Fix numerical problems in EMGLLF (R version)

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

#' valse 
#'
#' Main function
#'
#' @param X matrix of covariates (of size n*p)
#' @param Y matrix of responses (of size n*m)
#' @param procedure among 'LassoMLE' or 'LassoRank'
#' @param selecMod method to select a model among 'DDSE', 'DJump', 'BIC' or 'AIC'
#' @param gamma integer for the power in the penaly, by default = 1
#' @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 eps real, threshold to say the EM algorithm converges, by default = 1e-4
#' @param kmin integer, minimum number of clusters, by default = 2
#' @param kmax integer, maximum number of clusters, by default = 10
#' @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_outer Number of cores for the outer loop on k
#' @param ncores_inner Number of cores for the inner loop on lambda
#' @param thresh real, threshold to say a variable is relevant, by default = 1e-8
#' @param size_coll_mod (Maximum) size of a collection of models
#' @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 estimators of parameters
#'
#' @examples
#' #TODO: a few examples
#' @export
valse <- function(X, Y, procedure = "LassoMLE", selecMod = "DDSE", gamma = 1, mini = 10, 
  maxi = 50, eps = 1e-04, kmin = 2, kmax = 3, rank.min = 1, rank.max = 5, ncores_outer = 1, 
  ncores_inner = 1, thresh = 1e-08, size_coll_mod = 10, fast = TRUE, verbose = FALSE, 
  plot = TRUE)
{
  p <- dim(X)[2]
  m <- dim(Y)[2]
  n <- dim(X)[1]

  if (verbose) 
    print("main loop: over all k and all lambda")

  if (ncores_outer > 1) {
    cl <- parallel::makeCluster(ncores_outer, outfile = "")
    parallel::clusterExport(cl = cl, envir = environment(), varlist = c("X", 
      "Y", "procedure", "selecMod", "gamma", "mini", "maxi", "eps", "kmin", 
      "kmax", "rank.min", "rank.max", "ncores_outer", "ncores_inner", "thresh", 
      "size_coll_mod", "verbose", "p", "m"))
  }

  # Compute models with k components
  computeModels <- function(k)
  {
    if (ncores_outer > 1) 
      require("valse")  #nodes start with an empty environment

    if (verbose) 
      print(paste("Parameters initialization for k =", k))
    # smallEM initializes parameters by k-means and regression model in each
    # component, doing this 20 times, and keeping the values maximizing the
    # likelihood after 10 iterations of the EM algorithm.
    P <- initSmallEM(k, X, Y, fast)
    grid_lambda <- computeGridLambda(P$phiInit, P$rhoInit, P$piInit, P$gamInit, 
      X, Y, gamma, mini, maxi, eps, fast)
    if (length(grid_lambda) > size_coll_mod) 
      grid_lambda <- grid_lambda[seq(1, length(grid_lambda), length.out = size_coll_mod)]

    if (verbose) 
      print("Compute relevant parameters")
    # select variables according to each regularization parameter from the grid:
    # S$selected corresponding to selected variables
    S <- selectVariables(P$phiInit, P$rhoInit, P$piInit, P$gamInit, mini, maxi, 
      gamma, grid_lambda, X, Y, thresh, eps, ncores_inner, fast)

    if (procedure == "LassoMLE") {
      if (verbose) 
        print("run the procedure Lasso-MLE")
      # compute parameter estimations, with the Maximum Likelihood Estimator,
      # restricted on selected variables.
      models <- constructionModelesLassoMLE(P$phiInit, P$rhoInit, P$piInit, 
        P$gamInit, mini, maxi, gamma, X, Y, eps, S, ncores_inner, fast, verbose)
    } else {
      if (verbose) 
        print("run the procedure Lasso-Rank")
      # compute parameter estimations, with the Low Rank Estimator, restricted on
      # selected variables.
      models <- constructionModelesLassoRank(S, k, mini, maxi, X, Y, eps, rank.min, 
        rank.max, ncores_inner, fast, verbose)
    }
    # warning! Some models are NULL after running selectVariables
    models <- models[sapply(models, function(cell) !is.null(cell))]
    models
  }

  # List (index k) of lists (index lambda) of models
  models_list <-
    if (ncores_outer > 1) {
      parLapply(cl, kmin:kmax, computeModels)
    } else {
      lapply(kmin:kmax, computeModels)
    }
  if (ncores_outer > 1) 
    parallel::stopCluster(cl)

  if (!requireNamespace("capushe", quietly = TRUE))
  {
    warning("'capushe' not available: returning all models")
    return(models_list)
  }

  # Get summary 'tableauRecap' from models
  tableauRecap <- do.call(rbind, lapply(seq_along(models_list), function(i)
  {
    models <- models_list[[i]]
    # For a collection of models (same k, several lambda):
    LLH <- sapply(models, function(model) model$llh[1])
    k <- length(models[[1]]$pi)
    sumPen <- sapply(models, function(model) k * (dim(model$rho)[1] + sum(model$phi[, 
      , 1] != 0) + 1) - 1)
    data.frame(model = paste(i, ".", seq_along(models), sep = ""), pen = sumPen/n, 
      complexity = sumPen, contrast = -LLH)
  }))
  tableauRecap <- tableauRecap[which(tableauRecap[, 4] != Inf), ]

  modSel <- capushe::capushe(tableauRecap, n)
  indModSel <- if (selecMod == "DDSE") 
    as.numeric(modSel@DDSE@model) else if (selecMod == "Djump") 
    as.numeric(modSel@Djump@model) else if (selecMod == "BIC") 
    modSel@BIC_capushe$model else if (selecMod == "AIC") 
    modSel@AIC_capushe$model

  mod <- as.character(tableauRecap[indModSel, 1])
  listMod <- as.integer(unlist(strsplit(mod, "[.]")))
  modelSel <- models_list[[listMod[1]]][[listMod[2]]]

  ## Affectations
  Gam <- matrix(0, ncol = length(modelSel$pi), nrow = n)
  for (i in 1:n)
  {
    for (r in 1:length(modelSel$pi))
    {
      sqNorm2 <- sum((Y[i, ] %*% modelSel$rho[, , r] - X[i, ] %*% modelSel$phi[, , r])^2)
      Gam[i, r] <- modelSel$pi[r] * exp(-0.5 * sqNorm2) * det(modelSel$rho[, , r])
    }
  }
  Gam <- Gam/rowSums(Gam)
  modelSel$affec <- apply(Gam, 1, which.max)
  modelSel$proba <- Gam

  if (plot)
    print(plot_valse(X, Y, modelSel, n))

  return(modelSel)
}