions
n = 50
K = 3
p = 6
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 <- bdiag(blocs)
set.seed(11)
X <- rmvnorm(n, mean = rep(0,p), sigma = as.matrix(mat.covariance))
X <- scale(X)

## Initialization for Beta
Beta1 <- matrix(0, nrow = p, ncol = p)
for(i in 1:p){
  Beta1[i,-i] <- solve(t(X[,-i])%*%X[,-i]) %*% t(X[,-i]) %*% X[,i]
  }
lagrangian(Beta, X, 0, 0)
## Generation of K block partitions
n = 50
K = 3
p = 6
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 <- bdiag(blocs)
set.seed(11)
X <- rmvnorm(n, mean = rep(0,p), sigma = as.matrix(mat.covariance))
X <- scale(X)

## Initialization for Beta
Beta1 <- matrix(0, nrow = p, ncol = p)
for(i in 1:p){
  Beta1[i,-i] <- solve(t(X[,-i])%*%X[,-i]) %*% t(X[,-i]) %*% X[,i]
  }
lagrangian(Beta, X, 0, 0)

## Generation of K block partitions
n = 50
K = 3
p = 6
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 <- bdiag(blocs)
set.seed(11)
X <- rmvnorm(n, mean = rep(0,p), sigma = as.matrix(mat.covariance))
X <- scale(X)

## Initialization for Beta
Beta1 <- matrix(0, nrow = p, ncol = p)
for(i in 1:p){
  Beta1[i,-i] <- solve(t(X[,-i])%*%X[,-i]) %*% t(X[,-i]) %*% X[,i]
  }
lagrangian(Beta, X, 0, 0)

Check first estimate coeffs with glm

Description

Check first estimate coeffs with glm

Usage

lasso_estimate(response_variable_number, penalty_value)
lasso_estimate(response_variable_number, penalty_value)

mean of randomly simulated precision matrices in the same configuration

Description

mean of randomly simulated precision matrices in the same configuration

Usage

mean_prec_mat(nrep = 10, config = config_)
mean_prec_mat(nrep = 10, config = config_)

Merge Beta Different types of merging and their effect

Description

Merge Beta Different types of merging and their effect

Usage

merge_beta(Beta, pair_to_merge, clusters)
merge_beta(Beta, pair_to_merge, clusters)

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)
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.

Merge labels

Description

Merge labels

Usage

merge_labels(merged_pair, labels, level)
merge_labels(merged_pair, labels, level)

merge clusters from table

Description

merge clusters from table

Usage

merge_proc(
  pairs_to_merge,
  clusters,
  X,
  Beta,
  level,
  gain_level,
  gains,
  labels,
  merge
)
merge_proc(
  pairs_to_merge,
  clusters,
  X,
  Beta,
  level,
  gain_level,
  gains,
  labels,
  merge
)

Merge X

Description

weighted mean

Usage

mergeX(X, pair_to_merge, clusters)
mergeX(X, pair_to_merge, clusters)

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
)
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.

Examples

## Not run: 
mglasso::install_pylearn_parsimony(envname = "rmglasso", method = "conda")
reticulate::use_condaenv("rmglasso", required = TRUE)
reticulate::py_config()
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)
## Not run: 
mglasso::install_pylearn_parsimony(envname = "rmglasso", method = "conda")
reticulate::use_condaenv("rmglasso", required = TRUE)
reticulate::py_config()
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)

neighbor_select

Description

neighbor_select

Usage

neighbor_select(
  data = data$X,
  config,
  lambda_min_ratio = 0.01,
  nlambda = 10,
  nresamples = 20,
  lambdas = NULL,
  model = NULL,
  verbose = FALSE,
  estim_var = NULL
)
neighbor_select(
  data = data$X,
  config,
  lambda_min_ratio = 0.01,
  nlambda = 10,
  nresamples = 20,
  lambdas = NULL,
  model = NULL,
  verbose = FALSE,
  estim_var = NULL
)

One simulation configuration

Description

One simulation configuration

Usage

one_config(n, p, pi, alpha, rho)
one_config(n, p, pi, alpha, rho)

compute TPR, FPR, SHD given estimated and true precision matrices

Description

compute TPR, FPR, SHD given estimated and true precision matrices

Usage

perf_one(omega_hat, omega)
perf_one(omega_hat, omega)

Details

SHD: structural hamming distance

get performances from list of estimations

Description

get performances from list of estimations

Usage

perf_vec(omega_hat_list, omega)
perf_vec(omega_hat_list, omega)

Plot MGLasso Clusterpath

Description

Plot MGLasso Clusterpath

Usage

plot_clusterpath(X, mglasso_res, colnames_ = NULL)
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.

fonction qui affiche les matrices d'adjacence à chaque niveau de la hiérarchie à automatiser utiliser niveau de legende commune

Description

Plot the object returned by the mglasso function.

Usage

plot_mglasso(mglasso_, levels_ = NULL)

plot_mglasso(mglasso_, levels_ = NULL)
plot_mglasso(mglasso_, levels_ = NULL)

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)
precision_to_regression(K)

Arguments

`K`	precision matrix

Value

A numeric matrix.

pareil pour les clusters ACP dimensions ?

Description

pareil pour les clusters ACP dimensions ?

Usage

repart(cor_)
repart(cor_)

EBIC

Description

EBIC

Usage

select_ebic_weighted(Thetas, ploglik, n_edges, n, p, gam = 0.5, pen_params)
select_ebic_weighted(Thetas, ploglik, n_edges, n, p, gam = 0.5, pen_params)

K-fold cross validation neghborhood lasso selection

Description

K-fold cross validation neghborhood lasso selection

Usage

select_kfold(
  X,
  Thetas,
  lambdas = NULL,
  n_lambda,
  K_fold = 10,
  criterion = "ploglik",
  verbose = TRUE
)
select_kfold(
  X,
  Thetas,
  lambdas = NULL,
  n_lambda,
  K_fold = 10,
  criterion = "ploglik",
  verbose = TRUE
)

Arguments

criterion

c("ploglik", "rmse")

Details

if criterion = "ploglik" use pseudo-log likelihood formula from Huge paper with matrix approach if "rmse" use mean squarred prediction error

K-fold cross validation mglasso

Description

K-fold cross validation mglasso

Usage

select_kfold_mglasso(
  X,
  lambda1s = NULL,
  lambda2s = NULL,
  K_fold = 5,
  nl1 = 1,
  nl2 = 1,
  lam1_min_ratio,
  verbose = TRUE
)
select_kfold_mglasso(
  X,
  lambda1s = NULL,
  lambda2s = NULL,
  K_fold = 5,
  nl1 = 1,
  nl2 = 1,
  lam1_min_ratio,
  verbose = TRUE
)

Finds the optimal number of clusters using slope heuristic

Description

Finds the optimal number of clusters using slope heuristic

Usage

select_partition(gains)
select_partition(gains)

Value

integer scalar. The indice of the selected model.

stability selection mglasso

Description

stability selection mglasso

Usage

select_stab_mglasso(X, l1_, l2_, subsample_ratio, nrep, stab_thresh)
select_stab_mglasso(X, l1_, l2_, subsample_ratio, nrep, stab_thresh)

stability selection mglasso II stars way

Description

stability selection mglasso II stars way

Usage

select_stars_mglasso(
  X,
  lambda1s = NULL,
  lambda2s = NULL,
  subsample_ratio = NULL,
  nrep = 1,
  stars_thresh = 0.1,
  nl1 = 1,
  nl2 = 1
)
select_stars_mglasso(
  X,
  lambda1s = NULL,
  lambda2s = NULL,
  subsample_ratio = NULL,
  nrep = 1,
  stars_thresh = 0.1,
  nl1 = 1,
  nl2 = 1
)

def sequences for lambda1s and lambda2s not sure if max of lambda1 s still the same as in the lasso case. But if find better equivalence will update this part

Description

def sequences for lambda1s and lambda2s not sure if max of lambda1 s still the same as in the lasso case. But if find better equivalence will update this part

Usage

seq_l1l2(
  X,
  nlam1 = 2,
  nlam2 = 2,
  logscale = TRUE,
  mean = FALSE,
  lambda1_min_ratio = 0.01,
  require_non_list = FALSE,
  l2_max = NULL
)
seq_l1l2(
  X,
  nlam1 = 2,
  nlam2 = 2,
  logscale = TRUE,
  mean = FALSE,
  lambda1_min_ratio = 0.01,
  require_non_list = FALSE,
  l2_max = NULL
)

Arguments

mean

in conesta_rwrapper is the mean criterion used ie averaged by np

simulate data with given graph structure

Description

simulate data with given graph structure

Usage

sim_data(
  p = 20,
  np_ratio = 2,
  structure = c("block_diagonal", "hub", "scale_free", "erdos"),
  alpha,
  prob_mat,
  rho,
  g,
  inter_cluster_edge_prob = 0.01,
  p_erdos = 0.1,
  verbose = FALSE
)
sim_data(
  p = 20,
  np_ratio = 2,
  structure = c("block_diagonal", "hub", "scale_free", "erdos"),
  alpha,
  prob_mat,
  rho,
  g,
  inter_cluster_edge_prob = 0.01,
  p_erdos = 0.1,
  verbose = FALSE
)

Arguments

verbose

Value

A list: graph : precision

symmetrize matrix of regression vectors pxp

Description

symmetrize matrix of regression vectors pxp

Apply symmetrization on estimated graph

Usage

symmetrize(mat, rule = "and")

symmetrize(mat, rule = "and")
symmetrize(mat, rule = "and")

symmetrize(mat, rule = "and")

Arguments

`mat`	graph or precision matrix
`rule`	"and" or "or" rule

Value

A numeric matrix.

`mat`	matrix of regression coefficients
`sym_rule`	symmetrization rule, either AND or OR

Package 'mglasso'

Help Index

Adjacency matrix

Description

Usage

Arguments

Value

Init Beta 1 matrix

Description

Usage

Init Beta via OLS

Description

Usage

Arguments

Value

vectorize beta matrix

Description

Usage

Arguments

Value

return precision matrix

Description

Usage

cah_glasso

Description

Usage

CONESTA solver.

Description

Usage

Arguments

Details

Value

See Also

Examples

CONESTA solver for numerical experiments.

Description

Usage

Examples

cost function

Description

Usage

Arguments

Value

distances Beta

Description

Usage

Arguments

Value

Mean error from classical regression

Description

Usage

Formula from Huge paper

Description

Usage

TO DO: Fill upper triangular matrix then sum up with the transpose to have full matrix

Description

Usage

doesn't work when dealing with matrix where diagonal of zero should be adjusted

Description

Usage

extracts meta-variables indices

Description

Usage

weighted sum/difference of two regression vectors

Description

Usage

Arguments

Value

Examples

Plot ROC curve and calculate AUC

Description

Usage

Arguments

compute range of number of clusters from ROC outputs take in parameter an object from reorder_mglasso_roc_calculations

Description

Usage

Title

Description

Usage

Arguments