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#' constructionModelesLassoRank
#'
#' Construct a collection of models with the Lasso-Rank procedure.
#'
#' @param S output of selectVariables.R
#' @param k number of components
#' @param mini integer, minimum number of iterations in the EM algorithm, by default = 10
#' @param maxi integer, maximum number of iterations in the EM algorithm, by default = 100
#' @param X matrix of covariates (of size n*p)
#' @param Y matrix of responses (of size n*m)
#' @param eps real, threshold to say the EM algorithm converges, by default = 1e-4
#' @param rank.min integer, minimum rank in the low rank procedure, by default = 1
#' @param rank.max integer, maximum rank in the low rank procedure, by default = 5
#' @param ncores Number of cores, by default = 3
#' @param fast TRUE to use compiled C code, FALSE for R code only
#' @param verbose TRUE to show some execution traces
#'
#' @return a list with several models, defined by phi (the regression parameter reparametrized),
#' rho (the covariance parameter reparametrized), pi (the proportion parameter is the mixture model), llh
#' (the value of the loglikelihood function for this estimator on the training dataset). The list is given
#' for several levels of sparsity, given by several regularization parameters computed automatically,
#' and several ranks (between rank.min and rank.max).
#'
#' @export
constructionModelesLassoRank <- function(S, k, mini, maxi, X, Y, eps, rank.min, rank.max,
ncores, fast, verbose)
{
n <- nrow(X)
p <- ncol(X)
m <- ncol(Y)
L <- length(S)
# Possible interesting ranks
deltaRank <- rank.max - rank.min + 1
Size <- deltaRank^k
RankLambda <- matrix(0, nrow = Size * L, ncol = k + 1)
for (r in 1:k)
{
# On veut le tableau de toutes les combinaisons de rangs possibles, et des
# lambdas Dans la premiere colonne : on repete (rank.max-rank.min)^(k-1) chaque
# chiffre : ca remplit la colonne Dans la deuxieme : on repete
# (rank.max-rank.min)^(k-2) chaque chiffre, et on fait ca (rank.max-rank.min)^2
# fois ... Dans la derniere, on repete chaque chiffre une fois, et on fait ca
# (rank.min-rank.max)^(k-1) fois.
RankLambda[, r] <- rep(rank.min + rep(0:(deltaRank - 1), deltaRank^(r - 1),
each = deltaRank^(k - r)), each = L)
}
RankLambda[, k + 1] <- rep(1:L, times = Size)
if (ncores > 1)
{
cl <- parallel::makeCluster(ncores, outfile = "")
parallel::clusterExport(cl, envir = environment(), varlist = c("A1", "Size",
"Pi", "Rho", "mini", "maxi", "X", "Y", "eps", "Rank", "m", "phi", "ncores",
"verbose"))
}
computeAtLambda <- function(index)
{
lambdaIndex <- RankLambda[index, k + 1]
rankIndex <- RankLambda[index, 1:k]
if (ncores > 1)
require("valse") #workers start with an empty environment
# 'relevant' will be the set of relevant columns
selected <- S[[lambdaIndex]]$selected
relevant <- c()
for (j in 1:p)
{
if (length(selected[[j]]) > 0)
relevant <- c(relevant, j)
}
if (max(rankIndex) < length(relevant))
{
phi <- array(0, dim = c(p, m, k))
if (length(relevant) > 0)
{
res <- EMGrank(S[[lambdaIndex]]$Pi, S[[lambdaIndex]]$Rho, mini, maxi,
X[, relevant], Y, eps, rankIndex, fast)
llh <- c(res$LLF, sum(rankIndex * (length(relevant) - rankIndex + m)))
phi[relevant, , ] <- res$phi
}
list(llh = llh, phi = phi, pi = S[[lambdaIndex]]$Pi, rho = S[[lambdaIndex]]$Rho)
}
}
# For each lambda in the grid we compute the estimators
out <-
if (ncores > 1) {
parallel::parLapply(cl, seq_len(length(S) * Size), computeAtLambda)
} else {
lapply(seq_len(length(S) * Size), computeAtLambda)
}
if (ncores > 1)
parallel::stopCluster(cl)
out
}
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