+++ /dev/null
-#' EMGLLF
-#'
-#' Description de EMGLLF
-#'
-#' @param phiInit an initialization for phi
-#' @param rhoInit an initialization for rho
-#' @param piInit an initialization for pi
-#' @param gamInit initialization for the a posteriori probabilities
-#' @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 gamma integer for the power in the penaly, by default = 1
-#' @param lambda regularization parameter in the Lasso estimation
-#' @param X matrix of covariates (of size n*p)
-#' @param Y matrix of responses (of size n*m)
-#' @param eps real, threshold to say the EM algorithm converges, by default = 1e-4
-#'
-#' @return A list ... phi,rho,pi,LLF,S,affec:
-#' phi : parametre de moyenne renormalisé, calculé par l'EM
-#' rho : parametre de variance renormalisé, calculé par l'EM
-#' pi : parametre des proportions renormalisé, calculé par l'EM
-#' LLF : log vraisemblance associée à cet échantillon, pour les valeurs estimées des paramètres
-#' S : ... affec : ...
-#'
-#' @export
-EMGLLF <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
- X, Y, eps, fast = TRUE)
- {
- if (!fast)
- {
- # Function in R
- return(.EMGLLF_R(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
- X, Y, eps))
- }
-
- # Function in C
- n <- nrow(X) #nombre d'echantillons
- p <- ncol(X) #nombre de covariables
- m <- ncol(Y) #taille de Y (multivarié)
- k <- length(piInit) #nombre de composantes dans le mélange
- .Call("EMGLLF", phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
- X, Y, eps, phi = double(p * m * k), rho = double(m * m * k), pi = double(k),
- LLF = double(maxi), S = double(p * m * k), affec = integer(n), n, p, m, k,
- PACKAGE = "valse")
-}
-
-# R version - slow but easy to read
-.EMGLLF_R <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
- X2, Y, eps)
- {
- # Matrix dimensions
- n <- dim(Y)[1]
- if (length(dim(phiInit)) == 2)
- {
- p <- 1
- m <- dim(phiInit)[1]
- k <- dim(phiInit)[2]
- } else
- {
- p <- dim(phiInit)[1]
- m <- dim(phiInit)[2]
- k <- dim(phiInit)[3]
- }
- X <- matrix(nrow = n, ncol = p)
- X[1:n, 1:p] <- X2
- # Outputs
- phi <- array(NA, dim = c(p, m, k))
- phi[1:p, , ] <- phiInit
- rho <- rhoInit
- pi <- piInit
- llh <- -Inf
- S <- array(0, dim = c(p, m, k))
-
- # Algorithm variables
- gam <- gamInit
- Gram2 <- array(0, dim = c(p, p, k))
- ps2 <- array(0, dim = c(p, m, k))
- X2 <- array(0, dim = c(n, p, k))
- Y2 <- array(0, dim = c(n, m, k))
- EPS <- 1e-15
-
- for (ite in 1:maxi)
- {
- # Remember last pi,rho,phi values for exit condition in the end of loop
- Phi <- phi
- Rho <- rho
- Pi <- pi
-
- # Computations associated to X and Y
- for (r in 1:k)
- {
- for (mm in 1:m) Y2[, mm, r] <- sqrt(gam[, r]) * Y[, mm]
- for (i in 1:n) X2[i, , r] <- sqrt(gam[i, r]) * X[i, ]
- for (mm in 1:m) ps2[, mm, r] <- crossprod(X2[, , r], Y2[, mm, r])
- for (j in 1:p)
- {
- for (s in 1:p) Gram2[j, s, r] <- crossprod(X2[, j, r], X2[, s, r])
- }
- }
-
- ######### M step #
-
- # For pi
- b <- sapply(1:k, function(r) sum(abs(phi[, , r])))
- gam2 <- colSums(gam)
- a <- sum(gam %*% log(pi))
-
- # While the proportions are nonpositive
- kk <- 0
- pi2AllPositive <- FALSE
- while (!pi2AllPositive)
- {
- pi2 <- pi + 0.1^kk * ((1/n) * gam2 - pi)
- pi2AllPositive <- all(pi2 >= 0)
- kk <- kk + 1
- }
-
- # t(m) is the largest value in the grid O.1^k such that it is nonincreasing
- while (kk < 1000 && -a/n + lambda * sum(pi^gamma * b) < -sum(gam2 * log(pi2))/n +
- lambda * sum(pi2^gamma * b))
- {
- pi2 <- pi + 0.1^kk * (1/n * gam2 - pi)
- kk <- kk + 1
- }
- t <- 0.1^kk
- pi <- (pi + t * (pi2 - pi))/sum(pi + t * (pi2 - pi))
-
- # For phi and rho
- for (r in 1:k)
- {
- for (mm in 1:m)
- {
- ps <- 0
- for (i in 1:n) ps <- ps + Y2[i, mm, r] * sum(X2[i, , r] * phi[, mm,
- r])
- nY2 <- sum(Y2[, mm, r]^2)
- rho[mm, mm, r] <- (ps + sqrt(ps^2 + 4 * nY2 * gam2[r]))/(2 * nY2)
- }
- }
-
- for (r in 1:k)
- {
- for (j in 1:p)
- {
- for (mm in 1:m)
- {
- S[j, mm, r] <- -rho[mm, mm, r] * ps2[j, mm, r] + sum(phi[-j, mm,
- r] * Gram2[j, -j, r])
- if (abs(S[j, mm, r]) <= n * lambda * (pi[r]^gamma))
- {
- phi[j, mm, r] <- 0
- } else if (S[j, mm, r] > n * lambda * (pi[r]^gamma))
- {
- phi[j, mm, r] <- (n * lambda * (pi[r]^gamma) - S[j, mm, r])/Gram2[j,
- j, r]
- } else
- {
- phi[j, mm, r] <- -(n * lambda * (pi[r]^gamma) + S[j, mm, r])/Gram2[j,
- j, r]
- }
- }
- }
- }
-
- ######## E step#
-
- # Precompute det(rho[,,r]) for r in 1...k
- detRho <- sapply(1:k, function(r) det(rho[, , r]))
- gam1 <- matrix(0, nrow = n, ncol = k)
- for (i in 1:n)
- {
- # Update gam[,]
- for (r in 1:k) gam1[i, r] <- pi[r] * exp(-0.5 * sum((Y[i, ] %*% rho[,
- , r] - X[i, ] %*% phi[, , r])^2)) * detRho[r]
- }
- gam <- gam1/rowSums(gam1)
- sumLogLLH <- sum(log(rowSums(gam)) - log((2 * base::pi)^(m/2)))
- sumPen <- sum(pi^gamma * b)
- last_llh <- llh
- llh <- -sumLogLLH/n + lambda * sumPen
- dist <- ifelse(ite == 1, llh, (llh - last_llh)/(1 + abs(llh)))
- Dist1 <- max((abs(phi - Phi))/(1 + abs(phi)))
- Dist2 <- max((abs(rho - Rho))/(1 + abs(rho)))
- Dist3 <- max((abs(pi - Pi))/(1 + abs(Pi)))
- dist2 <- max(Dist1, Dist2, Dist3)
-
- if (ite >= mini && (dist >= eps || dist2 >= sqrt(eps)))
- break
- }
-
- list(phi = phi, rho = rho, pi = pi, llh = llh, S = S)
-}
projects / valse.git / blobdiff