Package 'dineR'

Data Generator

Description

This functions generates two $n$ by $p$ size samples of multivariate normal data. In doing this it also determines and provides the relevant covariance matrices.

Usage

data_generator(n, p, Delta = NULL, case = "sparse", seed = NULL)

Arguments

n	The number of observations generated.
p	The number of dimensions for the generated samples.
Delta	Optional parameter - Provides the differential network that will be used to obtain the sample covariance matrices.
case	Optional parameter - Selects under which case the covariance matrices are determined. Possible cases are: "sparse" - Sparse Case or "asymsparse"- Asymptotically Sparse Case. Defaults to "sparse".
seed	Optional parameter - Allows a seed to be set for reproducibility.

Value

A list of various outputs, namely:

• case - The case used.

• seed_option - The seed provided.

• X - The first multivariate normal sample.

• Y - The second multivariate normal sample.

• Sigma_X - The covariance matrix of X.

• Sigma_Y - The covariance matrix of Y.

• Omega_X - The precision matrix of X.

• Omega_Y - The precision matrix of Y.

• diff_Omega - The difference of precision matrices.

• Delta - The target differential network.

Examples

data <- data_generator(n = 100, p = 50, seed = 123)
data <- data_generator(n = 10, p = 50, case = "asymsparse")

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Estimation

Description

This function performs alternating direction method of multipliers optimization for a variety of loss functions to estimate the differential network given two samples of multivariate normal data.

Usage

estimation(
  X,
  Y,
  lambdas = NULL,
  lambda_min_ratio = 0.3,
  nlambda = 10,
  a = NULL,
  loss = "lasso",
  tuning = "none",
  perturb = FALSE,
  stop_tol = 1e-05,
  max_iter = 500,
  correlation = FALSE,
  Delta_init = NULL,
  rho = NULL,
  gamma = NULL,
  verbose = FALSE
)

Arguments

X	The first multivariate normal sample.
Y	The second multivariate normal sample.
lambdas	Optional parameter - A list of the regularization values to be used within the loss functions.
lambda_min_ratio	Optional parameter - Defines the smallest regularization values as this proportion of the largest regularization value. Defaults to 0.3.
nlambda	Optional parameter - The number of regularization values considered. Defaults to 10.
a	Optional parameter - The thresholding parameter used in SCAD and MCP loss functions. Defaults to 3.7 with SCAD, and 3 with MCP respectively.
loss	Optional parameter - The loss function of choice to implement. The function allows for four choices, namely "lasso", "scad", "mcp" and "d-trace". Defaults to "lasso".
tuning	Optional parameter - The tuning method selected to determine the optimal value for the regularization parameter. Options are "none", "AIC", "BIC" and "EBIC". Defaults to "none".
perturb	Optional parameter - When set to TRUE perturbation as done by the CLIME software to improve performance is implemented. Options are TRUE or FALSE, with the function defaulting to FALSE.
stop_tol	Optional parameter - The stop tolerance to determine whether convergence has occurred. Defaults to 1e-5.
max_iter	Optional parameter - The maximum number of iterations that can be perform for any one regularization value. Defaults to 100.
correlation	Optional parameter - Determines whether the sample correlation matrices should be used in the place of the sample covariance matrices. Choices are TRUE and FALSE with the function defaulting to FALSE.
Delta_init	Optional parameter - Allows for the algorithm to provided an initial estimate of the differential network to ease computation.
rho	Optional parameter - Allows the user to adjust the ADMM step-size. Defaults to 1.
gamma	Optional parameter - Allows the user to adjust the EBIC value when EBIC is the selected tuning method. Defaults to 0.5.
verbose	Optional parameter - Allows the user to obtain a summary of the estimation results. Options are TRUE or FALSE, where FALSE indicates the summary is not provided. Defaults to FALSE.

Value

A list of various outputs, namely:

• n_X - The number of observations in X.

• n_Y - The number of observations in Y.

• Sigma_X - The covariance matrix of X.

• Sigma_Y - The covariance matrix of Y.

• loss - The loss function implemented.

• tuning - The tuning method utilized.

• lip - The value of the lipschitz constant.

• iter - The iterations until convergence for each of the regularization values.

• elapse - The total system time (in seconds) elapsed from initialization to completion of the optimization.

• lambdas - The regularization parameter values used.

• sparsity - The level of sparsity of the differential network for each regularization value.

• path - The set of all differential networks for all regularization values considered.

• ic - The output obtained from any possible tuning.

• ic_index - The index at which the tuning is optimized.

• ic_value - The tuning method optimal value.

• chosen_lambda_ic - The regularization value that occurs at ic_index.

• loss_index - The index at which the loss function is optimized.

• loss_value - The loss function optimal value.

• chosen_lambda_loss - The regularization value that occurs at loss_index.

Examples

data <- data_generator(n = 100, p = 50, seed = 123)
X <- data$X
Y <- data$Y
result <- estimation(X,Y)

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NPN - Non paranormal Transformation

Description

This functions allows us to transform non-normal multivariate data to that of non paranormal data.

Usage

npn(x, npn_func = "shrinkage", npn_thresh = NULL, verbose = TRUE)

Arguments

x	The multivariate non-normal data to be transformed.
npn_func	Optional parameter - The method of transformation to be applied. Can either be "shrinkage" or "truncation" but defaults to "shrinkage".
npn_thresh	Optional parameter - The truncation threshold that is used when making use of truncation.
verbose	Optional parameter - Prints additional output of the selected approach. Can either be "TRUE" or "FALSE" and defaults to "TRUE".

Value

Returns the transformed data matrix.

Examples

data <- data_generator(n = 100, p = 50, seed = 123)
X <- data$X
X_transformed <- npn(X, npn_func = "truncation")

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