+++ /dev/null
-#' constructionModelesLassoMLE
-#'
-#' TODO: description
-#'
-#' @param ...
-#'
-#' @return ...
-#'
-#' export
-constructionModelesLassoMLE = function(phiInit, rhoInit, piInit, gamInit, mini, maxi,
- gamma, X, Y, seuil, tau, selected, ncores=3, verbose=FALSE)
-{
- if (ncores > 1)
- {
- cl = parallel::makeCluster(ncores)
- parallel::clusterExport( cl, envir=environment(),
- varlist=c("phiInit","rhoInit","gamInit","mini","maxi","gamma","X","Y","seuil",
- "tau","selected","ncores","verbose") )
- }
-
- # Individual model computation
- computeAtLambda <- function(lambda)
- {
- if (ncores > 1)
- require("valse") #// nodes start with an ampty environment
-
- if (verbose)
- print(paste("Computations for lambda=",lambda))
-
- n = dim(X)[1]
- p = dim(phiInit)[1]
- m = dim(phiInit)[2]
- k = dim(phiInit)[3]
-
- sel.lambda = selected[[lambda]]
-# col.sel = which(colSums(sel.lambda)!=0) #if boolean matrix
- col.sel <- which( sapply(sel.lambda,length) > 0 ) #if list of selected vars
-
- if (length(col.sel) == 0)
- return (NULL)
-
- # lambda == 0 because we compute the EMV: no penalization here
- res = EMGLLF(phiInit[col.sel,,],rhoInit,piInit,gamInit,mini,maxi,gamma,0,
- X[,col.sel],Y,tau)
-
- # Eval dimension from the result + selected
- phiLambda2 = res_EM$phi
- rhoLambda = res_EM$rho
- piLambda = res_EM$pi
- phiLambda = array(0, dim = c(p,m,k))
- for (j in seq_along(col.sel))
- phiLambda[col.sel[j],,] = phiLambda2[j,,]
-
- dimension = 0
- for (j in 1:p)
- {
- b = setdiff(1:m, sel.lambda[,j])
- if (length(b) > 0)
- phiLambda[j,b,] = 0.0
- dimension = dimension + sum(sel.lambda[,j]!=0)
- }
-
- # on veut calculer la vraisemblance avec toutes nos estimations
- densite = vector("double",n)
- for (r in 1:k)
- {
- delta = Y%*%rhoLambda[,,r] - (X[, col.sel]%*%phiLambda[col.sel,,r])
- densite = densite + piLambda[r] *
- det(rhoLambda[,,r])/(sqrt(2*base::pi))^m * exp(-tcrossprod(delta)/2.0)
- }
- llhLambda = c( sum(log(densite)), (dimension+m+1)*k-1 )
- list("phi"= phiLambda, "rho"= rhoLambda, "pi"= piLambda, "llh" = llhLambda)
- }
-
- #Pour chaque lambda de la grille, on calcule les coefficients
- out =
- if (ncores > 1)
- parLapply(cl, glambda, computeAtLambda)
- else
- lapply(glambda, computeAtLambda)
-
- if (ncores > 1)
- parallel::stopCluster(cl)
-
- out
-}
p <- dim(covX)[1]
m <- dim(covY)[1]
k <- dim(covY)[3]
-
+
X <- matrix(nrow=0, ncol=p)
Y <- matrix(nrow=0, ncol=m)
#random generation of the size of each population in X~Y (unordered)
- sizePop <- rmultinom(1, n, pi)
+ sizePop <- rmultinom(1, n, π)
class <- c() #map i in 1:n --> index of class in 1:k
for (i in 1:k)
class <- c(class, rep(i, sizePop[i]))
newBlockX <- MASS::mvrnorm(sizePop[i], meanX, covX)
X <- rbind( X, newBlockX )
- Y <- rbind( Y, apply( newBlockX, 1, function(row)
- mvrnorm(1, row %*% beta[,,i], covY[,,i]) ) )
+ Y <- rbind( Y, t(apply( newBlockX, 1, function(row)
+ MASS::mvrnorm(1, row %*% β[,,i], covY[,,i]) )) )
}
shuffle = sample(n)
EMGLLF_R = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau)
{
- #matrix dimensions
- n = dim(X)[1]
- p = dim(phiInit)[1]
- m = dim(phiInit)[2]
- k = dim(phiInit)[3]
-
- #init outputs
- phi = phiInit
- rho = rhoInit
- pi = piInit
- LLF = rep(0, maxi)
- S = array(0, dim=c(p,m,k))
-
- gam = gamInit
- Gram2 = array(0, dim=c(p,p,k))
- ps2 = array(0, dim=c(p,m,k))
- b = rep(0, k)
- X2 = array(0, dim=c(n,p,k))
- Y2 = array(0, dim=c(n,m,k))
- dist = 0
- dist2 = 0
- ite = 1
- pi2 = rep(0, k)
- ps = matrix(0, m,k)
- nY2 = matrix(0, m,k)
- ps1 = array(0, dim=c(n,m,k))
- Gam = matrix(0, n,k)
- EPS = 1E-15
-
- while(ite <= mini || (ite<= maxi && (dist>= tau || dist2 >= sqrt(tau))))
+ # 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)
{
- Phi = phi
- Rho = rho
- Pi = pi
+ # 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)
+ # 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 (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
- for (r in 1:k)
- b[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)
+ 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
- }
+ 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) <
+ # 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)
+ 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)
+ for (mm in 1:m)
{
- for (i in 1:n)
- {
- ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
- }
- ps[mm,r] = sum(ps1[,mm,r])
- nY2[mm,r] = sum(Y2[,mm,r]^2)
- rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*gam2[r])) / (2*nY2[mm,r])
+ 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 (r in 1:k)
{
- for (j in 1:p)
+ for (j in 1:p)
{
- for (mm in 1:m)
+ 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])
+ 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 #
- ##########
-
- sumLogLLF2 = 0
- for (i in 1:n)
+ 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)
{
- #precompute sq norms to numerically adjust their values
- sqNorm2 = rep(0,k)
- for (r in 1:k)
- sqNorm2[r] = sum( (Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])^2 )
-
- #compute Gam[,]
- sumLLF1 = 0.0;
- for (r in 1:k)
+ # Update gam[,]
+ sumGamI = 0
+ for (r in 1:k)
{
- Gam[i,r] = pi[r] * exp(-0.5*sqNorm2[r]) * det(rho[,,r])
- sumLLF1 = sumLLF1 + Gam[i,r] / (2*base::pi)^(m/2)
- }
- sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
- sumGamI = sum(Gam[i,])
- if(sumGamI > EPS)
- gam[i,] = Gam[i,] / sumGamI
- else
- gam[i,] = rep(0,k)
- }
-
- sumPen = sum(pi^gamma * b)
- LLF[ite] = -sumLogLLF2/n + lambda*sumPen
- dist = ifelse( ite == 1, LLF[ite], (LLF[ite]-LLF[ite-1]) / (1+abs(LLF[ite])) )
- 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)
-
- ite = ite+1
- }
-
- affec = apply(gam, 1, which.max)
- return(list("phi"=phi, "rho"=rho, "pi"=pi, "LLF"=LLF, "S"=S, "affec" = affec ))
+ 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 )
}
dir.create(testFolder, showWarnings=FALSE, mode="0755")
require(valse)
- params = valse:::basicInitParameters(n, p, m, k)
- xy = valse:::generateXYdefault(n, p, m, k)
+ params = basicInitParameters(n, p, m, k)
+ xy = generateXYdefault(n, p, m, k)
#save inputs
write.table(as.double(params$phiInit), paste(testFolder,"phiInit",sep=""),
write.table(as.double(res$phi), paste(testFolder,"phi",sep=""), row.names=F, col.names=F)
write.table(as.double(res$rho), paste(testFolder,"rho",sep=""), row.names=F, col.names=F)
write.table(as.double(res$pi), paste(testFolder,"pi",sep=""), row.names=F, col.names=F)
- write.table(as.double(res$LLF), paste(testFolder,"LLF",sep=""), row.names=F, col.names=F)
+ write.table(as.double(res$llh), paste(testFolder,"llh",sep=""), row.names=F, col.names=F)
write.table(as.double(res$S), paste(testFolder,"S",sep=""), row.names=F, col.names=F)
write.table(as.integer(res$affec), paste(testFolder,"affec",sep=""), row.names=F, col.names=F)
}
for(i in 1:k)
rho[,,i] = diag(1,m)
require(valse)
- xy = valse:::generateXYdefault(n, p, m, k)
+ xy = generateXYdefault(n, p, m, k)
testFolder = "../data/"
dir.create(testFolder, showWarnings=FALSE, mode="0755")
#' Generate a sample of (X,Y) of size n with default values
+#'
#' @param n sample size
#' @param p number of covariates
#' @param m size of the response
#' @param k number of clusters
+#'
#' @return list with X and Y
-#' @export
+#'
generateXYdefault = function(n, p, m, k)
{
meanX = rep(0, p)
covY = array(dim=c(m,m,k))
for(r in 1:k)
covY[,,r] = diag(m)
- pi = rep(1./k,k)
+ π = rep(1./k,k)
#initialize beta to a random number of non-zero random value
- beta = array(0, dim=c(p,m,k))
+ β = array(0, dim=c(p,m,k))
for (j in 1:p)
{
nonZeroCount = sample(1:m, 1)
- beta[j,1:nonZeroCount,] = matrix(runif(nonZeroCount*k), ncol=k)
+ β[j,1:nonZeroCount,] = matrix(runif(nonZeroCount*k), ncol=k)
}
- sample_IO = generateXY(meanX, covX, covY, pi, beta, n)
+ sample_IO = generateXY(n, π, meanX, β, covX, covY)
return (list(X=sample_IO$X,Y=sample_IO$Y))
}
-#' Initialize the parameters in a basic way (zero for the conditional mean, uniform for weights,
-#' identity for covariance matrices, and uniformly distributed for the clustering)
+#' Initialize the parameters in a basic way (zero for the conditional mean, uniform for
+#' weights, identity for covariance matrices, and uniformly distributed for the
+#' clustering)
+#'
#' @param n sample size
#' @param p number of covariates
#' @param m size of the response
#' @param k number of clusters
+#'
#' @return list with phiInit, rhoInit,piInit,gamInit
-#' @export
+#'
basicInitParameters = function(n,p,m,k)
{
phiInit = array(0, dim=c(p,m,k))
gamInit[i,R[i]] = 0.9
gamInit = gamInit/sum(gamInit[1,])
- return (list("phiInit" = phiInit, "rhoInit" = rhoInit, "piInit" = piInit, "gamInit" = gamInit))
+ return (list("phiInit"=phiInit, "rhoInit"=rhoInit, "piInit"=piInit, "gamInit"=gamInit))
}
Real* phi = (Real*)malloc(p*m*k*sizeof(Real));
Real* rho = (Real*)malloc(m*m*k*sizeof(Real));
Real* pi = (Real*)malloc(k*sizeof(Real));
- Real* LLF = (Real*)malloc(maxi*sizeof(Real));
+ Real llh;
Real* S = (Real*)malloc(p*m*k*sizeof(Real));
int* affec = (int*)malloc(n*sizeof(int));
/////////////
////////////////////
// Call to EMGLLF //
EMGLLF_core(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau,
- phi,rho,pi,LLF,S,affec,
+ phi,rho,pi,&llh,S,affec,
n,p,m,k);
////////////////////
free(pi);
free(ref_pi);
- Real* ref_LLF = readArray_real("LLF");
- compareArray_real("LLF", LLF, ref_LLF, maxi);
- free(LLF);
- free(ref_LLF);
+ Real ref_llh = read_real("llh");
+ compareArray_real("llh", &llh, &ref_llh, 1);
Real* ref_S = readArray_real("S");
compareArray_real("S", S, ref_S, p*m*k);
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