X-Git-Url: https://git.auder.net/?p=valse.git;a=blobdiff_plain;f=pkg%2FR%2FEMGLLF.R;h=13a08daf761997792eb1ee8da71b86bcfe59c64f;hp=e600032079b475bba29c227093c4d28228db3a34;hb=43d76c49d2f98490abc782c7e8a8b94baee40247;hpb=f87ff0f5116c0c1c59c5608e46563ff0f79e5d43

diff --git a/pkg/R/EMGLLF.R b/pkg/R/EMGLLF.R
index e600032..13a08da 100644
--- a/pkg/R/EMGLLF.R
+++ b/pkg/R/EMGLLF.R
@@ -1 +1,192 @@
-#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)
+}