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 (the regression parameter reparametrized),
  21 #' rho (the covariance parameter reparametrized), pi (the proportion parameter is the mixture model), llh
  22 #' (the value of the loglikelihood function for this estimator on the training dataset). The list is given
  23 #' for several levels of sparsity, given by several regularization parameters computed automatically.
  24 #'
  25 #' @export
  26 constructionModelesLassoMLE <- function(phiInit, rhoInit, piInit, gamInit, mini,
  27   maxi, gamma, X, Y, eps, S, ncores, fast, verbose)
  28 {
  29   if (ncores > 1)
  30   {
  31     cl <- parallel::makeCluster(ncores, outfile = "")
  32     parallel::clusterExport(cl, envir = environment(), varlist = c("phiInit",
  33       "rhoInit", "gamInit", "mini", "maxi", "gamma", "X", "Y", "eps", "S",
  34       "ncores", "fast", "verbose"))
  35   }
  36
  37   # Individual model computation
  38   computeAtLambda <- function(lambda)
  39   {
  40     if (ncores > 1)
  41       require("valse")  #nodes start with an empty environment
  42
  43     if (verbose)
  44       print(paste("Computations for lambda=", lambda))
  45
  46     n <- nrow(X)
  47     p <- ncol(X)
  48     m <- ncol(Y)
  49     k <- length(piInit)
  50     sel.lambda <- S[[lambda]]$selected
  51     # col.sel = which(colSums(sel.lambda)!=0) #if boolean matrix
  52     col.sel <- which(sapply(sel.lambda, length) > 0)  #if list of selected vars
  53     if (length(col.sel) == 0)
  54       return(NULL)
  55
  56     # lambda == 0 because we compute the EMV: no penalization here
  57     res <- EMGLLF(array(phiInit[col.sel, , ], dim=c(length(col.sel),m,k)),
  58       rhoInit, piInit, gamInit, mini, maxi, gamma, 0,
  59       as.matrix(X[, col.sel]), Y, eps, fast)
  60
  61     # Eval dimension from the result + selected
  62     phiLambda2 <- res$phi
  63     rhoLambda <- res$rho
  64     piLambda <- res$pi
  65     phiLambda <- array(0, dim = c(p, m, k))
  66     for (j in seq_along(col.sel))
  67       phiLambda[col.sel[j], sel.lambda[[j]], ] <- phiLambda2[j, sel.lambda[[j]], ]
  68     dimension <- length(unlist(sel.lambda))
  69
  70     ## Affectations
  71     Gam <- matrix(0, ncol = length(piLambda), nrow = n)
  72     for (i in 1:n)
  73     {
  74       for (r in 1:length(piLambda))
  75       {
  76         sqNorm2 <- sum((Y[i, ] %*% rhoLambda[, , r] - X[i, ] %*% phiLambda[, , r])^2)
  77         Gam[i, r] <- piLambda[r] * exp(-0.5 * sqNorm2) * det(rhoLambda[, , r])
  78       }
  79     }
  80     Gam2 <- Gam/rowSums(Gam)
  81     affec <- apply(Gam2, 1, which.max)
  82     proba <- Gam2
  83     LLH <- c(sum(log(apply(Gam,1,sum))), (dimension + m + 1) * k - 1)
  84     # ## Computation of the loglikelihood
  85     # # Precompute det(rhoLambda[,,r]) for r in 1...k
  86     # detRho <- sapply(1:k, function(r) gdet(rhoLambda[, , r]))
  87     # sumLogLLH <- 0
  88     # for (i in 1:n)
  89     # {
  90     #   # Update gam[,]; use log to avoid numerical problems
  91     #   logGam <- sapply(1:k, function(r) {
  92     #     log(piLambda[r]) + log(detRho[r]) - 0.5 *
  93     #       sum((Y[i, ] %*% rhoLambda[, , r] - X[i, ] %*% phiLambda[, , r])^2)
  94     #   })
  95     #
  96     #   #logGam <- logGam - max(logGam) #adjust without changing proportions -> change the LLH
  97     #   gam <- exp(logGam)
  98     #   norm_fact <- sum(gam)
  99     #   sumLogLLH <- sumLogLLH + log(norm_fact) - m/2* log(2 * base::pi)
 100     # }
 101     #llhLambda <- c(-sumLogLLH/n, (dimension + m + 1) * k - 1)
 102     list(phi = phiLambda, rho = rhoLambda, pi = piLambda, llh = LLH, affec = affec, proba = proba)
 103   }
 104
 105   # For each lambda, computation of the parameters
 106   out <-
 107     if (ncores > 1) {
 108       parallel::parLapply(cl, 1:length(S), computeAtLambda)
 109     } else {
 110       lapply(1:length(S), computeAtLambda)
 111     }
 112
 113   if (ncores > 1)
 114     parallel::stopCluster(cl)
 115
 116   out
 117 }