#' EMGrank
#'
-#' Description de EMGrank
+#' Run an generalized EM algorithm developped for mixture of Gaussian regression
+#' models with variable selection by an extension of the low rank estimator.
+#' Reparametrization is done to ensure invariance by homothetic transformation.
+#' It returns a collection of models, varying the number of clusters and the rank of the regression mean.
#'
-#' @param phiInit ...
-#' @param Pi Parametre de proportion
-#' @param Rho Parametre initial de variance renormalisé
-#' @param mini Nombre minimal d'itérations dans l'algorithme EM
-#' @param maxi Nombre maximal d'itérations dans l'algorithme EM
-#' @param X Régresseurs
-#' @param Y Réponse
-#' @param tau Seuil pour accepter la convergence
-#' @param rank Vecteur des rangs possibles
+#' @param Pi An initialization for pi
+#' @param Rho An initialization for rho, the variance parameter
+#' @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 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
+#' @param rank vector of possible ranks
+#' @param fast boolean to enable or not the C function call
#'
-#' @return A list ...
-#' phi : parametre de moyenne renormalisé, calculé par l'EM
-#' LLF : log vraisemblance associé à cet échantillon, pour les valeurs estimées des paramètres
+#' @return A list (corresponding to the model collection) defined by (phi,LLF):
+#' phi : regression mean for each cluster
+#' LLF : log likelihood with respect to the training set
#'
#' @export
-EMGrank <- function(Pi, Rho, mini, maxi, X, Y, tau, rank, fast=TRUE)
+EMGrank <- function(Pi, Rho, mini, maxi, X, Y, eps, rank, fast)
{
- if (!fast)
- {
- # Function in R
- return (EMGrank_R(Pi, Rho, mini, maxi, X, Y, tau, rank))
- }
+ if (!fast)
+ {
+ # Function in R
+ return(.EMGrank_R(Pi, Rho, mini, maxi, X, Y, eps, rank))
+ }
- # Function in C
- n = nrow(X) #nombre d'echantillons
- p = ncol(X) #nombre de covariables
- m = ncol(Y) #taille de Y (multivarié)
- k = length(Pi) #nombre de composantes dans le mélange
- .Call("EMGrank",
- Pi, Rho, mini, maxi, X, Y, tau, rank,
- phi=double(p*m*k), LLF=double(1),
- n, p, m, k,
- PACKAGE="valse")
+ # Function in C
+ .Call("EMGrank", Pi, Rho, mini, maxi, X, Y, eps, as.integer(rank), PACKAGE = "valse")
}
-#helper to always have matrices as arg (TODO: put this elsewhere? improve?)
-# --> Yes, we should use by-columns storage everywhere... [later!]
+# helper to always have matrices as arg (TODO: put this elsewhere? improve?) -->
+# Yes, we should use by-columns storage everywhere... [later!]
matricize <- function(X)
{
- if (!is.matrix(X))
- return (t(as.matrix(X)))
- return (X)
+ if (!is.matrix(X))
+ return(t(as.matrix(X)))
+ X
}
# R version - slow but easy to read
-EMGrank_R = function(Pi, Rho, mini, maxi, X, Y, tau, rank)
+.EMGrank_R <- function(Pi, Rho, mini, maxi, X, Y, eps, rank)
{
- #matrix dimensions
- n = dim(X)[1]
- p = dim(X)[2]
- m = dim(Rho)[2]
- k = dim(Rho)[3]
-
- #init outputs
- phi = array(0, dim=c(p,m,k))
- Z = rep(1, n)
- LLF = 0
+ # matrix dimensions
+ n <- nrow(X)
+ p <- ncol(X)
+ m <- ncol(Y)
+ k <- length(Pi)
- #local variables
- Phi = array(0, dim=c(p,m,k))
- deltaPhi = c()
- sumDeltaPhi = 0.
- deltaPhiBufferSize = 20
+ # init outputs
+ phi <- array(0, dim = c(p, m, k))
+ Z <- rep(1, n)
+ LLF <- 0
- #main loop
- ite = 1
- while (ite<=mini || (ite<=maxi && sumDeltaPhi>tau))
- {
- #M step: Mise à jour de Beta (et donc phi)
- for(r in 1:k)
- {
- Z_indice = seq_len(n)[Z==r] #indices où Z == r
+ # local variables
+ Phi <- array(0, dim = c(p, m, k))
+ deltaPhi <- c()
+ sumDeltaPhi <- 0
+ deltaPhiBufferSize <- 20
+
+ # main loop
+ ite <- 1
+ while (ite <= mini || (ite <= maxi && sumDeltaPhi > eps))
+ {
+ # M step: update for Beta ( and then phi)
+ for (r in 1:k)
+ {
+ Z_indice <- seq_len(n)[Z == r] #indices where Z == r
if (length(Z_indice) == 0)
next
- #U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr
- s = svd( ginv(crossprod(matricize(X[Z_indice,]))) %*%
- crossprod(matricize(X[Z_indice,]),matricize(Y[Z_indice,])) )
- S = s$d
- #Set m-rank(r) singular values to zero, and recompose
- #best rank(r) approximation of the initial product
- if(rank[r] < length(S))
- S[(rank[r]+1):length(S)] = 0
- phi[,,r] = s$u %*% diag(S) %*% t(s$v) %*% Rho[,,r]
+ # U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr
+ s <- svd(MASS::ginv(crossprod(matricize(X[Z_indice, ]))) %*%
+ crossprod(matricize(X[Z_indice, ]), matricize(Y[Z_indice, ])))
+ S <- s$d
+ # Set m-rank(r) singular values to zero, and recompose best rank(r) approximation
+ # of the initial product
+ if (rank[r] < length(S))
+ S[(rank[r] + 1):length(S)] <- 0
+ phi[, , r] <- s$u %*% diag(S) %*% t(s$v) %*% Rho[, , r]
}
- #Etape E et calcul de LLF
- sumLogLLF2 = 0
- for(i in seq_len(n))
- {
- sumLLF1 = 0
- maxLogGamIR = -Inf
- for (r in seq_len(k))
- {
- dotProduct = tcrossprod(Y[i,]%*%Rho[,,r]-X[i,]%*%phi[,,r])
- logGamIR = log(Pi[r]) + log(det(Rho[,,r])) - 0.5*dotProduct
- #Z[i] = index of max (gam[i,])
- if(logGamIR > maxLogGamIR)
- {
- Z[i] = r
- maxLogGamIR = logGamIR
- }
- sumLLF1 = sumLLF1 + exp(logGamIR) / (2*pi)^(m/2)
- }
- sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
- }
-
- LLF = -1/n * sumLogLLF2
+ # Step E and computation of the loglikelihood
+ sumLogLLF2 <- 0
+ for (i in seq_len(n))
+ {
+ sumLLF1 <- 0
+ maxLogGamIR <- -Inf
+ for (r in seq_len(k))
+ {
+ dotProduct <- tcrossprod(Y[i, ] %*% Rho[, , r] - X[i, ] %*% phi[, , r])
+ logGamIR <- log(Pi[r]) + log(gdet(Rho[, , r])) - 0.5 * dotProduct
+ # Z[i] = index of max (gam[i,])
+ if (logGamIR > maxLogGamIR)
+ {
+ Z[i] <- r
+ maxLogGamIR <- logGamIR
+ }
+ sumLLF1 <- sumLLF1 + exp(logGamIR)/(2 * pi)^(m/2)
+ }
+ sumLogLLF2 <- sumLogLLF2 + log(sumLLF1)
+ }
+
+ LLF <- -1/n * sumLogLLF2
- #update distance parameter to check algorithm convergence (delta(phi, Phi))
- deltaPhi = c( deltaPhi, max( (abs(phi-Phi)) / (1+abs(phi)) ) ) #TODO: explain?
- if (length(deltaPhi) > deltaPhiBufferSize)
- deltaPhi = deltaPhi[2:length(deltaPhi)]
- sumDeltaPhi = sum(abs(deltaPhi))
+ # update distance parameter to check algorithm convergence (delta(phi, Phi))
+ deltaPhi <- c(deltaPhi, max((abs(phi - Phi))/(1 + abs(phi)))) #TODO: explain?
+ if (length(deltaPhi) > deltaPhiBufferSize)
+ deltaPhi <- deltaPhi[2:length(deltaPhi)]
+ sumDeltaPhi <- sum(abs(deltaPhi))
- #update other local variables
- Phi = phi
- ite = ite+1
+ # update other local variables
+ Phi <- phi
+ ite <- ite + 1
}
- return(list("phi"=phi, "LLF"=LLF))
+ list(phi = phi, LLF = LLF)
}
projects / valse.git / blobdiff