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#' Sample approximate second-order multivariate Gaussian knockoff variables
#'
#' Samples approximate second-order multivariate Gaussian knockoff variables
#' for the original variables.
#'
#' @param X normalized n-by-p realization of the design matrix
#' @param method either 'equi', 'sdp' or 'asdp' (default:'asdp')
#' This will be computed according to 'method', if not supplied
#' @param shrink whether to shrink the estimated covariance matrix (default: FALSE)
#' @return n-by-p matrix of knockoff variables
#'
#' @family methods for creating knockoffs
#'
#' @details If the argument \code{shrink} is set to TRUE, a James-Stein-type shrinkage estimator for
#' the covariance matrix is used instead of the traditional maximum-likelihood estimate. This option
#' requires the package \code{corpcor}. Type \code{?corpcor::cov.shrink} for more details.
#'
#' Even if the argument \code{shrink} is set to FALSE, in the case that the estimated covariance
#' matrix is not positive-definite, this function will apply some shrinkage.
#'
#' To use SDP knockoffs, you must have a Python installation with
#' CVXPY. For more information, see the vignette on SDP knockoffs:
#' \code{vignette('sdp', package='MFKnockoffs')}
#'
#' @references
#' Candes et al., Panning for Gold: Model-free Knockoffs for High-dimensional Controlled Variable Selection,
#' arXiv:1610.02351 (2016).
#' \href{https://statweb.stanford.edu/~candes/MF_Knockoffs/index.html}{https://statweb.stanford.edu/~candes/MF_Knockoffs/index.html}
#'
#' @export
MFKnockoffs.create.approximate_gaussian <- function(X, method=c("asdp","equi","sdp"), shrink=F) {
method = match.arg(method)
# Estimate the mean vectorand covariance matrix
mu = colMeans(X)
# Estimate the covariance matrix
if(!shrink) {
Sigma = cov(X)
# Verify that the covariance matrix is positive-definite
if(!is_posdef(Sigma)) {
shrink=TRUE
}
}
if(shrink) {
if (!requireNamespace('corpcor', quietly=T))
stop('corpcor is not installed', call.=F)
Sigma = tryCatch({suppressWarnings(matrix(as.numeric(corpcor::cov.shrink(X,verbose=F)), nrow=ncol(X)))},
warning = function(w){}, error = function(e) {
stop("SVD failed in the shrinkage estimation of the covariance matrix. Try upgrading R to version >= 3.3.0")
}, finally = {})
}
# Sample the Gaussian knockoffs
MFKnockoffs.create.gaussian(X, mu, Sigma, method=method)
}
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