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#' constructionModelesLassoMLE
#'
#' Construct a collection of models with the Lasso-MLE procedure.
#'
#' @param phiInit an initialization for phi, get by initSmallEM.R
#' @param rhoInit an initialization for rho, get by initSmallEM.R
#' @param piInit an initialization for pi, get by initSmallEM.R
#' @param gamInit an initialization for gam, get by initSmallEM.R
#' @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 gamma integer for the power in the penaly, by default = 1
#' @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 S output of selectVariables.R
#' @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.
#'
#' @export
constructionModelesLassoMLE <- function(phiInit, rhoInit, piInit, gamInit, mini,
maxi, gamma, X, Y, eps, S, ncores, fast, verbose)
{
if (ncores > 1)
{
cl <- parallel::makeCluster(ncores, outfile = "")
parallel::clusterExport(cl, envir = environment(), varlist = c("phiInit",
"rhoInit", "gamInit", "mini", "maxi", "gamma", "X", "Y", "eps", "S",
"ncores", "fast", "verbose"))
}
# Individual model computation
computeAtLambda <- function(lambda)
{
if (ncores > 1)
require("valse") #nodes start with an empty environment
if (verbose)
print(paste("Computations for lambda=", lambda))
n <- nrow(X)
p <- ncol(X)
m <- ncol(Y)
k <- length(piInit)
sel.lambda <- S[[lambda]]$selected
# col.sel = which(colSums(sel.lambda)!=0) #if boolean matrix
col.sel <- which(sapply(sel.lambda, length) > 0) #if list of selected vars
if (length(col.sel) == 0)
return(NULL)
# lambda == 0 because we compute the EMV: no penalization here
res <- EMGLLF(array(phiInit[col.sel, , ], dim=c(length(col.sel),m,k)),
rhoInit, piInit, gamInit, mini, maxi, gamma, 0,
as.matrix(X[, col.sel]), Y, eps, fast)
# Eval dimension from the result + selected
phiLambda2 <- res$phi
rhoLambda <- res$rho
piLambda <- res$pi
phiLambda <- array(0, dim = c(p, m, k))
for (j in seq_along(col.sel))
phiLambda[col.sel[j], sel.lambda[[j]], ] <- phiLambda2[j, sel.lambda[[j]], ]
dimension <- length(unlist(sel.lambda))
## Affectations
Gam <- matrix(0, ncol = length(piLambda), nrow = n)
for (i in 1:n)
{
for (r in 1:length(piLambda))
{
sqNorm2 <- sum((Y[i, ] %*% rhoLambda[, , r] - X[i, ] %*% phiLambda[, , r])^2)
Gam[i, r] <- piLambda[r] * exp(-0.5 * sqNorm2) * det(rhoLambda[, , r])
}
}
Gam2 <- Gam/rowSums(Gam)
affec <- apply(Gam2, 1, which.max)
proba <- Gam2
LLH <- c(sum(log(apply(Gam,1,sum))), (dimension + m + 1) * k - 1)
# ## Computation of the loglikelihood
# # Precompute det(rhoLambda[,,r]) for r in 1...k
# detRho <- sapply(1:k, function(r) gdet(rhoLambda[, , r]))
# sumLogLLH <- 0
# for (i in 1:n)
# {
# # Update gam[,]; use log to avoid numerical problems
# logGam <- sapply(1:k, function(r) {
# log(piLambda[r]) + log(detRho[r]) - 0.5 *
# sum((Y[i, ] %*% rhoLambda[, , r] - X[i, ] %*% phiLambda[, , r])^2)
# })
#
# #logGam <- logGam - max(logGam) #adjust without changing proportions -> change the LLH
# gam <- exp(logGam)
# norm_fact <- sum(gam)
# sumLogLLH <- sumLogLLH + log(norm_fact) - m/2* log(2 * base::pi)
# }
#llhLambda <- c(-sumLogLLH/n, (dimension + m + 1) * k - 1)
list(phi = phiLambda, rho = rhoLambda, pi = piLambda, llh = LLH, affec = affec, proba = proba)
}
# For each lambda, computation of the parameters
out <-
if (ncores > 1) {
parallel::parLapply(cl, 1:length(S), computeAtLambda)
} else {
lapply(1:length(S), computeAtLambda)
}
if (ncores > 1)
parallel::stopCluster(cl)
out
}
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