--- /dev/null
+Package: valse
+Title: Variable Selection With Mixture Of Models
+Date: 2016-12-01
+Version: 0.1-0
+Description: Two methods are implemented to cluster data with finite mixture
+ regression models. Those procedures deal with high-dimensional covariates and
+ responses through a variable selection procedure based on the Lasso estimator.
+ A low-rank constraint could be added, computed for the Lasso-Rank procedure.
+ A collection of models is constructed, varying the level of sparsity and the
+ number of clusters, and a model is selected using a model selection criterion
+ (slope heuristic, BIC or AIC). Details of the procedure are provided in 'Model-
+ based clustering for high-dimensional data. Application to functional data' by
+ Emilie Devijver, published in Advances in Data Analysis and Clustering (2016).
+Author: Benjamin Auder <Benjamin.Auder@math.u-psud.fr> [aut,cre],
+ Emilie Devijver <Emilie.Devijver@kuleuven.be> [aut],
+ Benjamin Goehry <Benjamin.Goehry@math.u-psud.fr> [aut]
+Maintainer: Benjamin Auder <Benjamin.Auder@math.u-psud.fr>
+Depends:
+ R (>= 3.0.0)
+Imports:
+ MASS,
+ parallel
+Suggests:
+ capushe,
+ roxygen2,
+ testhat
+URL: http://git.auder.net/?p=valse.git
+License: MIT + file LICENSE
+RoxygenNote: 5.0.1
+Collate:
+ 'plot_valse.R'
+ 'main.R'
+ 'selectVariables.R'
+ 'constructionModelesLassoRank.R'
+ 'constructionModelesLassoMLE.R'
+ 'computeGridLambda.R'
+ 'initSmallEM.R'
+ 'EMGrank.R'
+ 'EMGLLF.R'
+ 'generateXY.R'
+ 'A_NAMESPACE.R'
+ 'util.R'
--- /dev/null
+Copyright (c)
+ 2014-2017, Benjamin Auder
+ 2014-2017, Emilie Devijver
+ 2016-2017, Benjamin Goehry
+
+Permission is hereby granted, free of charge, to any person obtaining
+a copy of this software and associated documentation files (the
+"Software"), to deal in the Software without restriction, including
+without limitation the rights to use, copy, modify, merge, publish,
+distribute, sublicense, and/or sell copies of the Software, and to
+permit persons to whom the Software is furnished to do so, subject to
+the following conditions:
+
+The above copyright notice and this permission notice shall be
+included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
+LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
+OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
+WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
--- /dev/null
+#' @include generateXY.R
+#' @include EMGLLF.R
+#' @include EMGrank.R
+#' @include initSmallEM.R
+#' @include computeGridLambda.R
+#' @include constructionModelesLassoMLE.R
+#' @include constructionModelesLassoRank.R
+#' @include selectVariables.R
+#' @include main.R
+#' @include plot_valse.R
+#'
+#' @useDynLib valse
+#'
+#' @importFrom parallel makeCluster parLapply stopCluster clusterExport
+#' @importFrom MASS ginv
+NULL
--- /dev/null
+#' 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)
+{
+ if (!fast)
+ {
+ # Function in R
+ 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")
+}
+
+# R version - slow but easy to read
+.EMGLLF_R <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
+ X, Y, eps)
+{
+ # Matrix dimensions
+ 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 <- 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) <
+ # 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])
+ 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) gdet(rho[, , r]))
+ sumLogLLH <- 0
+ for (i in 1:n)
+ {
+ # 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))
+ }
+
+ 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 >= eps || dist2 >= sqrt(eps)))
+ break
+ }
+
+ list(phi = phi, rho = rho, pi = pi, llh = llh, S = S)
+}
--- /dev/null
+#' 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)
+{
+ # matrix dimensions
+ n <- nrow(X)
+ p <- ncol(X)
+ m <- ncol(Y)
+ k <- length(Pi)
+
+ # 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(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$v) %*% Rho[, , r]
+ }
+
+ # Step E and computation of the loglikelihood
+ sumLogLLF2 <- 0
+ for (i in seq_len(n))
+ {
+ sumLLF1 <- 0
+ maxLogGamIR <- -Inf
+ for (r in seq_len(k))
+ {
+ dotProduct <- tcrossprod(Y[i, ] %*% Rho[, , r] - X[i, ] %*% phi[, , r])
+ logGamIR <- log(Pi[r]) + log(gdet(Rho[, , r])) - 0.5 * dotProduct
+ # Z[i] = index of max (gam[i,])
+ if (logGamIR > maxLogGamIR)
+ {
+ Z[i] <- r
+ maxLogGamIR <- logGamIR
+ }
+ sumLLF1 <- sumLLF1 + exp(logGamIR)/(2 * pi)^(m/2)
+ }
+ sumLogLLF2 <- sumLogLLF2 + log(sumLLF1)
+ }
+
+ LLF <- -1/n * sumLogLLF2
+
+ # update distance parameter to check algorithm convergence (delta(phi, Phi))
+ deltaPhi <- c(deltaPhi, max((abs(phi - Phi))/(1 + abs(phi)))) #TODO: explain?
+ if (length(deltaPhi) > deltaPhiBufferSize)
+ deltaPhi <- deltaPhi[2:length(deltaPhi)]
+ sumDeltaPhi <- sum(abs(deltaPhi))
+
+ # update other local variables
+ Phi <- phi
+ ite <- ite + 1
+ }
+ return(list(phi = phi, LLF = LLF))
+}
--- /dev/null
+#' computeGridLambda
+#'
+#' Construct the data-driven grid for the regularization parameters used for the Lasso estimator
+#'
+#' @param phiInit value for phi
+#' @param rhoInit for rho
+#' @param piInit for pi
+#' @param gamInit value for gamma
+#' @param X matrix of covariates (of size n*p)
+#' @param Y matrix of responses (of size n*m)
+#' @param gamma power of weights in the penalty
+#' @param mini minimum number of iterations in EM algorithm
+#' @param maxi maximum number of iterations in EM algorithm
+#' @param tau threshold to stop EM algorithm
+#'
+#' @return the grid of regularization parameters
+#'
+#' @export
+computeGridLambda <- function(phiInit, rhoInit, piInit, gamInit, X, Y, gamma, mini,
+ maxi, tau, fast)
+{
+ n <- nrow(X)
+ p <- ncol(X)
+ m <- ncol(Y)
+ k <- length(piInit)
+
+ list_EMG <- EMGLLF(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda = 0,
+ X, Y, tau, fast)
+ grid <- array(0, dim = c(p, m, k))
+ for (j in 1:p)
+ {
+ for (mm in 1:m)
+ grid[j, mm, ] <- abs(list_EMG$S[j, mm, ])/(n * list_EMG$pi^gamma)
+ }
+ sort(unique(grid))
+}
--- /dev/null
+#' constructionModelesLassoMLE
+#'
+#' Construct a collection of models with the Lasso-MLE procedure.
+#'
+#' @param phiInit an initialization for phi, get by initSmallEM.R
+#' @param rhoInit an initialization for rho, get by initSmallEM.R
+#' @param piInit an initialization for pi, get by initSmallEM.R
+#' @param gamInit an initialization for gam, get by initSmallEM.R
+#' @param mini integer, minimum number of iterations in the EM algorithm, by default = 10
+#' @param maxi integer, maximum number of iterations in the EM algorithm, by default = 100
+#' @param gamma integer for the power in the penaly, by default = 1
+#' @param X matrix of covariates (of size n*p)
+#' @param Y matrix of responses (of size n*m)
+#' @param eps real, threshold to say the EM algorithm converges, by default = 1e-4
+#' @param S output of selectVariables.R
+#' @param ncores Number of cores, by default = 3
+#' @param fast TRUE to use compiled C code, FALSE for R code only
+#' @param verbose TRUE to show some execution traces
+#'
+#' @return a list with several models, defined by phi, rho, pi, llh
+#'
+#' @export
+constructionModelesLassoMLE <- function(phiInit, rhoInit, piInit, gamInit, mini,
+ maxi, gamma, X, Y, eps, S, ncores = 3, fast, verbose)
+{
+ if (ncores > 1)
+ {
+ cl <- parallel::makeCluster(ncores, outfile = "")
+ parallel::clusterExport(cl, envir = environment(), varlist = c("phiInit",
+ "rhoInit", "gamInit", "mini", "maxi", "gamma", "X", "Y", "eps", "S",
+ "ncores", "fast", "verbose"))
+ }
+
+ # Individual model computation
+ computeAtLambda <- function(lambda)
+ {
+ if (ncores > 1)
+ require("valse") #nodes start with an empty environment
+
+ if (verbose)
+ print(paste("Computations for lambda=", lambda))
+
+ n <- dim(X)[1]
+ p <- dim(phiInit)[1]
+ m <- dim(phiInit)[2]
+ k <- dim(phiInit)[3]
+ sel.lambda <- S[[lambda]]$selected
+ # 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(array(phiInit[col.sel, , ],dim=c(length(col.sel),m,k)), rhoInit,
+ piInit, gamInit, mini, maxi, gamma, 0, as.matrix(X[, col.sel]), Y, eps, fast)
+
+ # Eval dimension from the result + selected
+ phiLambda2 <- res$phi
+ rhoLambda <- res$rho
+ piLambda <- res$pi
+ phiLambda <- array(0, dim = c(p, m, k))
+ for (j in seq_along(col.sel))
+ phiLambda[col.sel[j], sel.lambda[[j]], ] <- phiLambda2[j, sel.lambda[[j]], ]
+ dimension <- length(unlist(sel.lambda))
+
+ ## Computation of the loglikelihood
+ # Precompute det(rhoLambda[,,r]) for r in 1...k
+ detRho <- sapply(1:k, function(r) det(rhoLambda[, , r]))
+ sumLogLLH <- 0
+ for (i in 1:n)
+ {
+ # Update gam[,]; use log to avoid numerical problems
+ logGam <- sapply(1:k, function(r) {
+ log(piLambda[r]) + log(detRho[r]) - 0.5 *
+ sum((Y[i, ] %*% rhoLambda[, , r] - X[i, ] %*% phiLambda[, , r])^2)
+ })
+
+ logGam <- logGam - max(logGam) #adjust without changing proportions
+ gam <- exp(logGam)
+ print(gam)
+ norm_fact <- sum(gam)
+ sumLogLLH <- sumLogLLH + log(norm_fact) - log((2 * base::pi)^(m/2))
+ }
+ llhLambda <- c(sumLogLLH/n, (dimension + m + 1) * k - 1)
+ # densite <- vector("double", n)
+ # for (r in 1:k)
+ # {
+ # if (length(col.sel) == 1)
+ # {
+ # delta <- (Y %*% rhoLambda[, , r] - (X[, col.sel] %*% t(phiLambda[col.sel, , r])))
+ # } else delta <- (Y %*% rhoLambda[, , r] - (X[, col.sel] %*% phiLambda[col.sel, , r]))
+ # densite <- densite + piLambda[r] * det(rhoLambda[, , r])/(sqrt(2 * base::pi))^m *
+ # exp(-rowSums(delta^2)/2)
+ # }
+ # llhLambda <- c(mean(log(densite)), (dimension + m + 1) * k - 1)
+ list(phi = phiLambda, rho = rhoLambda, pi = piLambda, llh = llhLambda)
+ }
+
+ # For each lambda, computation of the parameters
+ out <-
+ if (ncores > 1) {
+ parLapply(cl, 1:length(S), computeAtLambda)
+ } else {
+ lapply(1:length(S), computeAtLambda)
+ }
+
+ if (ncores > 1)
+ parallel::stopCluster(cl)
+
+ out
+}
--- /dev/null
+#' constructionModelesLassoRank
+#'
+#' Construct a collection of models with the Lasso-Rank procedure.
+#'
+#' @param S output of selectVariables.R
+#' @param k number of components
+#' @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.min integer, minimum rank in the low rank procedure, by default = 1
+#' @param rank.max integer, maximum rank in the low rank procedure, by default = 5
+#' @param ncores Number of cores, by default = 3
+#' @param fast TRUE to use compiled C code, FALSE for R code only
+#' @param verbose TRUE to show some execution traces
+#'
+#' @return a list with several models, defined by phi, rho, pi, llh
+#'
+#' @export
+constructionModelesLassoRank <- function(S, k, mini, maxi, X, Y, eps, rank.min, rank.max,
+ ncores, fast, verbose)
+{
+ n <- nrow(X)
+ p <- ncol(X)
+ m <- ncol(Y)
+ L <- length(S)
+
+ # Possible interesting ranks
+ deltaRank <- rank.max - rank.min + 1
+ Size <- deltaRank^k
+ RankLambda <- matrix(0, nrow = Size * L, ncol = k + 1)
+ for (r in 1:k)
+ {
+ # On veut le tableau de toutes les combinaisons de rangs possibles, et des
+ # lambdas Dans la première colonne : on répète (rank.max-rank.min)^(k-1) chaque
+ # chiffre : ça remplit la colonne Dans la deuxieme : on répète
+ # (rank.max-rank.min)^(k-2) chaque chiffre, et on fait ça (rank.max-rank.min)^2
+ # fois ... Dans la dernière, on répète chaque chiffre une fois, et on fait ça
+ # (rank.min-rank.max)^(k-1) fois.
+ RankLambda[, r] <- rep(rank.min + rep(0:(deltaRank - 1), deltaRank^(r - 1),
+ each = deltaRank^(k - r)), each = L)
+ }
+ RankLambda[, k + 1] <- rep(1:L, times = Size)
+
+ if (ncores > 1)
+ {
+ cl <- parallel::makeCluster(ncores, outfile = "")
+ parallel::clusterExport(cl, envir = environment(), varlist = c("A1", "Size",
+ "Pi", "Rho", "mini", "maxi", "X", "Y", "eps", "Rank", "m", "phi", "ncores",
+ "verbose"))
+ }
+
+ computeAtLambda <- function(index)
+ {
+ lambdaIndex <- RankLambda[index, k + 1]
+ rankIndex <- RankLambda[index, 1:k]
+ if (ncores > 1)
+ require("valse") #workers start with an empty environment
+
+ # 'relevant' will be the set of relevant columns
+ selected <- S[[lambdaIndex]]$selected
+ relevant <- c()
+ for (j in 1:p)
+ {
+ if (length(selected[[j]]) > 0)
+ relevant <- c(relevant, j)
+ }
+ if (max(rankIndex) < length(relevant))
+ {
+ phi <- array(0, dim = c(p, m, k))
+ if (length(relevant) > 0)
+ {
+ res <- EMGrank(S[[lambdaIndex]]$Pi, S[[lambdaIndex]]$Rho, mini, maxi,
+ X[, relevant], Y, eps, rankIndex, fast)
+ llh <- c(res$LLF, sum(rankIndex * (length(relevant) - rankIndex + m)))
+ phi[relevant, , ] <- res$phi
+ }
+ list(llh = llh, phi = phi, pi = S[[lambdaIndex]]$Pi, rho = S[[lambdaIndex]]$Rho)
+ }
+ }
+
+ # For each lambda in the grid we compute the estimators
+ out <-
+ if (ncores > 1) {
+ parLapply(cl, seq_len(length(S) * Size), computeAtLambda)
+ } else {
+ lapply(seq_len(length(S) * Size), computeAtLambda)
+ }
+
+ if (ncores > 1)
+ parallel::stopCluster(cl)
+
+ out
+}
--- /dev/null
+#' generateXY
+#'
+#' Generate a sample of (X,Y) of size n
+#'
+#' @param n sample size
+#' @param π proportion for each cluster
+#' @param meanX matrix of group means for covariates (of size p)
+#' @param covX covariance for covariates (of size p*p)
+#' @param β regression matrix, of size p*m*k
+#' @param covY covariance for the response vector (of size m*m*K)
+#'
+#' @return list with X and Y
+#'
+#' @export
+generateXY <- function(n, π, meanX, β, covX, covY)
+{
+ 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, 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, t(apply(newBlockX, 1, function(row) MASS::mvrnorm(1, row %*%
+ β[, , i], covY[, , i]))))
+ }
+
+ shuffle <- sample(n)
+ list(X = X[shuffle, ], Y = Y[shuffle, ], class = class[shuffle])
+}
--- /dev/null
+#' initialization of the EM algorithm
+#'
+#' @param k number of components
+#' @param X matrix of covariates (of size n*p)
+#' @param Y matrix of responses (of size n*m)
+#'
+#' @return a list with phiInit, rhoInit, piInit, gamInit
+#' @export
+#' @importFrom methods new
+#' @importFrom stats cutree dist hclust runif
+initSmallEM <- function(k, X, Y, fast)
+{
+ n <- nrow(X)
+ p <- ncol(X)
+ m <- ncol(Y)
+ nIte <- 20
+ Zinit1 <- array(0, dim = c(n, nIte))
+ betaInit1 <- array(0, dim = c(p, m, k, nIte))
+ sigmaInit1 <- array(0, dim = c(m, m, k, nIte))
+ phiInit1 <- array(0, dim = c(p, m, k, nIte))
+ rhoInit1 <- array(0, dim = c(m, m, k, nIte))
+ Gam <- matrix(0, n, k)
+ piInit1 <- matrix(0, nIte, k)
+ gamInit1 <- array(0, dim = c(n, k, nIte))
+ LLFinit1 <- list()
+
+ # require(MASS) #Moore-Penrose generalized inverse of matrix
+ for (repet in 1:nIte)
+ {
+ distance_clus <- dist(cbind(X, Y))
+ tree_hier <- hclust(distance_clus)
+ Zinit1[, repet] <- cutree(tree_hier, k)
+
+ for (r in 1:k)
+ {
+ Z <- Zinit1[, repet]
+ Z_indice <- seq_len(n)[Z == r] #renvoit les indices où Z==r
+ if (length(Z_indice) == 1) {
+ betaInit1[, , r, repet] <- MASS::ginv(crossprod(t(X[Z_indice, ]))) %*%
+ crossprod(t(X[Z_indice, ]), Y[Z_indice, ])
+ } else {
+ betaInit1[, , r, repet] <- MASS::ginv(crossprod(X[Z_indice, ])) %*%
+ crossprod(X[Z_indice, ], Y[Z_indice, ])
+ }
+ sigmaInit1[, , r, repet] <- diag(m)
+ phiInit1[, , r, repet] <- betaInit1[, , r, repet] #/ sigmaInit1[,,r,repet]
+ rhoInit1[, , r, repet] <- solve(sigmaInit1[, , r, repet])
+ piInit1[repet, r] <- mean(Z == r)
+ }
+
+ for (i in 1:n)
+ {
+ for (r in 1:k)
+ {
+ dotProduct <- tcrossprod(Y[i, ] %*% rhoInit1[, , r, repet]
+ - X[i, ] %*% phiInit1[, , r, repet])
+ Gam[i, r] <- piInit1[repet, r] *
+ gdet(rhoInit1[, , r, repet]) * exp(-0.5 * dotProduct)
+ }
+ sumGamI <- sum(Gam[i, ])
+ gamInit1[i, , repet] <- Gam[i, ]/sumGamI
+ }
+
+ miniInit <- 10
+ maxiInit <- 11
+
+ init_EMG <- EMGLLF(phiInit1[, , , repet], rhoInit1[, , , repet], piInit1[repet, ],
+ gamInit1[, , repet], miniInit, maxiInit, gamma = 1, lambda = 0, X, Y,
+ eps = 1e-04, fast)
+ LLFinit1[[repet]] <- init_EMG$llh
+ }
+ b <- which.min(LLFinit1)
+ phiInit <- phiInit1[, , , b]
+ rhoInit <- rhoInit1[, , , b]
+ piInit <- piInit1[b, ]
+ gamInit <- gamInit1[, , b]
+
+ return(list(phiInit = phiInit, rhoInit = rhoInit, piInit = piInit, gamInit = gamInit))
+}
--- /dev/null
+#' valse
+#'
+#' Main function
+#'
+#' @param X matrix of covariates (of size n*p)
+#' @param Y matrix of responses (of size n*m)
+#' @param procedure among 'LassoMLE' or 'LassoRank'
+#' @param selecMod method to select a model among 'DDSE', 'DJump', 'BIC' or 'AIC'
+#' @param gamma integer for the power in the penaly, by default = 1
+#' @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 eps real, threshold to say the EM algorithm converges, by default = 1e-4
+#' @param kmin integer, minimum number of clusters, by default = 2
+#' @param kmax integer, maximum number of clusters, by default = 10
+#' @param rank.min integer, minimum rank in the low rank procedure, by default = 1
+#' @param rank.max integer, maximum rank in the low rank procedure, by default = 5
+#' @param ncores_outer Number of cores for the outer loop on k
+#' @param ncores_inner Number of cores for the inner loop on lambda
+#' @param thresh real, threshold to say a variable is relevant, by default = 1e-8
+#' @param compute_grid_lambda, TRUE to compute the grid, FALSE if known (in arguments)
+#' @param grid_lambda, a vector with regularization parameters if known, by default 0
+#' @param size_coll_mod (Maximum) size of a collection of models
+#' @param fast TRUE to use compiled C code, FALSE for R code only
+#' @param verbose TRUE to show some execution traces
+#'
+#' @return a list with estimators of parameters
+#'
+#' @examples
+#' #TODO: a few examples
+#' @export
+valse <- function(X, Y, procedure = "LassoMLE", selecMod = "DDSE", gamma = 1, mini = 10,
+ maxi = 50, eps = 1e-04, kmin = 2, kmax = 3, rank.min = 1, rank.max = 5, ncores_outer = 1,
+ ncores_inner = 1, thresh = 1e-08, compute_grid_lambda = TRUE, grid_lambda = 0, size_coll_mod = 10, fast = TRUE, verbose = FALSE,
+ plot = TRUE)
+{
+ n <- nrow(X)
+ p <- ncol(X)
+ m <- ncol(Y)
+
+ if (verbose)
+ print("main loop: over all k and all lambda")
+
+ if (ncores_outer > 1) {
+ cl <- parallel::makeCluster(ncores_outer, outfile = "")
+ parallel::clusterExport(cl = cl, envir = environment(), varlist = c("X",
+ "Y", "procedure", "selecMod", "gamma", "mini", "maxi", "eps", "kmin",
+ "kmax", "rank.min", "rank.max", "ncores_outer", "ncores_inner", "thresh",
+ "size_coll_mod", "verbose", "p", "m"))
+ }
+
+ # Compute models with k components
+ computeModels <- function(k)
+ {
+ if (ncores_outer > 1)
+ require("valse") #nodes start with an empty environment
+
+ if (verbose)
+ print(paste("Parameters initialization for k =", k))
+ # smallEM initializes parameters by k-means and regression model in each
+ # component, doing this 20 times, and keeping the values maximizing the
+ # likelihood after 10 iterations of the EM algorithm.
+ P <- initSmallEM(k, X, Y, fast)
+ if (compute_grid_lambda == TRUE)
+ {
+ grid_lambda <- computeGridLambda(P$phiInit, P$rhoInit, P$piInit, P$gamInit,
+ X, Y, gamma, mini, maxi, eps, fast)
+ }
+ if (length(grid_lambda) > size_coll_mod)
+ grid_lambda <- grid_lambda[seq(1, length(grid_lambda), length.out = size_coll_mod)]
+
+ if (verbose)
+ print("Compute relevant parameters")
+ # select variables according to each regularization parameter from the grid:
+ # S$selected corresponding to selected variables
+ S <- selectVariables(P$phiInit, P$rhoInit, P$piInit, P$gamInit, mini, maxi,
+ gamma, grid_lambda, X, Y, thresh, eps, ncores_inner, fast)
+
+ if (procedure == "LassoMLE") {
+ if (verbose)
+ print("run the procedure Lasso-MLE")
+ # compute parameter estimations, with the Maximum Likelihood Estimator,
+ # restricted on selected variables.
+ models <- constructionModelesLassoMLE(P$phiInit, P$rhoInit, P$piInit,
+ P$gamInit, mini, maxi, gamma, X, Y, eps, S, ncores_inner, fast, verbose)
+ } else {
+ if (verbose)
+ print("run the procedure Lasso-Rank")
+ # compute parameter estimations, with the Low Rank Estimator, restricted on
+ # selected variables.
+ models <- constructionModelesLassoRank(S, k, mini, maxi, X, Y, eps, rank.min,
+ rank.max, ncores_inner, fast, verbose)
+ }
+ # warning! Some models are NULL after running selectVariables
+ models <- models[sapply(models, function(cell) !is.null(cell))]
+ models
+ }
+
+ # List (index k) of lists (index lambda) of models
+ models_list <-
+ if (ncores_outer > 1) {
+ parLapply(cl, kmin:kmax, computeModels)
+ } else {
+ lapply(kmin:kmax, computeModels)
+ }
+ if (ncores_outer > 1)
+ parallel::stopCluster(cl)
+
+ if (!requireNamespace("capushe", quietly = TRUE))
+ {
+ warning("'capushe' not available: returning all models")
+ return(models_list)
+ }
+
+ # Get summary 'tableauRecap' from models
+ tableauRecap <- do.call(rbind, lapply(seq_along(models_list), function(i)
+ {
+ models <- models_list[[i]]
+ # For a collection of models (same k, several lambda):
+ LLH <- sapply(models, function(model) model$llh[1])
+ k <- length(models[[1]]$pi)
+ sumPen <- sapply(models, function(model) k * (dim(model$rho)[1] + sum(model$phi[,
+ , 1] != 0) + 1) - 1)
+ data.frame(model = paste(i, ".", seq_along(models), sep = ""), pen = sumPen/n,
+ complexity = sumPen, contrast = -LLH)
+ }))
+ tableauRecap <- tableauRecap[which(tableauRecap[, 4] != Inf), ]
+ if (verbose == TRUE)
+ {
+ print(tableauRecap)
+ }
+ modSel <- capushe::capushe(tableauRecap, n)
+ indModSel <- if (selecMod == "DDSE")
+ as.numeric(modSel@DDSE@model) else if (selecMod == "Djump")
+ as.numeric(modSel@Djump@model) else if (selecMod == "BIC")
+ modSel@BIC_capushe$model else if (selecMod == "AIC")
+ modSel@AIC_capushe$model
+
+ mod <- as.character(tableauRecap[indModSel, 1])
+ listMod <- as.integer(unlist(strsplit(mod, "[.]")))
+ modelSel <- models_list[[listMod[1]]][[listMod[2]]]
+
+ ## Affectations
+ Gam <- matrix(0, ncol = length(modelSel$pi), nrow = n)
+ for (i in 1:n)
+ {
+ for (r in 1:length(modelSel$pi))
+ {
+ sqNorm2 <- sum((Y[i, ] %*% modelSel$rho[, , r] - X[i, ] %*% modelSel$phi[, , r])^2)
+ Gam[i, r] <- modelSel$pi[r] * exp(-0.5 * sqNorm2) * gdet(modelSel$rho[, , r])
+ }
+ }
+ Gam <- Gam/rowSums(Gam)
+ modelSel$affec <- apply(Gam, 1, which.max)
+ modelSel$proba <- Gam
+ modelSel$tableau <- tableauRecap
+
+ if (plot)
+ print(plot_valse(X, Y, modelSel, n))
+
+ return(modelSel)
+}
--- /dev/null
+#' Plot
+#'
+#' It is a function which plots relevant parameters
+#'
+#' @param X matrix of covariates (of size n*p)
+#' @param Y matrix of responses (of size n*m)
+#' @param model the model constructed by valse procedure
+#' @param n sample size
+#' @return several plots
+#'
+#' @examples TODO
+#'
+#' @export
+#'
+plot_valse <- function(X, Y, model, n, comp = FALSE, k1 = NA, k2 = NA)
+{
+ require("gridExtra")
+ require("ggplot2")
+ require("reshape2")
+ require("cowplot")
+
+ K <- length(model$pi)
+ ## regression matrices
+ gReg <- list()
+ for (r in 1:K)
+ {
+ Melt <- melt(t((model$phi[, , r])))
+ gReg[[r]] <- ggplot(data = Melt, aes(x = Var1, y = Var2, fill = value)) +
+ geom_tile() + scale_fill_gradient2(low = "blue", high = "red", mid = "white",
+ midpoint = 0, space = "Lab") + ggtitle(paste("Regression matrices in cluster", r))
+ }
+ print(gReg)
+
+ ## Differences between two clusters
+ if (comp)
+ {
+ if (is.na(k1) || is.na(k))
+ print("k1 and k2 must be integers, representing the clusters you want to compare")
+ Melt <- melt(t(model$phi[, , k1] - model$phi[, , k2]))
+ gDiff <- ggplot(data = Melt, aes(x = Var1, y = Var2, fill = value))
+ + geom_tile()
+ + scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0,
+ space = "Lab")
+ + ggtitle(paste("Difference between regression matrices in cluster",
+ k1, "and", k2))
+ print(gDiff)
+ }
+
+ ### Covariance matrices
+ matCov <- matrix(NA, nrow = dim(model$rho[, , 1])[1], ncol = K)
+ for (r in 1:K)
+ matCov[, r] <- diag(model$rho[, , r])
+ MeltCov <- melt(matCov)
+ gCov <- ggplot(data = MeltCov, aes(x = Var1, y = Var2, fill = value)) + geom_tile()
+ + scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0,
+ space = "Lab")
+ + ggtitle("Covariance matrices")
+ print(gCov)
+
+ ### Proportions
+ gam2 <- matrix(NA, ncol = K, nrow = n)
+ for (i in 1:n)
+ gam2[i, ] <- c(model$proba[i, model$affec[i]], model$affec[i])
+
+ bp <- ggplot(data.frame(gam2), aes(x = X2, y = X1, color = X2, group = X2))
+ + geom_boxplot()
+ + theme(legend.position = "none")
+ + background_grid(major = "xy", minor = "none")
+ print(bp)
+
+ ### Mean in each cluster
+ XY <- cbind(X, Y)
+ XY_class <- list()
+ meanPerClass <- matrix(0, ncol = K, nrow = dim(XY)[2])
+ for (r in 1:K)
+ {
+ XY_class[[r]] <- XY[model$affec == r, ]
+ if (sum(model$affec == r) == 1) {
+ meanPerClass[, r] <- XY_class[[r]]
+ } else {
+ meanPerClass[, r] <- apply(XY_class[[r]], 2, mean)
+ }
+ }
+ data <- data.frame(mean = as.vector(meanPerClass),
+ cluster = as.character(rep(1:K, each = dim(XY)[2])), time = rep(1:dim(XY)[2], K))
+ g <- ggplot(data, aes(x = time, y = mean, group = cluster, color = cluster))
+ print(g + geom_line(aes(linetype = cluster, color = cluster))
+ + geom_point(aes(color = cluster)) + ggtitle("Mean per cluster"))
+}
--- /dev/null
+#' selectVariables
+#'
+#' It is a function which construct, for a given lambda, the sets of relevant variables.
+#'
+#' @param phiInit an initial estimator for phi (size: p*m*k)
+#' @param rhoInit an initial estimator for rho (size: m*m*k)
+#' @param piInit an initial estimator for pi (size : k)
+#' @param gamInit an initial estimator for gamma
+#' @param mini minimum number of iterations in EM algorithm
+#' @param maxi maximum number of iterations in EM algorithm
+#' @param gamma power in the penalty
+#' @param glambda grid of regularization parameters
+#' @param X matrix of regressors
+#' @param Y matrix of responses
+#' @param thresh real, threshold to say a variable is relevant, by default = 1e-8
+#' @param eps threshold to say that EM algorithm has converged
+#' @param ncores Number or cores for parallel execution (1 to disable)
+#'
+#' @return a list of outputs, for each lambda in grid: selected,Rho,Pi
+#'
+#' @examples TODO
+#'
+#' @export
+#'
+selectVariables <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma,
+ glambda, X, Y, thresh = 1e-08, eps, ncores = 3, fast)
+{
+ if (ncores > 1) {
+ cl <- parallel::makeCluster(ncores, outfile = "")
+ parallel::clusterExport(cl = cl, varlist = c("phiInit", "rhoInit", "gamInit",
+ "mini", "maxi", "glambda", "X", "Y", "thresh", "eps"), envir = environment())
+ }
+
+ # Computation for a fixed lambda
+ computeCoefs <- function(lambda)
+ {
+ params <- EMGLLF(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
+ X, Y, eps, fast)
+
+ p <- ncol(X)
+ m <- ncol(Y)
+
+ # selectedVariables: list where element j contains vector of selected variables
+ # in [1,m]
+ selectedVariables <- lapply(1:p, function(j) {
+ # from boolean matrix mxk of selected variables obtain the corresponding boolean
+ # m-vector, and finally return the corresponding indices
+ if (m>1) {
+ seq_len(m)[apply(abs(params$phi[j, , ]) > thresh, 1, any)]
+ } else {
+ if (any(params$phi[j, , ] > thresh))
+ 1
+ else
+ numeric(0)
+ }
+ })
+
+ list(selected = selectedVariables, Rho = params$rho, Pi = params$pi)
+ }
+
+ # For each lambda in the grid, we compute the coefficients
+ out <-
+ if (ncores > 1) {
+ parLapply(cl, glambda, computeCoefs)
+ } else {
+ lapply(glambda, computeCoefs)
+ }
+ if (ncores > 1)
+ parallel::stopCluster(cl)
+ # Suppress models which are computed twice En fait, ca ca fait la comparaison de
+ # tous les parametres On veut juste supprimer ceux qui ont les memes variables
+ # sélectionnées
+ # sha1_array <- lapply(out, digest::sha1) out[ duplicated(sha1_array) ]
+ selec <- lapply(out, function(model) model$selected)
+ ind_dup <- duplicated(selec)
+ ind_uniq <- which(!ind_dup)
+ out2 <- list()
+ for (l in 1:length(ind_uniq))
+ out2[[l]] <- out[[ind_uniq[l]]]
+ out2
+}
--- /dev/null
+# ...
+gdet <- function(M)
+{
+ if (is.matrix(M))
+ return (det(M))
+ return (M[1]) #numeric, double
+}
--- /dev/null
+m=11
+p=10
+
+covY = array(0,dim = c(m,m,2))
+covY[,,1] = diag(m)
+covY[,,2] = diag(m)
+
+Beta = array(0, dim = c(p, m, 2))
+Beta[1:4,1:4,1] = 3*diag(4)
+Beta[1:4,1:4,2] = -2*diag(4)
+
+Data = generateXY(100, c(0.5,0.5), rep(0,p), Beta, diag(p), covY)
+
+Res = valse(Data$X,Data$Y, fast=FALSE, plot=FALSE, verbose = TRUE, kmax=2, compute_grid_lambda = FALSE,
+ grid_lambda = seq(0.2,2,length = 50), size_coll_mod = 50)
--- /dev/null
+ou alors data_test.RData, possible aussi
--- /dev/null
+\name{valse-package}
+\alias{valse-package}
+\alias{valse}
+\docType{package}
+
+\title{
+ \packageTitle{valse}
+}
+
+\description{
+ \packageDescription{valse}
+}
+
+\details{
+ The package devtools should be useful in development stage, since we rely on testthat for
+ unit tests, and roxygen2 for documentation. knitr is used to generate the package vignette.
+ Concerning the other suggested packages:
+ \itemize{
+ \item{parallel (generally) permits to run the bootstrap method faster.}
+ }
+
+ The three main functions are ...
+}
+
+\author{
+ \packageAuthor{valse}
+
+ Maintainer: \packageMaintainer{valse}
+}
+
+%\references{
+% TODO: Literature or other references for background information
+%}
+
+%\examples{
+% TODO: simple examples of the most important functions
+%}
--- /dev/null
+#Debug flags
+PKG_CFLAGS=-g -I./sources
+
+#Prod flags:
+#PKG_CFLAGS=-O2 -I./sources
+
+PKG_LIBS=-lm -lgsl -lcblas
+
+SOURCES = $(wildcard adapters/*.c sources/*.c)
+
+OBJECTS = $(SOURCES:.c=.o)
--- /dev/null
+#include <R.h>
+#include <Rdefines.h>
+#include "EMGLLF.h"
+
+// See comments in src/sources/EMGLLF.c and R/EMGLLF.R (wrapper)
+SEXP EMGLLF(
+ SEXP phiInit_,
+ SEXP rhoInit_,
+ SEXP piInit_,
+ SEXP gamInit_,
+ SEXP mini_,
+ SEXP maxi_,
+ SEXP gamma_,
+ SEXP lambda_,
+ SEXP X_,
+ SEXP Y_,
+ SEXP tau_
+) {
+ // Get matrices dimensions
+ int n = INTEGER(getAttrib(X_, R_DimSymbol))[0];
+ SEXP dim = getAttrib(phiInit_, R_DimSymbol);
+ int p = INTEGER(dim)[0];
+ int m = INTEGER(dim)[1];
+ int k = INTEGER(dim)[2];
+
+ ////////////
+ // INPUTS //
+ ////////////
+
+ // get scalar parameters
+ int mini = INTEGER_VALUE(mini_);
+ int maxi = INTEGER_VALUE(maxi_);
+ double gamma = NUMERIC_VALUE(gamma_);
+ double lambda = NUMERIC_VALUE(lambda_);
+ double tau = NUMERIC_VALUE(tau_);
+
+ // Get pointers from SEXP arrays ; WARNING: by columns !
+ double* phiInit = REAL(phiInit_);
+ double* rhoInit = REAL(rhoInit_);
+ double* piInit = REAL(piInit_);
+ double* gamInit = REAL(gamInit_);
+ double* X = REAL(X_);
+ double* Y = REAL(Y_);
+
+ /////////////
+ // OUTPUTS //
+ /////////////
+
+ SEXP phi, rho, pi, LLF, S, affec, dimPhiS, dimRho;
+ PROTECT(dimPhiS = allocVector(INTSXP, 3));
+ int* pDimPhiS = INTEGER(dimPhiS);
+ pDimPhiS[0] = p; pDimPhiS[1] = m; pDimPhiS[2] = k;
+ PROTECT(dimRho = allocVector(INTSXP, 3));
+ int* pDimRho = INTEGER(dimRho);
+ pDimRho[0] = m; pDimRho[1] = m; pDimRho[2] = k;
+ PROTECT(phi = allocArray(REALSXP, dimPhiS));
+ PROTECT(rho = allocArray(REALSXP, dimRho));
+ PROTECT(pi = allocVector(REALSXP, k));
+ PROTECT(LLF = allocVector(REALSXP, maxi-mini+1));
+ PROTECT(S = allocArray(REALSXP, dimPhiS));
+ PROTECT(affec = allocVector(INTSXP, n));
+ double *pPhi=REAL(phi), *pRho=REAL(rho), *pPi=REAL(pi), *pLLF=REAL(LLF), *pS=REAL(S);
+ int *pAffec=INTEGER(affec);
+
+ ////////////////////
+ // Call to EMGLLF //
+ ////////////////////
+
+ EMGLLF_core(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau,
+ pPhi,pRho,pPi,pLLF,pS,pAffec,
+ n,p,m,k);
+
+ // Build list from OUT params and return it
+ SEXP listParams, listNames;
+ int nouts = 6;
+ PROTECT(listParams = allocVector(VECSXP, nouts));
+ char* lnames[6] = {"phi", "rho", "pi", "LLF", "S", "affec"}; //lists labels
+ PROTECT(listNames = allocVector(STRSXP,nouts));
+ for (int i=0; i<nouts; i++)
+ SET_STRING_ELT(listNames,i,mkChar(lnames[i]));
+ setAttrib(listParams, R_NamesSymbol, listNames);
+ SET_VECTOR_ELT(listParams, 0, phi);
+ SET_VECTOR_ELT(listParams, 1, rho);
+ SET_VECTOR_ELT(listParams, 2, pi);
+ SET_VECTOR_ELT(listParams, 3, LLF);
+ SET_VECTOR_ELT(listParams, 4, S);
+ SET_VECTOR_ELT(listParams, 5, affec);
+
+ UNPROTECT(10);
+ return listParams;
+}
--- /dev/null
+#include <R.h>
+#include <Rdefines.h>
+#include "EMGrank.h"
+
+// See comments in src/sources/EMGrank.c and R/EMGrank.R (wrapper)
+SEXP EMGrank(
+ SEXP Pi_,
+ SEXP Rho_,
+ SEXP mini_,
+ SEXP maxi_,
+ SEXP X_,
+ SEXP Y_,
+ SEXP tau_,
+ SEXP rank_
+) {
+ // Get matrices dimensions
+ SEXP dimX = getAttrib(X_, R_DimSymbol);
+ int n = INTEGER(dimX)[0];
+ int p = INTEGER(dimX)[1];
+ SEXP dimRho = getAttrib(Rho_, R_DimSymbol);
+ int m = INTEGER(dimRho)[0];
+ int k = INTEGER(dimRho)[2];
+
+ ////////////
+ // INPUTS //
+ ////////////
+
+ // get scalar parameters
+ int mini = INTEGER_VALUE(mini_);
+ int maxi = INTEGER_VALUE(maxi_);
+ double tau = NUMERIC_VALUE(tau_);
+
+ // Get pointers from SEXP arrays ; WARNING: by columns !
+ double* Pi = REAL(Pi_);
+ double* Rho = REAL(Rho_);
+ double* X = REAL(X_);
+ double* Y = REAL(Y_);
+ int* rank = INTEGER(rank_);
+
+ /////////////
+ // OUTPUTS //
+ /////////////
+
+ SEXP phi, LLF, dimPhi;
+ PROTECT(dimPhi = allocVector(INTSXP, 3));
+ int* pDimPhi = INTEGER(dimPhi);
+ pDimPhi[0] = p; pDimPhi[1] = m; pDimPhi[2] = k;
+ PROTECT(phi = allocArray(REALSXP, dimPhi));
+ PROTECT(LLF = allocVector(REALSXP, 1));
+ double *pPhi=REAL(phi), *pLLF=REAL(LLF);
+
+ /////////////////////
+ // Call to EMGrank //
+ /////////////////////
+
+ EMGrank_core(Pi, Rho, mini, maxi, X, Y, tau, rank,
+ pPhi,pLLF,
+ n,p,m,k);
+
+ // Build list from OUT params and return it
+ SEXP listParams, listNames;
+ PROTECT(listParams = allocVector(VECSXP, 2));
+ char* lnames[2] = {"phi", "LLF"}; //lists labels
+ PROTECT(listNames = allocVector(STRSXP,2));
+ for (int i=0; i<2; i++)
+ SET_STRING_ELT(listNames,i,mkChar(lnames[i]));
+ setAttrib(listParams, R_NamesSymbol, listNames);
+ SET_VECTOR_ELT(listParams, 0, phi);
+ SET_VECTOR_ELT(listParams, 1, LLF);
+
+ UNPROTECT(5);
+ return listParams;
+}
--- /dev/null
+#include "utils.h"
+#include <stdlib.h>
+#include <math.h>
+#include <gsl/gsl_linalg.h>
+
+// TODO: don't recompute indexes ai(...) and mi(...) when possible
+void EMGLLF_core(
+ // IN parameters
+ const Real* phiInit, // parametre initial de moyenne renormalisé
+ const Real* rhoInit, // parametre initial de variance renormalisé
+ const Real* piInit, // parametre initial des proportions
+ const Real* gamInit, // paramètre initial des probabilités a posteriori de chaque échantillon
+ int mini, // nombre minimal d'itérations dans l'algorithme EM
+ int maxi, // nombre maximal d'itérations dans l'algorithme EM
+ Real gamma, // puissance des proportions dans la pénalisation pour un Lasso adaptatif
+ Real lambda, // valeur du paramètre de régularisation du Lasso
+ const Real* X, // régresseurs
+ const Real* Y, // réponse
+ Real tau, // seuil pour accepter la convergence
+ // OUT parameters (all pointers, to be modified)
+ Real* phi, // parametre de moyenne renormalisé, calculé par l'EM
+ Real* rho, // parametre de variance renormalisé, calculé par l'EM
+ Real* pi, // parametre des proportions renormalisé, calculé par l'EM
+ Real* llh, // (derniere) log vraisemblance associée à cet échantillon,
+ // pour les valeurs estimées des paramètres
+ Real* S,
+ int* affec,
+ // additional size parameters
+ int n, // nombre d'echantillons
+ int p, // nombre de covariables
+ int m, // taille de Y (multivarié)
+ int k) // nombre de composantes dans le mélange
+{
+ //Initialize outputs
+ copyArray(phiInit, phi, p*m*k);
+ copyArray(rhoInit, rho, m*m*k);
+ copyArray(piInit, pi, k);
+ //S is already allocated, and doesn't need to be 'zeroed'
+
+ //Other local variables: same as in R
+ Real* gam = (Real*)malloc(n*k*sizeof(Real));
+ copyArray(gamInit, gam, n*k);
+ Real* Gram2 = (Real*)malloc(p*p*k*sizeof(Real));
+ Real* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
+ Real* b = (Real*)malloc(k*sizeof(Real));
+ Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
+ Real* Y2 = (Real*)malloc(n*m*k*sizeof(Real));
+ *llh = -INFINITY;
+ Real* pi2 = (Real*)malloc(k*sizeof(Real));
+ const Real EPS = 1e-15;
+ // Additional (not at this place, in R file)
+ Real* gam2 = (Real*)malloc(k*sizeof(Real));
+ Real* sqNorm2 = (Real*)malloc(k*sizeof(Real));
+ Real* detRho = (Real*)malloc(k*sizeof(Real));
+ gsl_matrix* matrix = gsl_matrix_alloc(m, m);
+ gsl_permutation* permutation = gsl_permutation_alloc(m);
+ Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
+ Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
+ const Real gaussConstM = pow(2.*M_PI,m/2.);
+ 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));
+
+ for (int ite=1; ite<=maxi; ite++)
+ {
+ copyArray(phi, Phi, p*m*k);
+ copyArray(rho, Rho, m*m*k);
+ copyArray(pi, Pi, k);
+
+ // Calculs associés a Y et X
+ for (int r=0; r<k; r++)
+ {
+ for (int mm=0; mm<m; mm++)
+ {
+ //Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
+ for (int u=0; u<n; u++)
+ Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,n,m)];
+ }
+ for (int i=0; i<n; i++)
+ {
+ //X2[i,,r] = sqrt(gam[i,r]) * X[i,]
+ for (int u=0; u<p; u++)
+ X2[ai(i,u,r,n,p,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
+ }
+ for (int mm=0; mm<m; mm++)
+ {
+ //ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
+ for (int u=0; u<p; u++)
+ {
+ Real dotProduct = 0.;
+ for (int v=0; v<n; v++)
+ dotProduct += X2[ai(v,u,r,n,p,k)] * Y2[ai(v,mm,r,n,m,k)];
+ ps2[ai(u,mm,r,p,m,k)] = dotProduct;
+ }
+ }
+ for (int j=0; j<p; j++)
+ {
+ for (int s=0; s<p; s++)
+ {
+ //Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
+ Real dotProduct = 0.;
+ for (int u=0; u<n; u++)
+ dotProduct += X2[ai(u,j,r,n,p,k)] * X2[ai(u,s,r,n,p,k)];
+ Gram2[ai(j,s,r,p,p,k)] = dotProduct;
+ }
+ }
+ }
+
+ /////////////
+ // Etape M //
+ /////////////
+
+ // Pour pi
+ for (int r=0; r<k; r++)
+ {
+ //b[r] = sum(abs(phi[,,r]))
+ Real sumAbsPhi = 0.;
+ for (int u=0; u<p; u++)
+ for (int v=0; v<m; v++)
+ sumAbsPhi += fabs(phi[ai(u,v,r,p,m,k)]);
+ b[r] = sumAbsPhi;
+ }
+ //gam2 = colSums(gam)
+ for (int u=0; u<k; u++)
+ {
+ Real sumOnColumn = 0.;
+ for (int v=0; v<n; v++)
+ sumOnColumn += gam[mi(v,u,n,k)];
+ gam2[u] = sumOnColumn;
+ }
+ //a = sum(gam %*% log(pi))
+ Real a = 0.;
+ for (int u=0; u<n; u++)
+ {
+ Real dotProduct = 0.;
+ for (int v=0; v<k; v++)
+ dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
+ a += dotProduct;
+ }
+
+ //tant que les proportions sont negatives
+ int kk = 0,
+ pi2AllPositive = 0;
+ Real invN = 1./n;
+ while (!pi2AllPositive)
+ {
+ //pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
+ Real pow_01_kk = pow(0.1,kk);
+ for (int r=0; r<k; r++)
+ pi2[r] = pi[r] + pow_01_kk * (invN*gam2[r] - pi[r]);
+ //pi2AllPositive = all(pi2 >= 0)
+ pi2AllPositive = 1;
+ for (int r=0; r<k; r++)
+ {
+ if (pi2[r] < 0)
+ {
+ pi2AllPositive = 0;
+ break;
+ }
+ }
+ kk++;
+ }
+
+ //sum(pi^gamma * b)
+ Real piPowGammaDotB = 0.;
+ for (int v=0; v<k; v++)
+ piPowGammaDotB += pow(pi[v],gamma) * b[v];
+ //sum(pi2^gamma * b)
+ Real pi2PowGammaDotB = 0.;
+ for (int v=0; v<k; v++)
+ pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
+ //sum(gam2 * log(pi2))
+ Real gam2DotLogPi2 = 0.;
+ for (int v=0; v<k; v++)
+ gam2DotLogPi2 += gam2[v] * log(pi2[v]);
+
+ //t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
+ while (-invN*a + lambda*piPowGammaDotB < -invN*gam2DotLogPi2 + lambda*pi2PowGammaDotB
+ && kk<1000)
+ {
+ Real pow_01_kk = pow(0.1,kk);
+ //pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
+ for (int v=0; v<k; v++)
+ pi2[v] = pi[v] + pow_01_kk * (invN*gam2[v] - pi[v]);
+ //pi2 was updated, so we recompute pi2PowGammaDotB and gam2DotLogPi2
+ pi2PowGammaDotB = 0.;
+ for (int v=0; v<k; v++)
+ pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
+ gam2DotLogPi2 = 0.;
+ for (int v=0; v<k; v++)
+ gam2DotLogPi2 += gam2[v] * log(pi2[v]);
+ kk++;
+ }
+ Real t = pow(0.1,kk);
+ //sum(pi + t*(pi2-pi))
+ Real sumPiPlusTbyDiff = 0.;
+ for (int v=0; v<k; v++)
+ sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
+ //pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
+ for (int v=0; v<k; v++)
+ pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
+
+ //Pour phi et rho
+ for (int r=0; r<k; r++)
+ {
+ for (int mm=0; mm<m; mm++)
+ {
+ Real ps = 0.,
+ nY2 = 0.;
+ // Compute ps, and nY2 = sum(Y2[,mm,r]^2)
+ for (int i=0; i<n; i++)
+ {
+ //< X2[i,,r] , phi[,mm,r] >
+ Real dotProduct = 0.;
+ for (int u=0; u<p; u++)
+ dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,p,m,k)];
+ //ps = ps + Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
+ ps += Y2[ai(i,mm,r,n,m,k)] * dotProduct;
+ nY2 += Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
+ }
+ //rho[mm,mm,r] = (ps+sqrt(ps^2+4*nY2*gam2[r])) / (2*nY2)
+ rho[ai(mm,mm,r,m,m,k)] = (ps + sqrt(ps*ps + 4*nY2 * gam2[r])) / (2*nY2);
+ }
+ }
+
+ for (int r=0; r<k; r++)
+ {
+ for (int j=0; j<p; j++)
+ {
+ for (int mm=0; mm<m; mm++)
+ {
+ //sum(phi[-j,mm,r] * Gram2[j,-j,r])
+ Real phiDotGram2 = 0.;
+ for (int u=0; u<p; u++)
+ {
+ if (u != j)
+ phiDotGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
+ }
+ //S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + sum(phi[-j,mm,r] * Gram2[j,-j,r])
+ S[ai(j,mm,r,p,m,k)] = -rho[ai(mm,mm,r,m,m,k)] * ps2[ai(j,mm,r,p,m,k)]
+ + phiDotGram2;
+ Real pirPowGamma = pow(pi[r],gamma);
+ if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pirPowGamma)
+ phi[ai(j,mm,r,p,m,k)] = 0.;
+ else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pirPowGamma)
+ {
+ phi[ai(j,mm,r,p,m,k)] = (n*lambda*pirPowGamma - S[ai(j,mm,r,p,m,k)])
+ / Gram2[ai(j,j,r,p,p,k)];
+ }
+ else
+ {
+ phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pirPowGamma + S[ai(j,mm,r,p,m,k)])
+ / Gram2[ai(j,j,r,p,p,k)];
+ }
+ }
+ }
+ }
+
+ /////////////
+ // Etape E //
+ /////////////
+
+ // Precompute det(rho[,,r]) for r in 1...k
+ int signum;
+ for (int r=0; r<k; r++)
+ {
+ for (int u=0; u<m; u++)
+ {
+ for (int v=0; v<m; v++)
+ matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
+ }
+ gsl_linalg_LU_decomp(matrix, permutation, &signum);
+ detRho[r] = gsl_linalg_LU_det(matrix, signum);
+ }
+
+ Real sumLogLLH = 0.;
+ for (int i=0; i<n; i++)
+ {
+ for (int r=0; r<k; r++)
+ {
+ //compute Y[i,]%*%rho[,,r]
+ for (int u=0; u<m; u++)
+ {
+ YiRhoR[u] = 0.;
+ for (int v=0; v<m; v++)
+ YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
+ }
+
+ //compute X[i,]%*%phi[,,r]
+ for (int u=0; u<m; u++)
+ {
+ XiPhiR[u] = 0.;
+ for (int v=0; v<p; v++)
+ XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
+ }
+
+ //compute sq norm || Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) ||_2^2
+ sqNorm2[r] = 0.;
+ for (int u=0; u<m; u++)
+ sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
+ }
+
+ Real sumGamI = 0.;
+ for (int r=0; r<k; r++)
+ {
+ gam[mi(i,r,n,k)] = pi[r] * exp(-.5*sqNorm2[r]) * detRho[r];
+ sumGamI += gam[mi(i,r,n,k)];
+ }
+
+ sumLogLLH += log(sumGamI) - log(gaussConstM);
+ if (sumGamI > EPS) //else: gam[i,] is already ~=0
+ {
+ for (int r=0; r<k; r++)
+ gam[mi(i,r,n,k)] /= sumGamI;
+ }
+ }
+
+ //sumPen = sum(pi^gamma * b)
+ Real sumPen = 0.;
+ for (int r=0; r<k; r++)
+ sumPen += pow(pi[r],gamma) * b[r];
+ Real last_llh = *llh;
+ //llh = -sumLogLLH/n + lambda*sumPen
+ *llh = -invN * sumLogLLH + lambda * sumPen;
+ Real dist = ite==1 ? *llh : (*llh - last_llh) / (1. + fabs(*llh));
+
+ //Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
+ Real Dist1 = 0.;
+ for (int u=0; u<p; u++)
+ {
+ for (int v=0; v<m; v++)
+ {
+ for (int w=0; w<k; w++)
+ {
+ Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
+ / (1.+fabs(phi[ai(u,v,w,p,m,k)]));
+ if (tmpDist > Dist1)
+ Dist1 = tmpDist;
+ }
+ }
+ }
+ //Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
+ Real Dist2 = 0.;
+ for (int u=0; u<m; u++)
+ {
+ for (int v=0; v<m; v++)
+ {
+ for (int w=0; w<k; w++)
+ {
+ Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
+ / (1.+fabs(rho[ai(u,v,w,m,m,k)]));
+ if (tmpDist > Dist2)
+ Dist2 = tmpDist;
+ }
+ }
+ }
+ //Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)))
+ Real Dist3 = 0.;
+ for (int u=0; u<n; u++)
+ {
+ for (int v=0; v<k; v++)
+ {
+ Real tmpDist = fabs(pi[v]-Pi[v]) / (1.+fabs(pi[v]));
+ if (tmpDist > Dist3)
+ Dist3 = tmpDist;
+ }
+ }
+ //dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
+ Real dist2 = Dist1;
+ if (Dist2 > dist2)
+ dist2 = Dist2;
+ if (Dist3 > dist2)
+ dist2 = Dist3;
+
+ if (ite >= mini && (dist >= tau || dist2 >= sqrt(tau)))
+ break;
+ }
+
+ //affec = apply(gam, 1, which.max)
+ for (int i=0; i<n; i++)
+ {
+ Real rowMax = 0.;
+ affec[i] = 0;
+ for (int j=0; j<k; j++)
+ {
+ if (gam[mi(i,j,n,k)] > rowMax)
+ {
+ affec[i] = j+1; //R indices start at 1
+ rowMax = gam[mi(i,j,n,k)];
+ }
+ }
+ }
+
+ //free memory
+ free(b);
+ free(gam);
+ free(Phi);
+ free(Rho);
+ free(Pi);
+ free(Gram2);
+ free(ps2);
+ free(detRho);
+ gsl_matrix_free(matrix);
+ gsl_permutation_free(permutation);
+ free(XiPhiR);
+ free(YiRhoR);
+ free(gam2);
+ free(pi2);
+ free(X2);
+ free(Y2);
+ free(sqNorm2);
+}
--- /dev/null
+#ifndef valse_EMGLLF_H
+#define valse_EMGLLF_H
+
+#include "utils.h"
+
+void EMGLLF_core(
+ // IN parameters
+ const Real* phiInit,
+ const Real* rhoInit,
+ const Real* piInit,
+ const Real* gamInit,
+ int mini,
+ int maxi,
+ Real gamma,
+ Real lambda,
+ const Real* X,
+ const Real* Y,
+ Real tau,
+ // OUT parameters
+ Real* phi,
+ Real* rho,
+ Real* pi,
+ Real* LLF,
+ Real* S,
+ int* affec,
+ // additional size parameters
+ int n,
+ int p,
+ int m,
+ int k);
+
+#endif
--- /dev/null
+#include <stdlib.h>
+#include <gsl/gsl_linalg.h>
+#include "utils.h"
+
+// Compute pseudo-inverse of a square matrix
+static Real* pinv(const Real* matrix, int dim)
+{
+ gsl_matrix* U = gsl_matrix_alloc(dim,dim);
+ gsl_matrix* V = gsl_matrix_alloc(dim,dim);
+ gsl_vector* S = gsl_vector_alloc(dim);
+ gsl_vector* work = gsl_vector_alloc(dim);
+ Real EPS = 1e-10; //threshold for singular value "== 0"
+
+ //copy matrix into U
+ copyArray(matrix, U->data, dim*dim);
+
+ //U,S,V = SVD of matrix
+ gsl_linalg_SV_decomp(U, V, S, work);
+ gsl_vector_free(work);
+
+ // Obtain pseudo-inverse by V*S^{-1}*t(U)
+ Real* inverse = (Real*)malloc(dim*dim*sizeof(Real));
+ for (int i=0; i<dim; i++)
+ {
+ for (int ii=0; ii<dim; ii++)
+ {
+ Real dotProduct = 0.0;
+ for (int j=0; j<dim; j++)
+ dotProduct += V->data[i*dim+j] * (S->data[j] > EPS ? 1.0/S->data[j] : 0.0) * U->data[ii*dim+j];
+ inverse[i*dim+ii] = dotProduct;
+ }
+ }
+
+ gsl_matrix_free(U);
+ gsl_matrix_free(V);
+ gsl_vector_free(S);
+ return inverse;
+}
+
+// TODO: comment EMGrank purpose
+void EMGrank_core(
+ // IN parameters
+ const Real* Pi, // parametre de proportion
+ const Real* Rho, // parametre initial de variance renormalisé
+ int mini, // nombre minimal d'itérations dans l'algorithme EM
+ int maxi, // nombre maximal d'itérations dans l'algorithme EM
+ const Real* X, // régresseurs
+ const Real* Y, // réponse
+ Real tau, // seuil pour accepter la convergence
+ const int* rank, // vecteur des rangs possibles
+ // OUT parameters
+ Real* phi, // parametre de moyenne renormalisé, calculé par l'EM
+ Real* LLF, // log vraisemblance associé à cet échantillon, pour les valeurs estimées des paramètres
+ // additional size parameters
+ int n, // taille de l'echantillon
+ int p, // nombre de covariables
+ int m, // taille de Y (multivarié)
+ int k) // nombre de composantes
+{
+ // Allocations, initializations
+ Real* Phi = (Real*)calloc(p*m*k,sizeof(Real));
+ Real* hatBetaR = (Real*)malloc(p*m*sizeof(Real));
+ int signum;
+ Real invN = 1.0/n;
+ int deltaPhiBufferSize = 20;
+ Real* deltaPhi = (Real*)malloc(deltaPhiBufferSize*sizeof(Real));
+ int ite = 0;
+ Real sumDeltaPhi = 0.0;
+ Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
+ Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
+ Real* Xr = (Real*)malloc(n*p*sizeof(Real));
+ Real* Yr = (Real*)malloc(n*m*sizeof(Real));
+ Real* tXrXr = (Real*)malloc(p*p*sizeof(Real));
+ Real* tXrYr = (Real*)malloc(p*m*sizeof(Real));
+ gsl_matrix* matrixM = gsl_matrix_alloc(p, m);
+ gsl_matrix* matrixE = gsl_matrix_alloc(m, m);
+ gsl_permutation* permutation = gsl_permutation_alloc(m);
+ gsl_matrix* V = gsl_matrix_alloc(m,m);
+ gsl_vector* S = gsl_vector_alloc(m);
+ gsl_vector* work = gsl_vector_alloc(m);
+
+ //Initialize class memberships (all elements in class 0; TODO: randomize ?)
+ int* Z = (int*)calloc(n, sizeof(int));
+
+ //Initialize phi to zero, because some M loops might exit before phi affectation
+ zeroArray(phi, p*m*k);
+
+ while (ite<mini || (ite<maxi && sumDeltaPhi>tau))
+ {
+ /////////////
+ // Etape M //
+ /////////////
+
+ //M step: Mise à jour de Beta (et donc phi)
+ for (int r=0; r<k; r++)
+ {
+ //Compute Xr = X(Z==r,:) and Yr = Y(Z==r,:)
+ int cardClustR=0;
+ for (int i=0; i<n; i++)
+ {
+ if (Z[i] == r)
+ {
+ for (int j=0; j<p; j++)
+ Xr[mi(cardClustR,j,n,p)] = X[mi(i,j,n,p)];
+ for (int j=0; j<m; j++)
+ Yr[mi(cardClustR,j,n,m)] = Y[mi(i,j,n,m)];
+ cardClustR++;
+ }
+ }
+ if (cardClustR == 0)
+ continue;
+
+ //Compute tXrXr = t(Xr) * Xr
+ for (int j=0; j<p; j++)
+ {
+ for (int jj=0; jj<p; jj++)
+ {
+ Real dotProduct = 0.0;
+ for (int u=0; u<cardClustR; u++)
+ dotProduct += Xr[mi(u,j,n,p)] * Xr[mi(u,jj,n,p)];
+ tXrXr[mi(j,jj,p,p)] = dotProduct;
+ }
+ }
+
+ //Get pseudo inverse = (t(Xr)*Xr)^{-1}
+ Real* invTXrXr = pinv(tXrXr, p);
+
+ // Compute tXrYr = t(Xr) * Yr
+ for (int j=0; j<p; j++)
+ {
+ for (int jj=0; jj<m; jj++)
+ {
+ Real dotProduct = 0.0;
+ for (int u=0; u<cardClustR; u++)
+ dotProduct += Xr[mi(u,j,n,p)] * Yr[mi(u,jj,n,m)];
+ tXrYr[mi(j,jj,p,m)] = dotProduct;
+ }
+ }
+
+ //Fill matrixM with inverse * tXrYr = (t(Xr)*Xr)^{-1} * t(Xr) * Yr
+ for (int j=0; j<p; j++)
+ {
+ for (int jj=0; jj<m; jj++)
+ {
+ Real dotProduct = 0.0;
+ for (int u=0; u<p; u++)
+ dotProduct += invTXrXr[mi(j,u,p,p)] * tXrYr[mi(u,jj,p,m)];
+ matrixM->data[j*m+jj] = dotProduct;
+ }
+ }
+ free(invTXrXr);
+
+ //U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr
+ gsl_linalg_SV_decomp(matrixM, V, S, work);
+
+ //Set m-rank(r) singular values to zero, and recompose
+ //best rank(r) approximation of the initial product
+ for (int j=rank[r]; j<m; j++)
+ S->data[j] = 0.0;
+
+ //[intermediate step] Compute hatBetaR = U * S * t(V)
+ double* U = matrixM->data; //GSL require double precision
+ for (int j=0; j<p; j++)
+ {
+ for (int jj=0; jj<m; jj++)
+ {
+ Real dotProduct = 0.0;
+ for (int u=0; u<m; u++)
+ dotProduct += U[j*m+u] * S->data[u] * V->data[jj*m+u];
+ hatBetaR[mi(j,jj,p,m)] = dotProduct;
+ }
+ }
+
+ //Compute phi(:,:,r) = hatBetaR * Rho(:,:,r)
+ for (int j=0; j<p; j++)
+ {
+ for (int jj=0; jj<m; jj++)
+ {
+ Real dotProduct=0.0;
+ for (int u=0; u<m; u++)
+ dotProduct += hatBetaR[mi(j,u,p,m)] * Rho[ai(u,jj,r,m,m,k)];
+ phi[ai(j,jj,r,p,m,k)] = dotProduct;
+ }
+ }
+ }
+
+ /////////////
+ // Etape E //
+ /////////////
+
+ Real sumLogLLF2 = 0.0;
+ for (int i=0; i<n; i++)
+ {
+ Real sumLLF1 = 0.0;
+ Real maxLogGamIR = -INFINITY;
+ for (int r=0; r<k; r++)
+ {
+ //Compute
+ //Gam(i,r) = Pi(r) * det(Rho(:,:,r)) * exp( -1/2 * (Y(i,:)*Rho(:,:,r) - X(i,:)...
+ //*phi(:,:,r)) * transpose( Y(i,:)*Rho(:,:,r) - X(i,:)*phi(:,:,r) ) );
+ //split in several sub-steps
+
+ //compute det(Rho(:,:,r)) [TODO: avoid re-computations]
+ for (int j=0; j<m; j++)
+ {
+ for (int jj=0; jj<m; jj++)
+ matrixE->data[j*m+jj] = Rho[ai(j,jj,r,m,m,k)];
+ }
+ gsl_linalg_LU_decomp(matrixE, permutation, &signum);
+ Real detRhoR = gsl_linalg_LU_det(matrixE, signum);
+
+ //compute Y(i,:)*Rho(:,:,r)
+ for (int j=0; j<m; j++)
+ {
+ YiRhoR[j] = 0.0;
+ for (int u=0; u<m; u++)
+ YiRhoR[j] += Y[mi(i,u,n,m)] * Rho[ai(u,j,r,m,m,k)];
+ }
+
+ //compute X(i,:)*phi(:,:,r)
+ for (int j=0; j<m; j++)
+ {
+ XiPhiR[j] = 0.0;
+ for (int u=0; u<p; u++)
+ XiPhiR[j] += X[mi(i,u,n,p)] * phi[ai(u,j,r,p,m,k)];
+ }
+
+ //compute dotProduct < Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) . Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) >
+ Real dotProduct = 0.0;
+ for (int u=0; u<m; u++)
+ dotProduct += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
+ Real logGamIR = log(Pi[r]) + log(detRhoR) - 0.5*dotProduct;
+
+ //Z(i) = index of max (gam(i,:))
+ if (logGamIR > maxLogGamIR)
+ {
+ Z[i] = r;
+ maxLogGamIR = logGamIR;
+ }
+ sumLLF1 += exp(logGamIR) / pow(2*M_PI,m/2.0);
+ }
+
+ sumLogLLF2 += log(sumLLF1);
+ }
+
+ // Assign output variable LLF
+ *LLF = -invN * sumLogLLF2;
+
+ //newDeltaPhi = max(max((abs(phi-Phi))./(1+abs(phi))));
+ Real newDeltaPhi = 0.0;
+ for (int j=0; j<p; j++)
+ {
+ for (int jj=0; jj<m; jj++)
+ {
+ for (int r=0; r<k; r++)
+ {
+ Real tmpDist = fabs(phi[ai(j,jj,r,p,m,k)]-Phi[ai(j,jj,r,p,m,k)])
+ / (1.0+fabs(phi[ai(j,jj,r,p,m,k)]));
+ if (tmpDist > newDeltaPhi)
+ newDeltaPhi = tmpDist;
+ }
+ }
+ }
+
+ //update distance parameter to check algorithm convergence (delta(phi, Phi))
+ //TODO: deltaPhi should be a linked list for perf.
+ if (ite < deltaPhiBufferSize)
+ deltaPhi[ite] = newDeltaPhi;
+ else
+ {
+ sumDeltaPhi -= deltaPhi[0];
+ for (int u=0; u<deltaPhiBufferSize-1; u++)
+ deltaPhi[u] = deltaPhi[u+1];
+ deltaPhi[deltaPhiBufferSize-1] = newDeltaPhi;
+ }
+ sumDeltaPhi += newDeltaPhi;
+
+ // update other local variables
+ for (int j=0; j<m; j++)
+ {
+ for (int jj=0; jj<p; jj++)
+ {
+ for (int r=0; r<k; r++)
+ Phi[ai(jj,j,r,p,m,k)] = phi[ai(jj,j,r,p,m,k)];
+ }
+ }
+ ite++;
+ }
+
+ //free memory
+ free(hatBetaR);
+ free(deltaPhi);
+ free(Phi);
+ gsl_matrix_free(matrixE);
+ gsl_matrix_free(matrixM);
+ gsl_permutation_free(permutation);
+ gsl_vector_free(work);
+ gsl_matrix_free(V);
+ gsl_vector_free(S);
+ free(XiPhiR);
+ free(YiRhoR);
+ free(Xr);
+ free(Yr);
+ free(tXrXr);
+ free(tXrYr);
+ free(Z);
+}
--- /dev/null
+#ifndef valse_EMGrank_H
+#define valse_EMGrank_H
+
+#include "utils.h"
+
+void EMGrank_core(
+ // IN parameters
+ const Real* Pi,
+ const Real* Rho,
+ int mini,
+ int maxi,
+ const Real* X,
+ const Real* Y,
+ Real tau,
+ const int* rank,
+ // OUT parameters
+ Real* phi,
+ Real* LLF,
+ // additional size parameters
+ int n,
+ int p,
+ int m,
+ int k);
+
+#endif
--- /dev/null
+#ifndef valse_utils_H
+#define valse_utils_H
+
+//#include <stdint.h>
+
+/********
+ * Types
+ *******/
+
+typedef double Real;
+//typedef uint32_t UInt;
+//typedef int32_t Int;
+
+/*******************************
+ * Matrix and arrays indexation
+ *******************************/
+
+// Matrix Index ; TODO? ncol unused
+#define mi(i,j,nrow,ncol)\
+ j*nrow + i
+
+// Array Index ; TODO? d3 unused
+#define ai(i,j,k,d1,d2,d3)\
+ k*d1*d2 + j*d1 + i
+
+// Array4 Index ; TODO? ...
+#define ai4(i,j,k,m,d1,d2,d3,d4)\
+ m*d1*d2*d3 + k*d1*d2 + j*d1 + i
+
+/*************************
+ * Array copy & "zeroing"
+ ************************/
+
+// Fill an array with zeros
+#define zeroArray(array, size)\
+{\
+ for (int u=0; u<size; u++)\
+ array[u] = 0;\
+}
+
+// Copy an 1D array
+#define copyArray(array, copy, size)\
+{\
+ for (int u=0; u<size; u++)\
+ copy[u] = array[u];\
+}
+
+#endif
--- /dev/null
+library(testthat)
+library(valse) #ou load_all()
+
+test_check("valse")
--- /dev/null
+# Potential helpers for context 1
+help <- function()
+{
+ #...
+}
--- /dev/null
+context("Context1")
+
+test_that("function 1...",
+{
+ #expect_lte( ..., ...)
+})
+
+test_that("function 2...",
+{
+ #expect_equal(..., ...)
+})
--- /dev/null
+#ignore jupyter generated file (ipynb, HTML)
+*.html
+*.ipynb
+
+#and various (pdf)LaTeX files, in case of
+*.tex
+*.pdf
+*.aux
+*.dvi
+*.log
+*.out
+*.toc
+*.synctex.gz
+/figure/
projects / valse.git / commitdiff
