Title:	Graphical Models Estimation from Multiple Sources
Version:	2.0.2
Description:	Estimates networks of conditional dependencies (Gaussian graphical models) from multiple classes of data (similar but not exactly, i.e. measurements on different equipment, in different locations or for various sub-types). Package also allows to generate simulation data and evaluate the performance. Implementation of the method described in Angelini, De Canditiis and Plaksienko (2022) <doi:10.3390/math10213983>.
Depends:	R (≥ 3.6.0)
Imports:	Matrix, matrixcalc, MASS, SMUT, igraph, parallel, purrr
URL:	https://github.com/annaplaksienko/jewel
License:	GPL-2
Encoding:	UTF-8
RoxygenNote:	7.3.1
Suggests:	knitr, rmarkdown
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2024-05-21 21:48:46 UTC; annapla
Author:	Anna Plaksienko [aut, cre], Claudia Angelini [aut], Daniela De Canditiis [aut]
Maintainer:	Anna Plaksienko <anna@plaxienko.com>
Repository:	CRAN
Date/Publication:	2024-05-22 21:20:07 UTC

Adding zero diagonal to a matrix

Description

Function adds zero diagonal to (p-1) by p matrix and returns p by p matrix

Usage

addZeroDiagonal(M)

Arguments

Construct weights for _jewel_ minimization problem from prior information on vertices degrees.

Description

Function takes a numerical vector of vertices degrees and constructs weights with the rule W_ij = 1 / sqrt(d_i * d_j) and then the whole matrix is normilized by the maximum.

Usage

constructWeights(d, K = NULL)

Arguments

Value

W - a list of K numeric matrices of the size p by p

Examples

{
K <- 3
p <- 50
n <- 20
data <- generateData_rewire(K = K, p = p, n = n, ncores = 1, verbose = FALSE)
G_list_true <- data$Graphs
true_degrees <- rowSums(G_list_true[[1]])
cut <- sort(true_degrees, decreasing = TRUE)[ceiling(p * 0.03)]
apriori_hubs <- ifelse(true_degrees >= cut, 10, 1)
W <- constructWeights(apriori_hubs, K = K)
}

Evaluation of graph estimation method's performance if the true graph is known.

Description

Function compares adjacency matrices of the true and estimated simple graphs and calculates the number of true positives (correctly estimated edges), true negatives (correctly estimated absence of edges), false positives (edges present in the estimator but not in the true graph) and false negatives (failure to identify an edge).

Usage

evaluatePerformance(G, G_hat)

Arguments

Value

performance - a numeric vector of length 4 with TP, TN, FP, FN.

Examples

{
K <- 3
p <- 50
n <- 20
data <- generateData_rewire(K = K, p = p, n = n, ncores = 1, verbose = FALSE)
G_common_true <- data$CommonGraph
X <- data$Data
res <- jewel(X, lambda1 = 0.25)
G_common_est <- res$CommonG
evaluatePerformance(G = G_common_true, G_hat = G_common_est)
}

Generate a set of scale-free graphs and corresponding datasets (using the graphs as their Gaussian graphical models)

Description

Function first generates K scale-free graphs with p vertices. They have the same order and degree distribution and share most of the edges, but some edges may vary (user can control how many). Function then generates corresponding precision and covariance matrices, all of the size p by p (see the paper for the details of the procedure). Then for each l-th element of vector n it generates K data matrices, each of the size n_l by p, i.e., for the same underlying graphs we can generate several sets of K datasets with different sample sizes.

Usage

generateData_rewire(
  K,
  p,
  n,
  power = 1,
  m = 1,
  perc = 0.05,
  int = NULL,
  ncores = NULL,
  makePlot = TRUE,
  verbose = TRUE
)

Arguments

Value

The following list is returned

• Graphs – a list of adjacency matrices of the K generated graphs.

• CommomGraph - a matrix, common part (intersection) of the K generated graphs.

• Data - a list of lists, for each sample size of the input vector n one obtains K data matrices, each of the size n_l by p.

• Sigma - a list of K covariance matrices of the size p by p.

Examples

data <- generateData_rewire(K = 3, p = 50, n = 20, ncores = 1, verbose = FALSE)

Estimate Gaussian graphical models from multiple datasets

Description

This function estimates Gaussian graphical models (i.e. networks of conditional dependencies, direct connections between variables) given multiple datasets. We assume that datasets contain measurements of the same variables collected under different conditions (different equipment, locations, even sub-types of disease).

Usage

jewel(
  X,
  lambda1,
  lambda2 = NULL,
  Theta = NULL,
  W = NULL,
  tol = 0.01,
  maxIter = 10000,
  stability = FALSE,
  stability_nsubsets = 25,
  stability_frac = 0.8,
  verbose = TRUE
)

Arguments

Value

The following list is returned

• CommonG - an adjacency matrix of the common estimated graph (intersection of K estimated graphs).

• G_list - a list of K adjacency matrices for each estimated graph.

• Theta - a list of K estimated covariance matrices (when stability selection is disabled).

• BIC – a number, value of Bayesian information criterion for resulting graphs (when stability selection is disabled).

Examples

{
K <- 3
p <- 50
n <- 20
data <- generateData_rewire(K = K, p = p, n = n, ncores = 1, verbose = FALSE)
G_list_true <- data$Graphs
X <- data$Data
true_degrees <- rowSums(G_list_true[[1]])
cut <- sort(true_degrees, decreasing = TRUE)[ceiling(p * 0.03)]
apriori_hubs <- ifelse(true_degrees >= cut, 10, 1)
W <- constructWeights(apriori_hubs, K = K)
res <- jewel(X, lambda1 = 0.25, W = W, verbose = FALSE)
}

Estimate Gaussian graphical models from multiple datasets

Description

This function estimates Gaussian graphical models (i.e. networks of conditional dependencies, direct connections between variables) given several datasets. We assume that datasets contain measurements of the same variables collected under different conditions (different equipment, locations, even sub-types of disease).

Usage

jewel_inner(
  X,
  lambda1,
  lambda2 = NULL,
  Theta = NULL,
  W = NULL,
  tol = 0.01,
  maxIter = 10000,
  verbose = TRUE
)

Arguments

Value

The following list is returned

• CommonG - an adjacency matrix of the common estimated graph (intersection of K estimated graphs).

• G_list - a list of K adjacency matrices for each estimated graph.

• Theta - a list of K estimated covariance matrices.

• BIC – a number, value of Bayesian information criterion for resulting graphs.

Removing diagonal from a matrix

Description

Function removes a diagonal from a square p by p matrix and returns (p-1) by p matrix

Usage

removeDiagonal(M)

Arguments