+++ /dev/null
-#' EMGrank
-#'
-#' Description de EMGrank
-#'
-#' @param Pi Parametre de proportion
-#' @param Rho Parametre initial de variance renormalisé
-#' @param mini Nombre minimal d'itérations dans l'algorithme EM
-#' @param maxi Nombre maximal d'itérations dans l'algorithme EM
-#' @param X Régresseurs
-#' @param Y Réponse
-#' @param tau Seuil pour accepter la convergence
-#' @param rank Vecteur des rangs possibles
-#'
-#' @return A list ...
-#' phi : parametre de moyenne renormalisé, calculé par l'EM
-#' LLF : log vraisemblance associé à cet échantillon, pour les valeurs estimées des paramètres
-#'
-#' @export
-EMGrank <- function(Pi, Rho, mini, maxi, X, Y, tau, rank, fast = TRUE)
-{
- if (!fast)
- {
- # Function in R
- return(.EMGrank_R(Pi, Rho, mini, maxi, X, Y, tau, rank))
- }
-
- # Function in C
- n <- nrow(X) #nombre d'echantillons
- p <- ncol(X) #nombre de covariables
- m <- ncol(Y) #taille de Y (multivarié)
- k <- length(Pi) #nombre de composantes dans le mélange
- .Call("EMGrank", Pi, Rho, mini, maxi, X, Y, tau, rank, phi = double(p * m * k),
- LLF = double(1), n, p, m, k, PACKAGE = "valse")
-}
-
-# helper to always have matrices as arg (TODO: put this elsewhere? improve?) -->
-# Yes, we should use by-columns storage everywhere... [later!]
-matricize <- function(X)
-{
- if (!is.matrix(X))
- return(t(as.matrix(X)))
- return(X)
-}
-
-# R version - slow but easy to read
-.EMGrank_R <- function(Pi, Rho, mini, maxi, X, Y, tau, rank)
-{
- # matrix dimensions
- n <- dim(X)[1]
- p <- dim(X)[2]
- m <- dim(Rho)[2]
- k <- dim(Rho)[3]
-
- # init outputs
- phi <- array(0, dim = c(p, m, k))
- Z <- rep(1, n)
- LLF <- 0
-
- # local variables
- Phi <- array(0, dim = c(p, m, k))
- deltaPhi <- c()
- sumDeltaPhi <- 0
- deltaPhiBufferSize <- 20
-
- # main loop
- ite <- 1
- while (ite <= mini || (ite <= maxi && sumDeltaPhi > tau))
- {
- # M step: update for Beta ( and then phi)
- for (r in 1:k)
- {
- Z_indice <- seq_len(n)[Z == r] #indices where Z == r
- if (length(Z_indice) == 0)
- next
- # U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr
- s <- svd(MASS::ginv(crossprod(matricize(X[Z_indice, ]))) %*% crossprod(matricize(X[Z_indice,
- ]), matricize(Y[Z_indice, ])))
- S <- s$d
- # Set m-rank(r) singular values to zero, and recompose best rank(r) approximation
- # of the initial product
- if (rank[r] < length(S))
- S[(rank[r] + 1):length(S)] <- 0
- phi[, , r] <- s$u %*% diag(S) %*% t(s$v) %*% Rho[, , r]
- }
-
- # Step E and computation of the loglikelihood
- sumLogLLF2 <- 0
- for (i in seq_len(n))
- {
- sumLLF1 <- 0
- maxLogGamIR <- -Inf
- for (r in seq_len(k))
- {
- dotProduct <- tcrossprod(Y[i, ] %*% Rho[, , r] - X[i, ] %*% phi[,
- , r])
- logGamIR <- log(Pi[r]) + log(det(Rho[, , r])) - 0.5 * dotProduct
- # Z[i] = index of max (gam[i,])
- if (logGamIR > maxLogGamIR)
- {
- Z[i] <- r
- maxLogGamIR <- logGamIR
- }
- sumLLF1 <- sumLLF1 + exp(logGamIR)/(2 * pi)^(m/2)
- }
- sumLogLLF2 <- sumLogLLF2 + log(sumLLF1)
- }
-
- LLF <- -1/n * sumLogLLF2
-
- # update distance parameter to check algorithm convergence (delta(phi, Phi))
- deltaPhi <- c(deltaPhi, max((abs(phi - Phi))/(1 + abs(phi)))) #TODO: explain?
- if (length(deltaPhi) > deltaPhiBufferSize)
- deltaPhi <- deltaPhi[2:length(deltaPhi)]
- sumDeltaPhi <- sum(abs(deltaPhi))
-
- # update other local variables
- Phi <- phi
- ite <- ite + 1
- }
- return(list(phi = phi, LLF = LLF))
-}