-#TODO: wrapper on C function
+#' 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)
+{
+ 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,
+ X, Y, eps)
+{
+ # Matrix dimensions: NOTE: phiInit *must* be an array (even if p==1)
+ n <- dim(Y)[1]
+ p <- dim(phiInit)[1]
+ m <- dim(phiInit)[2]
+ k <- dim(phiInit)[3]
+
+ # 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) <
+ # na.rm=TRUE to handle 0*log(0)
+ -sum(gam2 * log(pi2), na.rm=TRUE)/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]))
+ sumLogLLH <- 0
+ for (i in 1:n)
+ {
+ # Update gam[,]; use log to avoid numerical problems
+ logGam <- sapply(1:k, function(r) {
+ log(pi[r]) + log(detRho[r]) - 0.5 *
+ sum((Y[i, ] %*% rho[, , r] - X[i, ] %*% phi[, , r])^2)
+ })
+
+ logGam <- logGam - max(logGam) #adjust without changing proportions
+ gam[i, ] <- exp(logGam)
+ norm_fact <- sum(gam[i, ])
+ gam[i, ] <- gam[i, ] / norm_fact
+ sumLogLLH <- sumLogLLH + log(norm_fact) - 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