-#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=TRUE)
+{
+ 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")
+}
+
+# R version - slow but easy to read
+.EMGLLF_R = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X2,Y,tau)
+{
+ # 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 >= tau || dist2 >= sqrt(tau)))
+ break
+ }
+
+ list( "phi"=phi, "rho"=rho, "pi"=pi, "llh"=llh, "S"=S)
+}
projects / valse.git / blobdiff