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[valse.git] / pkg / R / constructionModelesLassoMLE.R

#' 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, rho, pi, llh
#'
#' @export
constructionModelesLassoMLE <- function(phiInit, rhoInit, piInit, gamInit, mini, 
  maxi, gamma, X, Y, eps, S, ncores = 3, 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 <- dim(X)[1]
    p <- dim(phiInit)[1]
    m <- dim(phiInit)[2]
    k <- dim(phiInit)[3]
    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))

    ## Computation of the loglikelihood
    # Precompute det(rhoLambda[,,r]) for r in 1...k
    detRho <- sapply(1:k, function(r) det(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
      gam <- exp(logGam)
      norm_fact <- sum(gam)
      sumLogLLH <- sumLogLLH + log(norm_fact) - log((2 * base::pi)^(m/2))
    }
    llhLambda <- c(-sumLogLLH/n, (dimension + m + 1) * k - 1)
    # densite <- vector("double", n)
    # for (r in 1:k)
    # {
    #   if (length(col.sel) == 1)
    #   {
    #     delta <- (Y %*% rhoLambda[, , r] - (X[, col.sel] %*% t(phiLambda[col.sel, , r])))
    #   } else delta <- (Y %*% rhoLambda[, , r] - (X[, col.sel] %*% phiLambda[col.sel, , r]))
    #   densite <- densite + piLambda[r] * det(rhoLambda[, , r])/(sqrt(2 * base::pi))^m * 
    #     exp(-rowSums(delta^2)/2)
    # }
    # llhLambda <- c(mean(log(densite)), (dimension + m + 1) * k - 1)
    list(phi = phiLambda, rho = rhoLambda, pi = piLambda, llh = llhLambda)
  }

  # For each lambda, computation of the parameters
  out <-
    if (ncores > 1) {
      parLapply(cl, 1:length(S), computeAtLambda)
    } else {
      lapply(1:length(S), computeAtLambda)
    }

  if (ncores > 1) 
    parallel::stopCluster(cl)

  out
}