Description Usage Arguments Value Examples
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.
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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. |
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.
1 2 3 4 | data <- data_generator(n = 100, p = 50, seed = 123)
X <- data$X
Y <- data$Y
result <- estimation(X,Y)
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