#' Projected covariance matrices for BD-CoCoLasso
#'
#' Creating projected nearest positive semi-definite covariance matrices for the cross validation step of the BD-CoCoLasso algorithm. In that case, the design matrix must be organized as follozs : uncorrupted features must be the first block of the matrix, and corrupted features must be the second block of the matrix.
#'
#' @param K Number of folds for the cross validation
#' @param mat Covariance matrix to be projected
#' @param y Response vector
#' @param p Number of predictors
#' @param p1 Number of uncorrupted predictors
#' @param p2 Number of corrupted predictors containing additive error
#' @param p3 Number of corrupted predictors containing missingness
#' @param mu Penalty parameter for the ADMM algorithm.
#' @param tau Standard error of the additive error matrix when the chosen setting is the additive error setting
#' @param ratio_matrix Observation matrix used in the missing data setting
#' @param etol Tolerance used in the ADMM algorithm
#' @param mode ADMM or HM
#'
#' @return list containing \itemize{
#' \item \code{sigma_global} projected matrix for \code{mat}
#' \item \code{rho_global} rho parameter for \code{mat}
#' \item \code{list_matrices_lasso} list of the projected matrices for \code{mat} deprived of the k-fold during cross validation
#' \item \code{list_matrices_error} list of the projected matrices for the k-fold of \code{mat}
#' \item \code{list_rho_lasso} list of the modified \code{rho} for \code{mat} deprived of the K-fold during cross validation
#' \item \code{list_rho_error} list of the modified \code{rho} for the k-fold of \code{mat}
#' }
#'
#'
#' @export
cv_covariance_matrices_block_descent_general <- function(K,
mat,
y,
p,
p1,
p2,
p3,
mu,
tau=NULL,
ratio_matrix=NULL,
etol=1e-4,
mode="ADMM"){
n = nrow(mat)
p = ncol(mat)
start = p1 + 1
n_without_fold = n - floor(n/K)
n_one_fold = floor(n/K)
folds = sample(cut(seq(1,n),breaks=K,labels=FALSE))
list_PSD_lasso_additive <- list()
list_PSD_error_additive <- list()
list_PSD_lasso_missing <- list()
list_PSD_error_missing <- list()
list_sigma_lasso <- list()
list_sigma_error <- list()
print("Processing the global data")
if (p1 != 0) {
mat_uncorrupted <- mat[,1:p1]
sigma_global_uncorrupted <- 1/n * t(mat_uncorrupted)%*%mat_uncorrupted
}
mat_corrupted_additive <- mat[,start:(p1+p2)]
mat_corrupted_missing <- mat[,(p1+p2+1):p]
cov_modified_additive <- 1/n*t(mat_corrupted_additive)%*%mat_corrupted_additive - tau**2*diag(p2)
cov_modified_missing <- 1/n*t(mat_corrupted_missing)%*%mat_corrupted_missing / ratio_matrix
if (mode=="ADMM") {
sigma_global_corrupted_additive <- ADMM_proj(cov_modified_additive,mu=mu, etol = etol)$mat
sigma_global_corrupted_missing <- ADMM_proj(cov_modified_missing,mu=mu, etol = etol)$mat
}
if (mode=="HM") {
sigma_global_corrupted_additive <- HM_proj(sigmaHat = cov_modified_additive,mu=mu, tolerance = etol)
sigma_global_corrupted_missing <- HM_proj(sigmaHat = cov_modified_missing,R=ratio_matrix,mu=mu, tolerance = etol)
}
for (i in 1:K){
# We calculate the necessary matrices for the cross validation
print(paste("Processing the",i,"fold"))
index <- which(folds==i, arr.ind= TRUE)
#Calculating the nearest PSD cov matrix when we remove the kth fold, to resolve lasso problem during cross validation
mat_train <- mat[-index,start:(p1+p2)]
cov_modified_train <- 1/n_without_fold*t(mat_train)%*%mat_train - tau**2*diag(p2)
if (mode=="ADMM") {
mat_cov_train <- ADMM_proj(cov_modified_train,mu=mu, etol = etol)$mat
}
if (mode=="HM") {
mat_cov_train <- HM_proj(sigmaHat = cov_modified_train,mu = mu, tolerance = etol)
}
list_PSD_lasso_additive <- rlist::list.append(list_PSD_lasso_additive,mat_cov_train)
mat_train <- mat[-index,(p1+p2+1):p]
cov_modified_train <- 1/n_without_fold*t(mat_train)%*%mat_train / ratio_matrix
if (mode=="ADMM") {
mat_cov_train <- ADMM_proj(cov_modified_train,mu=mu, etol = etol)$mat
}
if (mode=="HM") {
mat_cov_train <- HM_proj(sigmaHat = cov_modified_train,R=ratio_matrix,mu = mu, tolerance = etol)
}
list_PSD_lasso_missing <- rlist::list.append(list_PSD_lasso_missing,mat_cov_train)
#Calculating the nearest PSD cov matrix for the kth fold, to calculate the error on the problem solved without the kth fold
mat_test <- mat[index,start:(p1+p2)]
cov_modified_test <- 1/n_one_fold*t(mat_test)%*%mat_test - tau**2*diag(p2)
if (mode=="ADMM") {
mat_cov_test <- ADMM_proj(cov_modified_test,mu=mu, etol = etol)$mat
}
if (mode=="HM") {
mat_cov_test <- HM_proj(sigmaHat = cov_modified_test,mu = mu, tolerance = etol)
}
list_PSD_error_additive <- rlist::list.append(list_PSD_error_additive,mat_cov_test)
mat_test <- mat[index,(p1+p2+1):p]
cov_modified_test <- 1/n_one_fold*t(mat_test)%*%mat_test / ratio_matrix
mat_cov_test <- ADMM_proj(cov_modified_test,mu=mu, etol = etol)$mat
if (mode=="ADMM") {
mat_cov_test <- ADMM_proj(cov_modified_test,mu=mu, etol = etol)$mat
}
if (mode=="HM") {
mat_cov_test <- HM_proj(sigmaHat = cov_modified_test,R=ratio_matrix,mu = mu, tolerance = etol)
}
list_PSD_error_missing <- rlist::list.append(list_PSD_error_missing,mat_cov_test)
#Calculating the cov matrix when we remove the kth fold, to resolve lasso problem during cross validation
mat_train <- mat[-index,1:p1]
cov_train <- 1/n_without_fold*t(mat_train)%*%mat_train
list_sigma_lasso <- rlist::list.append(list_sigma_lasso,cov_train)
#Calculating the cov matrix for the kth fold, to calculate the error on the problem solved without the kth fold
mat_test <- mat[index,1:p1]
cov_test <- 1/n_one_fold*t(mat_test)%*%mat_test
list_sigma_error <- rlist::list.append(list_sigma_error,cov_test)
}
if (p1 != 0) {
return(list(sigma_global_uncorrupted = sigma_global_uncorrupted,
sigma_global_corrupted_additive = sigma_global_corrupted_additive,
sigma_global_corrupted_missing = sigma_global_corrupted_missing,
list_PSD_lasso_additive = list_PSD_lasso_additive, list_PSD_error_additive = list_PSD_error_additive,
list_PSD_lasso_missing =list_PSD_lasso_missing, list_PSD_error_missing = list_PSD_error_missing,
list_sigma_lasso=list_sigma_lasso, list_sigma_error=list_sigma_error, folds = folds))
}
if (p1 == 0) {
return(list(sigma_global_corrupted_additive = sigma_global_corrupted_additive,
sigma_global_corrupted_missing = sigma_global_corrupted_missing,
list_PSD_lasso_additive = list_PSD_lasso_additive, list_PSD_error_additive = list_PSD_error_additive,
list_PSD_lasso_missing =list_PSD_lasso_missing, list_PSD_error_missing = list_PSD_error_missing,
folds = folds))
}
}
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