#' EMGrank #' #' Description de EMGrank #' #' @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 #' #' @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 #' #' @export EMGrank <- function(Pi, Rho, mini, maxi, X, Y, tau, rank, fast=TRUE) { if (!fast) { # Function in R return (.EMGrank_R(Pi, Rho, mini, maxi, X, Y, tau, 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") } #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) } # R version - slow but easy to read .EMGrank_R = function(Pi, Rho, mini, maxi, X, Y, tau, rank) { require(MASS) #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 #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>tau)) { #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] } #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(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 #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 } return(list("phi"=phi, "LLF"=LLF)) }