pkg/R/constructionModelesLassoMLE.R

   1 #' constructionModelesLassoMLE
   2 #'
   3 #' Construct a collection of models with the Lasso-MLE procedure.
   4 #'
   5 #' @param phiInit an initialization for phi, get by initSmallEM.R
   6 #' @param rhoInit an initialization for rho, get by initSmallEM.R
   7 #' @param piInit an initialization for pi, get by initSmallEM.R
   8 #' @param gamInit an initialization for gam, get by initSmallEM.R
   9 #' @param mini integer, minimum number of iterations in the EM algorithm, by default = 10
  10 #' @param maxi integer, maximum number of iterations in the EM algorithm, by default = 100
  11 #' @param gamma integer for the power in the penaly, by default = 1
  12 #' @param X matrix of covariates (of size n*p)
  13 #' @param Y matrix of responses (of size n*m)
  14 #' @param eps real, threshold to say the EM algorithm converges, by default = 1e-4
  15 #' @param S output of selectVariables.R
  16 #' @param ncores Number of cores, by default = 3
  17 #' @param fast TRUE to use compiled C code, FALSE for R code only
  18 #' @param verbose TRUE to show some execution traces
  19 #'
  20 #' @return a list with several models, defined by phi, rho, pi, llh
  21 #'
  22 #' @export
  23 constructionModelesLassoMLE <- function(phiInit, rhoInit, piInit, gamInit, mini,
  24   maxi, gamma, X, Y, eps, S, ncores = 3, fast, verbose)
  25 {
  26   if (ncores > 1)
  27   {
  28     cl <- parallel::makeCluster(ncores, outfile = "")
  29     parallel::clusterExport(cl, envir = environment(), varlist = c("phiInit",
  30       "rhoInit", "gamInit", "mini", "maxi", "gamma", "X", "Y", "eps", "S",
  31       "ncores", "fast", "verbose"))
  32   }
  33
  34   # Individual model computation
  35   computeAtLambda <- function(lambda)
  36   {
  37     if (ncores > 1)
  38       require("valse")  #nodes start with an empty environment
  39
  40     if (verbose)
  41       print(paste("Computations for lambda=", lambda))
  42
  43     n <- dim(X)[1]
  44     p <- dim(phiInit)[1]
  45     m <- dim(phiInit)[2]
  46     k <- dim(phiInit)[3]
  47     sel.lambda <- S[[lambda]]$selected
  48     # col.sel = which(colSums(sel.lambda)!=0) #if boolean matrix
  49     col.sel <- which(sapply(sel.lambda, length) > 0)  #if list of selected vars
  50     if (length(col.sel) == 0)
  51       return(NULL)
  52
  53     # lambda == 0 because we compute the EMV: no penalization here
  54     res <- EMGLLF(array(phiInit[col.sel, , ],dim=c(length(col.sel),m,k)), rhoInit,
  55       piInit, gamInit, mini, maxi, gamma, 0, as.matrix(X[, col.sel]), Y, eps, fast)
  56
  57     # Eval dimension from the result + selected
  58     phiLambda2 <- res$phi
  59     rhoLambda <- res$rho
  60     piLambda <- res$pi
  61     phiLambda <- array(0, dim = c(p, m, k))
  62     for (j in seq_along(col.sel))
  63       phiLambda[col.sel[j], sel.lambda[[j]], ] <- phiLambda2[j, sel.lambda[[j]], ]
  64     dimension <- length(unlist(sel.lambda))
  65
  66     ## Computation of the loglikelihood
  67     # Precompute det(rhoLambda[,,r]) for r in 1...k
  68     detRho <- sapply(1:k, function(r) det(rhoLambda[, , r]))
  69     sumLogLLH <- 0
  70     for (i in 1:n)
  71     {
  72       # Update gam[,]; use log to avoid numerical problems
  73       logGam <- sapply(1:k, function(r) {
  74         log(piLambda[r]) + log(detRho[r]) - 0.5 *
  75           sum((Y[i, ] %*% rhoLambda[, , r] - X[i, ] %*% phiLambda[, , r])^2)
  76       })
  77
  78       logGam <- logGam - max(logGam) #adjust without changing proportions
  79       gam <- exp(logGam)
  80       norm_fact <- sum(gam)
  81       sumLogLLH <- sumLogLLH + log(norm_fact) - log((2 * base::pi)^(m/2))
  82     }
  83     llhLambda <- c(-sumLogLLH/n, (dimension + m + 1) * k - 1)
  84     # densite <- vector("double", n)
  85     # for (r in 1:k)
  86     # {
  87     #   if (length(col.sel) == 1)
  88     #   {
  89     #     delta <- (Y %*% rhoLambda[, , r] - (X[, col.sel] %*% t(phiLambda[col.sel, , r])))
  90     #   } else delta <- (Y %*% rhoLambda[, , r] - (X[, col.sel] %*% phiLambda[col.sel, , r]))
  91     #   densite <- densite + piLambda[r] * det(rhoLambda[, , r])/(sqrt(2 * base::pi))^m *
  92     #     exp(-rowSums(delta^2)/2)
  93     # }
  94     # llhLambda <- c(mean(log(densite)), (dimension + m + 1) * k - 1)
  95     list(phi = phiLambda, rho = rhoLambda, pi = piLambda, llh = llhLambda)
  96   }
  97
  98   # For each lambda, computation of the parameters
  99   out <-
 100     if (ncores > 1) {
 101       parLapply(cl, 1:length(S), computeAtLambda)
 102     } else {
 103       lapply(1:length(S), computeAtLambda)
 104     }
 105
 106   if (ncores > 1)
 107     parallel::stopCluster(cl)
 108
 109   out
 110 }