-#' EMGLLF
+#' EMGLLF
#'
#' Description de EMGLLF
#'
-#' @param phiInit Parametre initial de moyenne renormalisé
-#' @param rhoInit Parametre initial de variance renormalisé
-#' @param piInit Parametre initial des proportions
-#' @param gamInit Paramètre initial des probabilités a posteriori de chaque échantillon
-#' @param mini Nombre minimal d'itérations dans l'algorithme EM
-#' @param maxi Nombre maximal d'itérations dans l'algorithme EM
-#' @param gamma Puissance des proportions dans la pénalisation pour un Lasso adaptatif
-#' @param lambda Valeur du paramètre de régularisation du Lasso
-#' @param X Régresseurs
-#' @param Y Réponse
-#' @param tau Seuil pour accepter la convergence
+#' @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
#' S : ... affec : ...
#'
#' @export
-EMGLLF <- function(phiInit, rhoInit, piInit, gamInit,
- mini, maxi, gamma, lambda, X, Y, tau, fast=TRUE)
+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,tau))
- }
-
- # 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, tau,
- 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")
+ 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,tau)
+.EMGLLF_R <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
+ X, Y, eps)
{
- # Matrix dimensions
- n = dim(X)[1]
- p = dim(phiInit)[1]
- m = dim(phiInit)[2]
- k = dim(phiInit)[3]
-
- # Outputs
- phi = 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
-
- # Calcul associé à Y et X
- 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])
- }
- }
-
- ##########
- #Etape M #
- ##########
-
- # Pour pi
- b = sapply( 1:k, function(r) sum(abs(phi[,,r])) )
- gam2 = colSums(gam)
- a = sum(gam %*% log(pi))
-
- # Tant que les props sont negatives
- kk = 0
- pi2AllPositive = FALSE
- while (!pi2AllPositive)
- {
- pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
- pi2AllPositive = all(pi2 >= 0)
- kk = kk+1
- }
-
- # t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
- 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))
-
- #Pour phi et 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]
- }
- }
- }
-
- ##########
- #Etape E #
- ##########
-
- # 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[,]
- sumGamI = 0
- for (r in 1:k)
- {
- gam[i,r] = pi[r]*exp(-0.5*sum((Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])^2))*detRho[r]
- sumGamI = sumGamI + gam[i,r]
- }
- sumLogLLH = sumLogLLH + log(sumGamI) - log((2*base::pi)^(m/2))
- if (sumGamI > EPS) #else: gam[i,] is already ~=0
- gam[i,] = gam[i,] / sumGamI
- }
-
- 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 >= tau || dist2 >= sqrt(tau)))
- break
- }
-
- affec = apply(gam, 1, which.max)
- list( "phi"=phi, "rho"=rho, "pi"=pi, "llh"=llh, "S"=S, "affec"=affec )
+ # 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