Package 'CVN' reference manual

Title:	Covariate-varying Networks
Description:	A package for inferring high-dimensional Gaussian graphical networks that change with multiple discrete covariates
Authors:	Louis Dijkstra [aut, cre]
Maintainer:	Louis Dijkstra <[email protected]>
License:	GPL (>= 3)
Version:	1.1
Built:	2025-01-04 06:12:55 UTC
Source:	https://github.com/bips-hb/CVN

Check whether Input is Valid

Description

Checks whether the input for the function CVN is valid. This function does not return anything. The execution of the function halts when an issue has been detected.

Usage

check_correctness_input(raw_data, W, lambda1, lambda2, gamma1, gamma2, rho)
check_correctness_input(raw_data, W, lambda1, lambda2, gamma1, gamma2, rho)

Arguments

`raw_data`	A list with matrices. The number of columns should be the same for each matrix
`W`	The $(m \times m)$ -dimensional upper-triangular weight matrix $W$
`lambda1`	A vector of $\lambda_1$ 's LASSO penalty terms
`lambda2`	A vector of $\lambda_2$ 's global smoothing parameters
`gamma1`	A vector of $\gamma_1$ 's LASSO penalty terms. Note that $\gamma_1 = \frac{2 \lambda_1}{m p (1 - p)}$
`gamma2`	A vector of $\gamma_2$ 's global smoothing parameters. Note that $\gamma_2 = \frac{4 \lambda_2}{m(m-1)p(p-1)}$
`rho`	The $\rho$ ADMM's penalty parameter

Create a `data.frame` for the Edges for `visNetwork`

Description

In order to visualize a graph, we need to create a data.frame that can be used by the visNetwork package. This function returns the needed data.frame given a adjacency matrix.

Usage

create_edges_visnetwork(adj_matrix)
create_edges_visnetwork(adj_matrix)

Arguments

adj_matrix

A symmetric adjacency matrix

Value

Data frame that be used as input for visNetwork

Create matrix $D$ to be used for the Generalized LASSO

Description

Generates a matrix $D$ to be used for the generalized LASSO. We solve a generalized LASSO problem for each edge $(s,t)$ for each update step for $Z$ .

Usage

create_matrix_D(W, lambda1, lambda2, rho = 1, remove_zero_row = TRUE)
create_matrix_D(W, lambda1, lambda2, rho = 1, remove_zero_row = TRUE)

Arguments

`W`	The $(m \times m)$ -dimensional upper-triangular weight matrix $W$
`lambda1`	The $\lambda_1$ LASSO penalty term
`lambda2`	The $\lambda_2$ global smoothing parameter
`rho`	The $\rho$ ADMM's penalty parameter (Default: `1`)
`remove_zero_row`	If `TRUE`, rows with zeros are removed. (Default: `TRUE`)

Value

A $((m \cdot (m+1)/2) \times m)$ -dimensional matrix

References

Tibshirani, R. J., & Taylor, J. (2011). The solution path of the generalized lasso. Annals of Statistics, 39(3), 1335–1371. https://doi.org/10.1214/11-AOS878

Examples

m <- 4 # number of graphs
W <- matrix(1, nrow = m, ncol = m) 

# penalty terms:
lambda1 <- .2
lambda2 <- .4
rho <- 1

CVN::create_matrix_D(W, lambda1, lambda2, rho) 
#      [,1] [,2] [,3] [,4]
# [1,]  0.2  0.0  0.0  0.0
# [2,]  0.0  0.2  0.0  0.0
# [3,]  0.0  0.0  0.2  0.0
# [4,]  0.0  0.0  0.0  0.2
# [5,]  0.4 -0.4  0.0  0.0
# [6,]  0.4  0.0 -0.4  0.0
# [7,]  0.4  0.0  0.0 -0.4
# [8,]  0.0  0.4 -0.4  0.0
# [9,]  0.0  0.4  0.0 -0.4
# [10,]  0.0  0.0  0.4 -0.4
m <- 4 # number of graphs
W <- matrix(1, nrow = m, ncol = m) 

# penalty terms:
lambda1 <- .2
lambda2 <- .4
rho <- 1

CVN::create_matrix_D(W, lambda1, lambda2, rho) 
#      [,1] [,2] [,3] [,4]
# [1,]  0.2  0.0  0.0  0.0
# [2,]  0.0  0.2  0.0  0.0
# [3,]  0.0  0.0  0.2  0.0
# [4,]  0.0  0.0  0.0  0.2
# [5,]  0.4 -0.4  0.0  0.0
# [6,]  0.4  0.0 -0.4  0.0
# [7,]  0.4  0.0  0.0 -0.4
# [8,]  0.0  0.4 -0.4  0.0
# [9,]  0.0  0.4  0.0 -0.4
# [10,]  0.0  0.0  0.4 -0.4

Nodes for the `visNetwork` package

Description

Creates a data frame that can be used for the visNetwork package.

Usage

create_nodes_visnetwork(n_nodes, labels = 1:n_nodes)
create_nodes_visnetwork(n_nodes, labels = 1:n_nodes)

Arguments

`n_nodes`	Number of nodes in the graph
`labels`	The labels for the individual nodes (Default: `1:n_nodes`)

Value

Data frame with two columns: id and title

Estimating a Covariate-Varying Network (CVN)

Description

Estimates a covariate-varying network model (CVN), i.e., $m$ Gaussian graphical models that change with (multiple) external covariate(s). The smoothing between the graphs is specified by the $(m \times m)$ -dimensional weight matrix $W$ . The function returns the estimated precision matrices for each graph.

Usage

CVN(
  data,
  W,
  lambda1 = 1:2,
  lambda2 = 1:2,
  gamma1 = NULL,
  gamma2 = NULL,
  rho = 1,
  eps = 1e-04,
  maxiter = 100,
  truncate = 1e-05,
  rho_genlasso = 1,
  eps_genlasso = 1e-10,
  maxiter_genlasso = 100,
  truncate_genlasso = 1e-04,
  n_cores = min(length(lambda1) * length(lambda2), parallel::detectCores() - 1),
  normalized = FALSE,
  warmstart = TRUE,
  minimal = FALSE,
  verbose = TRUE
)
CVN(
  data,
  W,
  lambda1 = 1:2,
  lambda2 = 1:2,
  gamma1 = NULL,
  gamma2 = NULL,
  rho = 1,
  eps = 1e-04,
  maxiter = 100,
  truncate = 1e-05,
  rho_genlasso = 1,
  eps_genlasso = 1e-10,
  maxiter_genlasso = 100,
  truncate_genlasso = 1e-04,
  n_cores = min(length(lambda1) * length(lambda2), parallel::detectCores() - 1),
  normalized = FALSE,
  warmstart = TRUE,
  minimal = FALSE,
  verbose = TRUE
)

Arguments

`data`	A list with matrices, each entry associated with a single graph. The number of columns should be the same for each matrix. Number of observations can differ
`W`	The $(m \times m)$ -dimensional symmetric weight matrix $W$
`lambda1`	Vector with different $\lambda_1$ LASSO penalty terms (Default: `1:2`)
`lambda2`	Vector with different $\lambda_2$ global smoothing parameter values (Default: `1:2`)
`gamma1`	A vector of $\gamma_1$ 's LASSO penalty terms, where $\gamma_1 = \frac{2 \lambda_1}{m p (1 - p)}$ . If `gamma1` is set, the value of `lambda1` is ignored. (Default: `NULL`).
`gamma2`	A vector of $\gamma_2$ 's global smoothing parameters, where that $\gamma_2 = \frac{4 \lambda_2}{m(m-1)p(p-1)}$ . If `gamma2` is set, the value of `lambda2` is ignored.(Default: `NULL`).
`rho`	The $\rho$ penalty parameter for the global ADMM algorithm (Default: `1`)
`eps`	If the relative difference between two update steps is smaller than $\epsilon$ , the algorithm stops. See `relative_difference_precision_matrices` (Default: `1e-4`)
`maxiter`	Maximum number of iterations (Default: `100`)
`truncate`	All values of the final $\hat{\Theta}_i$ 's below `truncate` will be set to `0`. (Default: `1e-5`)
`rho_genlasso`	The $\rho$ penalty parameter for the ADMM algorithm used to solve the generalized LASSO (Default: `1`)
`eps_genlasso`	If the relative difference between two update steps is smaller than $\epsilon$ , the algorithm stops. (Default: `1e-10`)
`maxiter_genlasso`	Maximum number of iterations for solving the generalized LASSO problem (Default: `100`)
`truncate_genlasso`	All values of the final $\hat{\beta}$ below `truncate_genlasso` will be set to `0`. (Default: `1e-4`)
`n_cores`	Number of cores used (Default: max. number of cores - 1, or the total number penalty term pairs if that is less)
`normalized`	Data is normalized if `TRUE`. Otherwise the data is only centered (Default: `FALSE`)
`warmstart`	If `TRUE`, use the `huge` package for estimating the individual graphs first (Default: `TRUE`)
`minimal`	If `TRUE`, the returned `cvn` is minimal in terms of memory, i.e., `Theta`, `data` and `Sigma` are not returned (Default: `FALSE`)
`verbose`	Verbose (Default: `TRUE`)

Value

A CVN object containing the estimates for all the graphs for each different value of $(\lambda_1, \lambda_2)$ . General results for the different values of $(\lambda_1, \lambda_2)$ can be found in the data frame results. It consists of multiple columns, namely:

`lambda1`	$\lambda_1$ value
`lambda2`	$\lambda_2$ value
`converged`	whether algorithm converged or not
`value`	value of the negative log-likelihood function
`n_iterations`	number of iterations of the ADMM
`aic`	Aikake information criterion
`gamma1`	$\gamma_1$ value
`gamma2`	$\gamma_2$ value
`id`	The id. This corresponds to the indices of the lists
`bic`	Bayesian information criterion

The estimates of the precision matrices and the corresponding adjacency matrices for the different values of $(\lambda_1, \lambda_2)$ can be found

`Theta`	A list with the estimated precision matrices $\{ \hat{\Theta}_i(\lambda_1, \lambda_2) \}_{i = 1}^m$ , (only if `minimal = FALSE`)
`adj_matrices`	A list with the estimated adjacency matrices corresponding to the estimated precision matrices in `Theta`. The entries are `1` if there is an edge, `0` otherwise. The matrices are sparse using package `Matrix`

In addition, the input given to the CVN function is stored in the object as well:

`Sigma`	Empirical covariance matrices $\{\hat{\Sigma}_i\}_{i = 1}^m$ , (only if `minimal = FALSE`)
`m`	Number of graphs
`p`	Number of variables
`n_obs`	Vector of length $m$ with number of observations for each graph
`data`	The `data`, but then normalized or centered (only if `minimal = FALSE`)
`W`	The $(m \times m)$ -dimensional weight matrix $W$
`maxiter`	Maximum number of iterations for the ADMM
`rho`	The $\rho$ ADMM's penalty parameter
`eps`	The stopping criterion $\epsilon$
`truncate`	Truncation value for $\{ \hat{\Theta}_i \}_{i = 1}^m$
`maxiter_genlasso`	Maximum number of iterations for the generarlzed LASSO
`rho_genlasso`	The $\rho$ generalized LASSO penalty parameter
`eps_genlasso`	The stopping criterion $\epsilon$ for the generalized LASSO
`truncate_genlasso`	Truncation value for $\beta$ of the generalized LASSO
`n_lambda_values`	Total number of $(\lambda_1, \lambda_2)$ value combinations
`normalized`	If `TRUE`, `data` was normalized. Otherwise `data` was only centered
`warmstart`	If `TRUE`, warmstart was used
`minimal`	If `TRUE`, `data`, `Theta` and `Sigma` are not added
`hits_border_aic`	If `TRUE`, the optimal model based on the AIC hits the border of $(\lambda_1, \lambda_2)$
`hits_border_bic`	If `TRUE`, the optimal model based on the BIC hits the border of $(\lambda_1, \lambda_2)$

Reusing Estimates

When estimating the graph for different values of $\lambda_1$ and $\lambda_2$ , we use the graph estimated (if available) for other $\lambda_1$ and $\lambda_2$ values closest to them.

Examples

data(grid)
m <- 9 # must be 9 for this example

#' Choice of the weight matrix W.
#' (uniform random)
W <- matrix(runif(m*m), ncol = m)
W <- W %*% t(W)
W <- W / max(W)
diag(W) <- 0

# lambdas:
lambda1 = 1:2
lambda2 = 1:2

(cvn <- CVN::CVN(grid, W, lambda1 = lambda1, lambda2 = lambda2,
                 eps = 1e-3, maxiter = 1000, verbose = TRUE))
data(grid)
m <- 9 # must be 9 for this example

#' Choice of the weight matrix W.
#' (uniform random)
W <- matrix(runif(m*m), ncol = m)
W <- W %*% t(W)
W <- W / max(W)
diag(W) <- 0

# lambdas:
lambda1 = 1:2
lambda2 = 1:2

(cvn <- CVN::CVN(grid, W, lambda1 = lambda1, lambda2 = lambda2,
                 eps = 1e-3, maxiter = 1000, verbose = TRUE))

Information Criteria for a `cvn` object

Description

Determines a given information criteria for a cvn object, see CVN.

Usage

determine_information_criterion_cvn(cvn, type = c("AIC", "BIC"))
determine_information_criterion_cvn(cvn, type = c("AIC", "BIC"))

Estimate a CVN

Description

A function for estimating a CVN for a single $(\lambda_1, \lambda_2)$ -value. See for more details CVN

Usage

estimate(
  m,
  p,
  W,
  Theta0,
  Z0,
  Y0,
  a,
  eta1,
  eta2,
  Sigma,
  n_obs,
  rho,
  rho_genlasso,
  eps,
  eps_genlasso,
  maxiter,
  maxiter_genlasso,
  truncate,
  truncate_genlasso,
  verbose = FALSE
)
estimate(
  m,
  p,
  W,
  Theta0,
  Z0,
  Y0,
  a,
  eta1,
  eta2,
  Sigma,
  n_obs,
  rho,
  rho_genlasso,
  eps,
  eps_genlasso,
  maxiter,
  maxiter_genlasso,
  truncate,
  truncate_genlasso,
  verbose = FALSE
)

The Core Graph

Description

Finds the 'core graph', i.e., those edges that are present in all of the estimated graphs

Usage

find_core_graph(cvn)
find_core_graph(cvn)

Arguments

cvn

A cvn object

Value

A list of adjacency matrix, one for each value of (lambda1, lambda2)

Wrapper for `genlassoRcpp`

Description

See for details genlassoRcpp

Usage

genlasso_wrapper(y, W, m, c, eta1, eta2, a, rho, max_iter, eps, truncate)
genlasso_wrapper(y, W, m, c, eta1, eta2, a, rho, max_iter, eps, truncate)

Solving Generalized LASSO with fixed $\lambda = 1$

Description

Solves efficiently the generalized LASSO problem of the form

$\hat{\beta} = \text{argmin } \frac{1}{2} || y - \beta ||_2^2 + ||D\beta||_1$

where $\beta$ and $y$ are $m$ -dimensional vectors and $D$ is a $(c \times m)$ -matrix where $c \geq m$ . We solve this optimization problem using an adaption of the ADMM algorithm presented in Zhu (2017).

Usage

genlassoRcpp(Y, W, m, eta1, eta2, a, rho, max_iter, eps, truncate)
genlassoRcpp(Y, W, m, eta1, eta2, a, rho, max_iter, eps, truncate)

Arguments

`W`	The weight matrix $W$ of dimensions $m x m$
`m`	The number of graphs
`eta1`	Equals $\lambda_1 / rho$
`eta2`	Equals $\lambda_2 / rho$
`a`	Value added to the diagonal of $-D'D$ so that the matrix is positive definite, see `matrix_A_inner_ADMM`
`rho`	The ADMM's parameter
`max_iter`	Maximum number of iterations
`eps`	Stopping criterion. If differences are smaller than $\epsilon$ , algorithm is halted
`truncate`	Values below `truncate` are set to `0`
`y`	The $y$ vector of length $m$

Value

The estimated vector $\hat{\beta}$

References

Zhu, Y. (2017). An Augmented ADMM Algorithm With Application to the Generalized Lasso Problem. Journal of Computational and Graphical Statistics, 26(1), 195–204. https://doi.org/10.1080/10618600.2015.1114491

Estimating Multiple Networks Separately

Description

A wrapper for the GLASSO in the context of CVNs. Each graph is estimated individually. There is NO smoothing between the graphs. This function relies completely on the glasso package. The output is, therefore, slightly different than for the CVN function.

Usage

glasso(
  data,
  lambda1 = 1:2,
  eps = 1e-04,
  maxiter = 10000,
  n_cores = min(length(lambda1), parallel::detectCores() - 1),
  normalized = FALSE,
  verbose = TRUE
)
glasso(
  data,
  lambda1 = 1:2,
  eps = 1e-04,
  maxiter = 10000,
  n_cores = min(length(lambda1), parallel::detectCores() - 1),
  normalized = FALSE,
  verbose = TRUE
)

Arguments

`data`	A list with matrices, each entry associated with a single graph. The number of columns should be the same for each matrix. Number of observations can differ
`lambda1`	Vector with different $\lambda_1$ LASSO penalty terms (Default: `1:2`)
`eps`	Threshold for convergence (Default: `1e-4`; the same as in the `glasso` package)
`maxiter`	Maximum number of iterations (Default: 10,000)
`n_cores`	Number of cores used (Default: max. number of cores - 1, or the total number penalty term pairs if that is less)
`normalized`	Data is normalized if `TRUE`. Otherwise the data is only centered (Default: `FALSE`)
`verbose`	Verbose (Default: `TRUE`)

Value

A CVN object containing the estimates for all the graphs for different value of $\lambda_1$ . General results for the different value of $\lambda_1$ can be found in the data frame results. It consists of multiple columns, namely:

`lambda1`	$\lambda_1$ value
`value`	value of the negative log-likelihood function
`aic`	Aikake information criteration
`id`	The id. This corresponds to the indices of the lists

The estimates of the precision matrices and the corresponding adjacency matrices for the different values of $\lambda_1$ can be found

`Theta`	A list with the estimated precision matrices $\{ \hat{\Theta}_i(\lambda_1) \}_{i = 1}^m$
`adj_matrices`	A list with the estimated adjacency matrices corresponding to the estimated precision matrices in `Theta`. The entries are `1` if there is an edge, `0` otherwise. The matrices are sparse using package `Matrix`

In addition, the input given to this function is stored in the object as well:

`Sigma`	Empirical covariance matrices $\{\hat{\Sigma}_i\}_{i = 1}^m$
`m`	Number of graphs
`p`	Number of variables
`n_obs`	Vector of length $m$ with number of observations for each graph
`data`	The `data`, but then normalized or centered
`maxiter`	Maximum number of iterations for the ADMM
`eps`	The stopping criterion $\epsilon$
`n_lambda_values`	Total number of $\lambda_1$ values
`normalized`	If `TRUE`, `data` was normalized. Otherwise `data` was only centered

Examples

data(grid)
m <- 9 # must be 9 for this example

#' Choice of the weight matrix W.
#' (uniform random)
W <- matrix(runif(m*m), ncol = m)
W <- W %*% t(W)
W <- W / max(W)
diag(W) <- 0

# lambdas:
lambda1 = 1:4

(glasso_est <- CVN::glasso(grid, lambda1 = lambda1))
data(grid)
m <- 9 # must be 9 for this example

#' Choice of the weight matrix W.
#' (uniform random)
W <- matrix(runif(m*m), ncol = m)
W <- W %*% t(W)
W <- W / max(W)
diag(W) <- 0

# lambdas:
lambda1 = 1:4

(glasso_est <- CVN::glasso(grid, lambda1 = lambda1))

Data for a grid of graphs (3 x 3)

Description

Data generated for 9 graphs in total, organized in a grid of (3x3). See the package CVNSim for more information on how the grid is constructed: https://github.com/bips-hb/CVNSim

Usage

data(grid)
data(grid)

Format

List

References

https://github.com/bips-hb/CVNSim

Structural Hamming Distance for a `cvn` Object

Description

Returns the structural Hamming distances

Usage

hamming_distance(cvn, verbose = TRUE)
hamming_distance(cvn, verbose = TRUE)

Arguments

`cvn`	A `cvn` or `cvn:glasso` object created by either the `CVN::CVN` or the `CVN::glasso` function
`verbose`	If `TRUE`, shows a progress bar

Value

A list of symmetric matrices. Each matrix contains the structural Hamming distances between the different graphs. Each item in the list corresponds to one $(\lambda_1, \lambda_2)$ pair

Structural Hamming Distance

Description

Returns the structural Hamming distance between multiple graphs

Usage

hamming_distance_adj_matrices(adj_matrices)
hamming_distance_adj_matrices(adj_matrices)

Arguments

adj_matrices

A list of adjacency matrices

Value

Matrix of Hamming distances

Hitting the end points of $(\lambda_1, \lambda_2)$ interval

Description

One often selected the optimal model for the $(\lambda_1, \lambda_2)$ -values based on the AIC and BIC. This function checks and warns when the optimal value lies on the border of the values $(\lambda_1, \lambda_2)$ takes.

Usage

hits_end_lambda_intervals(results)
hits_end_lambda_intervals(results)

Arguments

results

Results of the CVN function

Value

List with two values:

`hits_border_aic`	If `TRUE`, hits the border for the AIC
`hits_border_bic`	If `TRUE`, hits the border for the BIC

Interpolation of a Graph

Description

Estimates a graph for which there are no observation based on a previously fitted CVN model

Usage

interpolate(cvn, weights, truncate = NULL)
interpolate(cvn, weights, truncate = NULL)

Arguments

`cvn`	A CVN fit with $m$ graphs
`weights`	A vector of length $m$ with the regression coefficients
`truncate`	Truncation value. When a value in the precision matrix is considered 0. If `NULL`, the same truncation is used as for the fitted CVN model (Default)

Value

A list with

`adj_matrices`	A list of adjacency matrix. One for each pair of $(\lambda_1, \lambda_2)$ values. The entries are `1` if there is an edge, `0` otherwise. The matrices are sparse using package `Matrix`
`m`	Number of graphs
`p`	Number of variables
`weights`	The weights used for interpolation
`truncate`	Truncation value
`n_lambda_values`	Total number of $(\lambda_1, \lambda_2)$ value combinations

results. It consists of two columns:

`lambda1`	$\lambda_1$ value
`lambda2`	$\lambda_2$ value

Determine matrix $A$ for inner-ADMM for the $Z$ -update step

Description

The $Z$ -update step, see updateZ, requires us to solve a special Generalized LASSO problem of the form

$\hat{\beta} = \text{argmin } \frac{1}{2} || y - \beta ||_2^2 + ||D\beta||_1$

where $\beta$ and $y$ are $m$ -dimensional vectors and $D$ is a $(c \times m)$ -matrix where $c = (m^2 + m) / 2$ . We solve this optimization problem using an adaption of the ADMM algorithm presented in Zhu (2017). This algorithm requires the choice of a matrix $A$ such that $A - D'D$ is positive semidefinite. In order to optimize the ADMM, we choose the matrix $A$ to be diagonal with a fixed value $a$ . This function determines the smallest value of $a$ such that $A - D'D$ is indeed positive semidefinite. We do this be determining the largest eigenvalue

Usage

matrix_A_inner_ADMM(W, eta1, eta2)
matrix_A_inner_ADMM(W, eta1, eta2)

Arguments

`W`	Weight matrix $W$
`eta1`, `eta2`	The values $\eta_1 = \lambda_1 / \rho$ and $\eta_2 = \lambda_2 / \rho$

Value

Value of $a$

References

Heat Map of the Distances between Graphs

Description

Returns a heat map of the distance matrix for a particular CVN

Usage

plot_hamming_distances(
  distance_matrix,
  absolute = TRUE,
  limits = c(NA, NA),
  title = "",
  legend_label = "Hamming Distance",
  add_counts_to_cells = TRUE,
  add_ticks_labels = TRUE,
  t = -6,
  r = -8
)
plot_hamming_distances(
  distance_matrix,
  absolute = TRUE,
  limits = c(NA, NA),
  title = "",
  legend_label = "Hamming Distance",
  add_counts_to_cells = TRUE,
  add_ticks_labels = TRUE,
  t = -6,
  r = -8
)

Arguments

`distance_matrix`	Symmetric matrix with distances
`absolute`	If `FALSE`, rescaled to [0,1]
`limits`	The limits for the values of the Hamming distance
`title`	Title plot (Default is none)
`legend_label`	Title of the legend (Default: "Hamming Distance")
`add_counts_to_cells`	If `TRUE`, counts from the matrix are added to the plot (Default: `TRUE`)
`add_ticks_labels`	If `TRUE`, the number corresponding to the graph is add to the plot (Default: `TRUE`)
`t`	Distance between tick labels and x-axis (Default: -6)
`r`	Distance between tick labels and y-axis (Default: -8)

Value

A heatmap plot

Heatmaps for a CVN

Description

Creates all the heatmaps for a CVN, a heatmap for each pair of $(\lambda_1, \lambda_2)$

Usage

plot_hamming_distances_cvn(
  cvn,
  absolute = TRUE,
  same_range = TRUE,
  titles = rep("", cvn$n_lambda_values),
  legend_label = "Hamming Distance",
  add_counts_to_cells = TRUE,
  add_ticks_labels = TRUE,
  t = -6,
  r = -8,
  verbose = TRUE
)
plot_hamming_distances_cvn(
  cvn,
  absolute = TRUE,
  same_range = TRUE,
  titles = rep("", cvn$n_lambda_values),
  legend_label = "Hamming Distance",
  add_counts_to_cells = TRUE,
  add_ticks_labels = TRUE,
  t = -6,
  r = -8,
  verbose = TRUE
)

Arguments

`cvn`	A `cvn` object
`absolute`	If `FALSE`, rescaled to [0,1]
`same_range`	If `TRUE`, all heatmaps have the same range of values of the Hamming distance shown (Default: TRUE)
`titles`	Title of the plots (Default is none)
`legend_label`	Title of the legend (Default: "Hamming Distance")
`add_counts_to_cells`	If `TRUE`, counts from the matrix are added to the plot (Default: `TRUE`)
`add_ticks_labels`	If `TRUE`, the number corresponding to the graph is add to the plot (Default: `TRUE`)
`t`	Distance between tick labels and x-axis (Default: -6)
`r`	Distance between tick labels and y-axis (Default: -8)
`verbose`	If `TRUE`, shows progress bar (Default: `TRUE`)

Value

List of plots

Heat Map of an Information Criterion (AIC or BIC)

Description

Returns a heat map of the AIC or BIC for a fitted CVN

Usage

plot_information_criterion(
  cvn,
  criterion = c("bic", "aic"),
  use_gammas = TRUE,
  show_minimum = TRUE,
  title = "",
  xlabel = NULL,
  ylabel = NULL,
  legend_label = NULL,
  limits = c(NA, NA)
)
plot_information_criterion(
  cvn,
  criterion = c("bic", "aic"),
  use_gammas = TRUE,
  show_minimum = TRUE,
  title = "",
  xlabel = NULL,
  ylabel = NULL,
  legend_label = NULL,
  limits = c(NA, NA)
)

Arguments

`cvn`	Fitted CVN, see `CVN`
`criterion`	The information criterion, must be either `'aic'` or `'bic'`. Default: `'bic'`
`use_gammas`	If `TRUE`, plots the $\gamma$ -values. Otherwise, the $\lambda$ -values are used
`show_minimum`	If `TRUE`, an orange dot is put on the point with the minimum value of the information criterion is. If `FALSE`, no dot is added. Default: `TRUE`.
`title`	Title plot (Default is none)
`xlabel`	Label for the $x$ -axis. Default depends on `use_gammas`. If `use_gammas = TRUE`, then the label is 'gamma1'. Otherwise, 'lambda1'
`ylabel`	Label for the $x$ -axis. Default depends on `use_gammas`. If `use_gammas = TRUE`, then the label is 'gamma1'. Otherwise, 'lambda1'
`legend_label`	Title for the legend. Default depends on `criterion`. If `'aic'`, then the label is 'AIC'. Otherwise, 'BIC'.
`limits`	The limits for the values of the Hamming distance

Value

A heatmap plot

Plot Weight Matrix

Description

Returns a heat map of a weight matrix

Usage

plot_weight_matrix(
  W,
  title = "",
  legend_label = "weight",
  add_counts_to_cells = TRUE,
  add_ticks_labels = TRUE,
  t = -6,
  r = -8
)
plot_weight_matrix(
  W,
  title = "",
  legend_label = "weight",
  add_counts_to_cells = TRUE,
  add_ticks_labels = TRUE,
  t = -6,
  r = -8
)

Arguments

`W`	Symmetric weight matrix
`title`	Title plot (Default is none)
`legend_label`	Title of the legend (Default: "weight")
`add_counts_to_cells`	If `TRUE`, counts from the matrix are added to the plot (Default: `TRUE`)
`add_ticks_labels`	If `TRUE`, the number corresponding to the graph is add to the plot (Default: `TRUE`)
`t`	Distance between tick labels and x-axis (Default: -6)
`r`	Distance between tick labels and y-axis (Default: -8)

Value

A heatmap plot

Plot Function for CVN Object Class

Description

Plot Function for CVN Object Class

Usage

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

Print Function for the CVN Object Class

Description

Print Function for the CVN Object Class

Usage

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

The Relative Difference between two Precision Matrices

Description

Returns the relative $L1$ difference between precision matrix $\Theta(k+1)$ (parameter Theta_new) and $\Theta(k)$ (parameter Theta_old).

Usage

relative_difference_precision_matrices(Theta_new, Theta_old)
relative_difference_precision_matrices(Theta_new, Theta_old)

Arguments

`Theta_new`	A list with matrices with the updated values of $\Theta$
`Theta_old`	A list with matrices with the old values of $\Theta$

Details

This is used for checking whether the stopping condition has been met.

Value

The relative difference between $\Theta(k+1)$ and $\Theta(k)$

Add Attributes to Subset of Edges for `visNetwork`

Description

A subset of edges can be assign a different thickness or color.

Usage

set_attributes_to_edges_visnetwork(
  edges,
  subset_edges,
  width = c(NA, NA),
  color = c(NULL, NULL)
)
set_attributes_to_edges_visnetwork(
  edges,
  subset_edges,
  width = c(NA, NA),
  color = c(NULL, NULL)
)

Arguments

`edges`	A data.frame create by `create_edges_visnetwork`
`subset_edges`	A list with the elements `from` and `to`. Both `from` and `to` are vectors of the same length denoting the different edges
`width`	Vector with two values. The first is assigned to the edges in the subset given by `subset_edges`. The second value is assigned to the rest. If `width = c(NA,NA)`, no width is assigned
`color`	Vector with two values. The first is assigned to the edges in the subset given by `subset_edges`. The second value is assigned to the rest. If `color = c(NULL,NULL)`, no color is assigned

Value

A data frame that can be used by the visNetwork package

Strip CVN

Description

Function that removes most of the items to make the CVN object more memory sufficient. This is especially important when the graphs are rather larger

Usage

strip_cvn(cvn)
strip_cvn(cvn)

Arguments

cvn

cvn object

Value

Reduced cvn where Theta, data and Sigma are removed

The $\Theta$ -update step for the ADMM

Description

updateTheta returns the updated value of $\Theta$ for the ADMM given the previously updated values of $Z$ and $Y$

Usage

updateTheta(m, Z, Y, Sigma, n_obs, rho = 1)
updateTheta(m, Z, Y, Sigma, n_obs, rho = 1)

Arguments

`m`	Number of graphs
`Z`	A list with matrices with the current values of $Z$
`Y`	A list with matrices with the current values of $Y$
`Sigma`	A list with empirical covariance matrices ${\Sigma}$
`n_obs`	A $m$ -dimensional vector with the number of observations per graph
`rho`	The $\rho$ ADMM's penalty parameter (Default: 1)

Value

A list with matrices with the new values of $\Theta$

The $Y$ -update step for the ADMM

Description

Returns the updated value of $Y$ for the ADMM given the previously updated values of $\Theta$ and $Z$

Usage

updateY(Theta, Z, Y)
updateY(Theta, Z, Y)

Arguments

`Theta`	A list with matrices with the current values of $\Theta$
`Z`	A list with matrices with the current values of $Z$
`Y`	A list with matrices with the current values of $Y$

Value

A list with matrices with the new values of $Y$

Wrapper for the $Z$ -update Step for the ADMM

Description

A wrapper for the C function that returns the updated value of $Z$ for the ADMM given the previously updated values of $\Theta$ and $Y$

Usage

updateZ_wrapper(
  m,
  p,
  nrow_D,
  Theta,
  Y,
  W,
  eta1,
  eta2,
  a,
  rho_genlasso,
  maxiter_genlasso,
  eps_genlasso,
  truncate_genlasso
)
updateZ_wrapper(
  m,
  p,
  nrow_D,
  Theta,
  Y,
  W,
  eta1,
  eta2,
  a,
  rho_genlasso,
  maxiter_genlasso,
  eps_genlasso,
  truncate_genlasso
)

Arguments

`m`	Number of graphs
`p`	Number of variables
`nrow_D`	Number of rows of the $D$ -matrix
`Theta`	A list with matrices with the current values of $\Theta$
`Y`	A list with matrices with the current values of $Y$
`W`	Weight matrix
`eta1`	TODO
`rho_genlasso`	The $\rho$ penalty parameter for the ADMM algorithm
`maxiter_genlasso`	Maximum number of iterations for solving the generalized LASSO problem
`eps_genlasso`	If the relative difference between two update steps is smaller than $\epsilon$ , the algorithm stops
`truncate_genlasso`	All values of the final $\hat{\beta}$ below `truncate_genlasso` will be set to `0`.

Value

A list with matrices with the new values of $Z$

The $Z$ -update Step

Description

A C implementation of the $Z$ -update step. We solve a generalized LASSO problem repeatedly for each of the individual edges

Usage

updateZRcpp(m, p, Theta, Y, W, eta1, eta2, a, rho, max_iter, eps, truncate)
updateZRcpp(m, p, Theta, Y, W, eta1, eta2, a, rho, max_iter, eps, truncate)

Arguments

`m`	The number of graphs
`p`	The number of variables
`Theta`	A list of matrices with the $\Theta$ -matrices
`Y`	A list of matrices with the $Y$ -matrices
`eta1`	Equals $\lambda_1 / rho$
`eta2`	Equals $\lambda_2 / rho$
`a`	Value added to the diagonal of $-D'D$ so that the matrix is positive definite, see `matrix_A_inner_ADMM`
`rho`	The ADMM's parameter
`max_iter`	Maximum number of iterations
`eps`	Stopping criterion. If differences are smaller than $\epsilon$ , algorithm is halted
`truncate`	Values below `truncate` are set to `0`

Value

The estimated vector $\hat{\beta}$

A `visNetwork` plot

Description

Creates a visNetwork plot given a list of nodes and edges. The nodes data frame can be created with create_nodes_visnetwork; the edges with create_edges_visnetwork. In order to highlight edges, you can use set_attributes_to_edges_visnetwork.

Usage

visnetwork(
  nodes,
  edges,
  node_titles = nodes$id,
  title = "",
  igraph_layout = "layout_in_circle"
)
visnetwork(
  nodes,
  edges,
  node_titles = nodes$id,
  title = "",
  igraph_layout = "layout_in_circle"
)

Value

A visNetwork plot

Examples

nodes <- CVN::create_nodes_visnetwork(n_nodes = 5, labels = LETTERS[1:5])

adj_matrix <- matrix(c(0, 1, 0, 1, 0,
                       1, 0, 1, 0, 0,
                       0, 1, 0, 0, 0,
                       1, 0, 0, 0, 1,
                       0, 0, 0, 1, 0), ncol = 5)

edges <- CVN::create_edges_visnetwork(adj_matrix)

edges <- set_attributes_to_edges_visnetwork(edges,
                                            subset_edges = list(from = c(1, 2), to = c(4, 3)),
                                            width = c(3, .5),
                                            color = c("red", "blue"))

CVN::visnetwork(nodes, edges)
nodes <- CVN::create_nodes_visnetwork(n_nodes = 5, labels = LETTERS[1:5])

adj_matrix <- matrix(c(0, 1, 0, 1, 0,
                       1, 0, 1, 0, 0,
                       0, 1, 0, 0, 0,
                       1, 0, 0, 0, 1,
                       0, 0, 0, 1, 0), ncol = 5)

edges <- CVN::create_edges_visnetwork(adj_matrix)

edges <- set_attributes_to_edges_visnetwork(edges,
                                            subset_edges = list(from = c(1, 2), to = c(4, 3)),
                                            width = c(3, .5),
                                            color = c("red", "blue"))

CVN::visnetwork(nodes, edges)

All `visNetwork` plots for a CVN object

Description

Creates all visNetwork plots, see CVN::visnetwork, for all graphs in a cvn object

Usage

visnetwork_cvn(
  cvn,
  node_titles = 1:cvn$p,
  titles = lapply(1:cvn$n_lambda_values, function(i) sapply(1:cvn$m, function(j) "")),
  show_core_graph = TRUE,
  width = c(3, 1),
  color = c("red", "blue"),
  igraph_layout = "layout_in_circle",
  verbose = TRUE
)
visnetwork_cvn(
  cvn,
  node_titles = 1:cvn$p,
  titles = lapply(1:cvn$n_lambda_values, function(i) sapply(1:cvn$m, function(j) "")),
  show_core_graph = TRUE,
  width = c(3, 1),
  color = c("red", "blue"),
  igraph_layout = "layout_in_circle",
  verbose = TRUE
)

Arguments

`cvn`	A `cvn` object, see `CVN::CVN` or `CVN::glasso`
`node_titles`	Vector with title of the nodes (Default: `1:p`)
`titles`	A list with `n_lambda_values` vectors. Each vector is of the lenght `m`. Regulates the titles of the graphs (Default: no title)
`show_core_graph`, `width`, `color`	Show the core graph using the width and colors

Value

List

Package 'CVN'

Help Index

Check whether Input is Valid

Description

Usage

Arguments

See Also

Create a data.frame for the Edges for visNetwork

Description

Usage

Arguments

Value

Create matrix DDD to be used for the Generalized LASSO

Description

Usage

Arguments

Value

References

Examples

Nodes for the visNetwork package

Description

Usage

Arguments

Value

Different Weight Matrices

Description

Usage

Arguments

Value

Estimating a Covariate-Varying Network (CVN)

Description

Usage

Arguments

Value

Reusing Estimates

Examples

Information Criteria for a cvn object

Description

Usage

Estimate a CVN

Description

Usage

The Core Graph

Description

Usage

Arguments

Value

Wrapper for genlassoRcpp

Description

Usage

See Also

Solving Generalized LASSO with fixed λ=1\lambda = 1λ=1

Description

Usage

Arguments

Value

References

See Also

Estimating Multiple Networks Separately

Description

Usage

Arguments

Value

Examples

Data for a grid of graphs (3 x 3)

Description

Usage

Format

References

Structural Hamming Distance for a cvn Object

Description

Usage

Arguments

Value

Structural Hamming Distance

Description

Usage

Arguments

Value

Hitting the end points of (λ1,λ2)(\lambda_1, \lambda_2)(λ1​,λ2​) interval

Create a `data.frame` for the Edges for `visNetwork`

Create matrix $D$ to be used for the Generalized LASSO

Nodes for the `visNetwork` package

Information Criteria for a `cvn` object

Wrapper for `genlassoRcpp`

Solving Generalized LASSO with fixed $\lambda = 1$

Structural Hamming Distance for a `cvn` Object

Hitting the end points of $(\lambda_1, \lambda_2)$ interval

Determine matrix $A$ for inner-ADMM for the $Z$ -update step

Add Attributes to Subset of Edges for `visNetwork`

The $\Theta$ -update step for the ADMM

The $Y$ -update step for the ADMM

Wrapper for the $Z$ -update Step for the ADMM