X-Git-Url: https://git.auder.net/?p=valse.git;a=blobdiff_plain;f=pkg%2FR%2FEMGLLF.R;h=1633821a344996c75aec2c85a5371d8c80d08423;hp=5ef231eec46bdb5b890620f2bae76373ce12ceb4;hb=3921ba9b5ea85bcc190245ac7da9ee9da1658b9f;hpb=ffdf94474d96cdd3e9d304ce809df7e62aa957ed diff --git a/pkg/R/EMGLLF.R b/pkg/R/EMGLLF.R index 5ef231e..1633821 100644 --- a/pkg/R/EMGLLF.R +++ b/pkg/R/EMGLLF.R @@ -1,6 +1,9 @@ -#' EMGLLF +#' EMGLLF #' -#' Description de EMGLLF +#' Run a generalized EM algorithm developped for mixture of Gaussian regression +#' models with variable selection by an extension of the Lasso estimator (regularization parameter lambda). +#' Reparametrization is done to ensure invariance by homothetic transformation. +#' It returns a collection of models, varying the number of clusters and the sparsity in the regression mean. #' #' @param phiInit an initialization for phi #' @param rhoInit an initialization for rho @@ -13,97 +16,92 @@ #' @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 fast boolean to enable or not the C function call #' -#' @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 : ... +#' @return A list (corresponding to the model collection) defined by (phi,rho,pi,LLF,S,affec): +#' phi : regression mean for each cluster +#' rho : variance (homothetic) for each cluster +#' pi : proportion for each cluster +#' LLF : log likelihood with respect to the training set +#' S : selected variables indexes +#' affec : cluster affectation for each observation (of the training set) #' #' @export -EMGLLF <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda, - X, Y, eps, fast = TRUE) - { +EMGLLF <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda, + X, Y, eps, fast) +{ if (!fast) { # Function in R - return(.EMGLLF_R(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda, + return(.EMGLLF_R(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda, X, Y, eps)) } - + # 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, eps, 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") + .Call("EMGLLF", phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda, + X, Y, eps, PACKAGE = "valse") } # R version - slow but easy to read -.EMGLLF_R <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda, - X2, Y, eps) - { +.EMGLLF_R <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda, + X, Y, eps) +{ # 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 + n <- nrow(X) + p <- ncol(X) + m <- ncol(Y) + k <- length(piInit) + + # Adjustments required when p==1 or m==1 (var.sel. or output dim 1) + if (p==1 || m==1) + phiInit <- array(phiInit, dim=c(p,m,k)) + if (m==1) + rhoInit <- array(rhoInit, dim=c(m,m,k)) + # Outputs - phi <- array(NA, dim = c(p, m, k)) - phi[1:p, , ] <- phiInit + 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) { # 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 (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]) + for (s in 1:p) + Gram2[j, s, r] <- crossprod(X2[, j, r], X2[, s, r]) } } - - ######### M step # - + + ## 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 @@ -113,75 +111,83 @@ EMGLLF <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda, 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)) - { + while (kk < 1000 && -a/n + lambda * sum(pi^gamma * b) < + # na.rm=TRUE to handle 0*log(0) + -sum(gam2 * log(pi2), na.rm=TRUE)/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]) + 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] + 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# - + + ## 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) + detRho <- sapply(1:k, function(r) gdet(rho[, , r])) + sumLogLLH <- 0 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] - } + # Update gam[,]; use log to avoid numerical problems + logGam <- sapply(1:k, function(r) { + log(pi[r]) + log(detRho[r]) - 0.5 * + sum((Y[i, ] %*% rho[, , r] - X[i, ] %*% phi[, , r])^2) + }) + + logGam <- logGam - max(logGam) #adjust without changing proportions + gam[i, ] <- exp(logGam) + norm_fact <- sum(gam[i, ]) + gam[i, ] <- gam[i, ] / norm_fact + sumLogLLH <- sumLogLLH + log(norm_fact) - log((2 * base::pi)^(m/2)) } - 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 + 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 >= eps || dist2 >= sqrt(eps))) + + if (ite >= mini && (dist >= eps || dist2 >= sqrt(eps))) break } - - list(phi = phi, rho = rho, pi = pi, llh = llh, S = S) + + affec = apply(gam, 1, which.max) + list(phi = phi, rho = rho, pi = pi, llh = llh, S = S, affec=affec) }