CV_ADMMc function

CV ADMM penalized precision matrix estimation (c++)

Cross validation function for ADMMsigma.

CV_ADMMc(X, S, lam, alpha, diagonal = FALSE, path = FALSE, rho = 2,
  mu = 10, tau_inc = 2, tau_dec = 2, crit = "ADMM", tol_abs = 1e-04,
  tol_rel = 1e-04, maxit = 10000L, adjmaxit = 10000L, K = 5L,
  crit_cv = "loglik", start = "warm", trace = "progress")

Arguments

• X: option to provide a nxp matrix. Each row corresponds to a single observation and each column contains n observations of a single feature/variable.
• S: option to provide a pxp sample covariance matrix (denominator n). If argument is NULL and X is provided instead then S will be computed automatically.
• lam: positive tuning parameters for elastic net penalty. If a vector of parameters is provided, they should be in increasing order.
• alpha: elastic net mixing parameter contained in [0, 1]. 0 = ridge, 1 = lasso. If a vector of parameters is provided, they should be in increasing order.
• diagonal: option to penalize the diagonal elements of the estimated precision matrix ($\Omega$). Defaults to FALSE.
• path: option to return the regularization path. This option should be used with extreme care if the dimension is large. If set to TRUE, cores will be set to 1 and errors and optimal tuning parameters will based on the full sample. Defaults to FALSE.
• rho: initial step size for ADMM algorithm.
• mu: factor for primal and residual norms in the ADMM algorithm. This will be used to adjust the step size rho after each iteration.
• tau_inc: factor in which to increase step size rho
• tau_dec: factor in which to decrease step size rho
• crit: criterion for convergence (ADMM or loglik). If crit = loglik then iterations will stop when the relative change in log-likelihood is less than tol.abs. Default is ADMM and follows the procedure outlined in Boyd, et al.
• tol_rel: relative convergence tolerance. Defaults to 1e-4.
• maxit: maximum number of iterations. Defaults to 1e4.
• adjmaxit: adjusted maximum number of iterations. During cross validation this option allows the user to adjust the maximum number of iterations after the first lam tuning parameter has converged (for each alpha). This option is intended to be paired with warm starts and allows for "one-step" estimators. Defaults to 1e4.
• K: specify the number of folds for cross validation.
• crit_cv: cross validation criterion (loglik penloglik, AIC, or BIC). Defaults to loglik.
• start: specify warm or cold start for cross validation. Default is warm.
• trace: option to display progress of CV. Choose one of progress to print a progress bar, print to print completed tuning parameters, or none.

Returns

list of returns includes: - lam: optimal tuning parameter.

• alpha: optimal tuning parameter.

• path: array containing the solution path. Solutions will be ordered in ascending alpha values for each lambda.

• min.error: minimum average cross validation error (cv_crit) for optimal parameters.

• avg.error: average cross validation error (cv_crit) across all folds.

• cv.error: cross validation errors (cv_crit).