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