pkg/R/main.R

   1 #' valse
   2 #'
   3 #' Main function
   4 #'
   5 #' @param X matrix of covariates (of size n*p)
   6 #' @param Y matrix of responses (of size n*m)
   7 #' @param procedure among 'LassoMLE' or 'LassoRank'
   8 #' @param selecMod method to select a model among 'DDSE', 'DJump', 'BIC' or 'AIC'
   9 #' @param gamma integer for the power in the penaly, by default = 1
  10 #' @param mini integer, minimum number of iterations in the EM algorithm, by default = 10
  11 #' @param maxi integer, maximum number of iterations in the EM algorithm, by default = 100
  12 #' @param eps real, threshold to say the EM algorithm converges, by default = 1e-4
  13 #' @param kmin integer, minimum number of clusters, by default = 2
  14 #' @param kmax integer, maximum number of clusters, by default = 10
  15 #' @param rank.min integer, minimum rank in the low rank procedure, by default = 1
  16 #' @param rank.max integer, maximum rank in the low rank procedure, by default = 5
  17 #' @param ncores_outer Number of cores for the outer loop on k
  18 #' @param ncores_inner Number of cores for the inner loop on lambda
  19 #' @param thresh real, threshold to say a variable is relevant, by default = 1e-8
  20 #' @param compute_grid_lambda, TRUE to compute the grid, FALSE if known (in arguments)
  21 #' @param grid_lambda, a vector with regularization parameters if known, by default 0
  22 #' @param size_coll_mod (Maximum) size of a collection of models
  23 #' @param fast TRUE to use compiled C code, FALSE for R code only
  24 #' @param verbose TRUE to show some execution traces
  25 #'
  26 #' @return a list with estimators of parameters
  27 #'
  28 #' @examples
  29 #' #TODO: a few examples
  30 #' @export
  31 valse <- function(X, Y, procedure = "LassoMLE", selecMod = "DDSE", gamma = 1, mini = 10,
  32   maxi = 50, eps = 1e-04, kmin = 2, kmax = 3, rank.min = 1, rank.max = 5, ncores_outer = 1,
  33   ncores_inner = 1, thresh = 1e-08, compute_grid_lambda = TRUE, grid_lambda = 0, size_coll_mod = 10, fast = TRUE, verbose = FALSE,
  34   plot = TRUE)
  35 {
  36   p <- dim(X)[2]
  37   m <- dim(Y)[2]
  38   n <- dim(X)[1]
  39
  40   if (verbose)
  41     print("main loop: over all k and all lambda")
  42
  43   if (ncores_outer > 1) {
  44     cl <- parallel::makeCluster(ncores_outer, outfile = "")
  45     parallel::clusterExport(cl = cl, envir = environment(), varlist = c("X",
  46       "Y", "procedure", "selecMod", "gamma", "mini", "maxi", "eps", "kmin",
  47       "kmax", "rank.min", "rank.max", "ncores_outer", "ncores_inner", "thresh",
  48       "size_coll_mod", "verbose", "p", "m"))
  49   }
  50
  51   # Compute models with k components
  52   computeModels <- function(k)
  53   {
  54     if (ncores_outer > 1)
  55       require("valse")  #nodes start with an empty environment
  56
  57     if (verbose)
  58       print(paste("Parameters initialization for k =", k))
  59     # smallEM initializes parameters by k-means and regression model in each
  60     # component, doing this 20 times, and keeping the values maximizing the
  61     # likelihood after 10 iterations of the EM algorithm.
  62     P <- initSmallEM(k, X, Y, fast)
  63     if (compute_grid_lambda == TRUE)
  64     {
  65       grid_lambda <- computeGridLambda(P$phiInit, P$rhoInit, P$piInit, P$gamInit,
  66                                        X, Y, gamma, mini, maxi, eps, fast)
  67     }
  68     if (length(grid_lambda) > size_coll_mod)
  69       grid_lambda <- grid_lambda[seq(1, length(grid_lambda), length.out = size_coll_mod)]
  70
  71     if (verbose)
  72       print("Compute relevant parameters")
  73     # select variables according to each regularization parameter from the grid:
  74     # S$selected corresponding to selected variables
  75     S <- selectVariables(P$phiInit, P$rhoInit, P$piInit, P$gamInit, mini, maxi,
  76       gamma, grid_lambda, X, Y, thresh, eps, ncores_inner, fast)
  77
  78     if (procedure == "LassoMLE") {
  79       if (verbose)
  80         print("run the procedure Lasso-MLE")
  81       # compute parameter estimations, with the Maximum Likelihood Estimator,
  82       # restricted on selected variables.
  83       models <- constructionModelesLassoMLE(P$phiInit, P$rhoInit, P$piInit,
  84         P$gamInit, mini, maxi, gamma, X, Y, eps, S, ncores_inner, fast, verbose)
  85     } else {
  86       if (verbose)
  87         print("run the procedure Lasso-Rank")
  88       # compute parameter estimations, with the Low Rank Estimator, restricted on
  89       # selected variables.
  90       models <- constructionModelesLassoRank(S, k, mini, maxi, X, Y, eps, rank.min,
  91         rank.max, ncores_inner, fast, verbose)
  92     }
  93     # warning! Some models are NULL after running selectVariables
  94     models <- models[sapply(models, function(cell) !is.null(cell))]
  95     models
  96   }
  97
  98   # List (index k) of lists (index lambda) of models
  99   models_list <-
 100     if (ncores_outer > 1) {
 101       parLapply(cl, kmin:kmax, computeModels)
 102     } else {
 103       lapply(kmin:kmax, computeModels)
 104     }
 105   if (ncores_outer > 1)
 106     parallel::stopCluster(cl)
 107
 108   if (!requireNamespace("capushe", quietly = TRUE))
 109   {
 110     warning("'capushe' not available: returning all models")
 111     return(models_list)
 112   }
 113
 114   # Get summary 'tableauRecap' from models
 115   tableauRecap <- do.call(rbind, lapply(seq_along(models_list), function(i)
 116   {
 117     models <- models_list[[i]]
 118     # For a collection of models (same k, several lambda):
 119     LLH <- sapply(models, function(model) model$llh[1])
 120     k <- length(models[[1]]$pi)
 121     sumPen <- sapply(models, function(model) k * (dim(model$rho)[1] + sum(model$phi[,
 122       , 1] != 0) + 1) - 1)
 123     data.frame(model = paste(i, ".", seq_along(models), sep = ""), pen = sumPen/n,
 124       complexity = sumPen, contrast = -LLH)
 125   }))
 126   tableauRecap <- tableauRecap[which(tableauRecap[, 4] != Inf), ]
 127   if (verbose == TRUE)
 128   {
 129     print(tableauRecap)
 130   }
 131   modSel <- capushe::capushe(tableauRecap, n)
 132   indModSel <- if (selecMod == "DDSE")
 133     as.numeric(modSel@DDSE@model) else if (selecMod == "Djump")
 134     as.numeric(modSel@Djump@model) else if (selecMod == "BIC")
 135     modSel@BIC_capushe$model else if (selecMod == "AIC")
 136     modSel@AIC_capushe$model
 137
 138   mod <- as.character(tableauRecap[indModSel, 1])
 139   listMod <- as.integer(unlist(strsplit(mod, "[.]")))
 140   modelSel <- models_list[[listMod[1]]][[listMod[2]]]
 141
 142   ## Affectations
 143   Gam <- matrix(0, ncol = length(modelSel$pi), nrow = n)
 144   for (i in 1:n)
 145   {
 146     for (r in 1:length(modelSel$pi))
 147     {
 148       sqNorm2 <- sum((Y[i, ] %*% modelSel$rho[, , r] - X[i, ] %*% modelSel$phi[, , r])^2)
 149       Gam[i, r] <- modelSel$pi[r] * exp(-0.5 * sqNorm2) * det(modelSel$rho[, , r])
 150     }
 151   }
 152   Gam <- Gam/rowSums(Gam)
 153   modelSel$affec <- apply(Gam, 1, which.max)
 154   modelSel$proba <- Gam
 155   modelSel$tableau <- tableauRecap
 156
 157   if (plot)
 158     print(plot_valse(X, Y, modelSel, n))
 159
 160   return(modelSel)
 161 }