| 1 | #' EMGrank |
| 2 | #' |
| 3 | #' Description de EMGrank |
| 4 | #' |
| 5 | #' @param Pi Parametre de proportion |
| 6 | #' @param Rho Parametre initial de variance renormalisé |
| 7 | #' @param mini Nombre minimal d'itérations dans l'algorithme EM |
| 8 | #' @param maxi Nombre maximal d'itérations dans l'algorithme EM |
| 9 | #' @param X Régresseurs |
| 10 | #' @param Y Réponse |
| 11 | #' @param eps Seuil pour accepter la convergence |
| 12 | #' @param rank Vecteur des rangs possibles |
| 13 | #' |
| 14 | #' @return A list ... |
| 15 | #' phi : parametre de moyenne renormalisé, calculé par l'EM |
| 16 | #' LLF : log vraisemblance associé à cet échantillon, pour les valeurs estimées des paramètres |
| 17 | #' |
| 18 | #' @export |
| 19 | EMGrank <- function(Pi, Rho, mini, maxi, X, Y, eps, rank, fast = TRUE) |
| 20 | { |
| 21 | if (!fast) |
| 22 | { |
| 23 | # Function in R |
| 24 | return(.EMGrank_R(Pi, Rho, mini, maxi, X, Y, eps, rank)) |
| 25 | } |
| 26 | |
| 27 | # Function in C |
| 28 | n <- nrow(X) #nombre d'echantillons |
| 29 | p <- ncol(X) #nombre de covariables |
| 30 | m <- ncol(Y) #taille de Y (multivarié) |
| 31 | k <- length(Pi) #nombre de composantes dans le mélange |
| 32 | .Call("EMGrank", Pi, Rho, mini, maxi, X, Y, eps, as.integer(rank), phi = double(p * m * k), |
| 33 | LLF = double(1), n, p, m, k, PACKAGE = "valse") |
| 34 | } |
| 35 | |
| 36 | # helper to always have matrices as arg (TODO: put this elsewhere? improve?) --> |
| 37 | # Yes, we should use by-columns storage everywhere... [later!] |
| 38 | matricize <- function(X) |
| 39 | { |
| 40 | if (!is.matrix(X)) |
| 41 | return(t(as.matrix(X))) |
| 42 | return(X) |
| 43 | } |
| 44 | |
| 45 | # R version - slow but easy to read |
| 46 | .EMGrank_R <- function(Pi, Rho, mini, maxi, X, Y, eps, rank) |
| 47 | { |
| 48 | # matrix dimensions |
| 49 | n <- nrow(X) |
| 50 | p <- ncol(X) |
| 51 | m <- ncol(Y) |
| 52 | k <- length(Pi) |
| 53 | |
| 54 | # init outputs |
| 55 | phi <- array(0, dim = c(p, m, k)) |
| 56 | Z <- rep(1, n) |
| 57 | LLF <- 0 |
| 58 | |
| 59 | # local variables |
| 60 | Phi <- array(0, dim = c(p, m, k)) |
| 61 | deltaPhi <- c() |
| 62 | sumDeltaPhi <- 0 |
| 63 | deltaPhiBufferSize <- 20 |
| 64 | |
| 65 | # main loop |
| 66 | ite <- 1 |
| 67 | while (ite <= mini || (ite <= maxi && sumDeltaPhi > eps)) |
| 68 | { |
| 69 | # M step: update for Beta ( and then phi) |
| 70 | for (r in 1:k) |
| 71 | { |
| 72 | Z_indice <- seq_len(n)[Z == r] #indices where Z == r |
| 73 | if (length(Z_indice) == 0) |
| 74 | next |
| 75 | # U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr |
| 76 | s <- svd(MASS::ginv(crossprod(matricize(X[Z_indice, ]))) %*% |
| 77 | crossprod(matricize(X[Z_indice, ]), matricize(Y[Z_indice, ]))) |
| 78 | S <- s$d |
| 79 | # Set m-rank(r) singular values to zero, and recompose best rank(r) approximation |
| 80 | # of the initial product |
| 81 | if (rank[r] < length(S)) |
| 82 | S[(rank[r] + 1):length(S)] <- 0 |
| 83 | phi[, , r] <- s$u %*% diag(S) %*% t(s$v) %*% Rho[, , r] |
| 84 | } |
| 85 | |
| 86 | # Step E and computation of the loglikelihood |
| 87 | sumLogLLF2 <- 0 |
| 88 | for (i in seq_len(n)) |
| 89 | { |
| 90 | sumLLF1 <- 0 |
| 91 | maxLogGamIR <- -Inf |
| 92 | for (r in seq_len(k)) |
| 93 | { |
| 94 | dotProduct <- tcrossprod(Y[i, ] %*% Rho[, , r] - X[i, ] %*% phi[, , r]) |
| 95 | logGamIR <- log(Pi[r]) + log(gdet(Rho[, , r])) - 0.5 * dotProduct |
| 96 | # Z[i] = index of max (gam[i,]) |
| 97 | if (logGamIR > maxLogGamIR) |
| 98 | { |
| 99 | Z[i] <- r |
| 100 | maxLogGamIR <- logGamIR |
| 101 | } |
| 102 | sumLLF1 <- sumLLF1 + exp(logGamIR)/(2 * pi)^(m/2) |
| 103 | } |
| 104 | sumLogLLF2 <- sumLogLLF2 + log(sumLLF1) |
| 105 | } |
| 106 | |
| 107 | LLF <- -1/n * sumLogLLF2 |
| 108 | |
| 109 | # update distance parameter to check algorithm convergence (delta(phi, Phi)) |
| 110 | deltaPhi <- c(deltaPhi, max((abs(phi - Phi))/(1 + abs(phi)))) #TODO: explain? |
| 111 | if (length(deltaPhi) > deltaPhiBufferSize) |
| 112 | deltaPhi <- deltaPhi[2:length(deltaPhi)] |
| 113 | sumDeltaPhi <- sum(abs(deltaPhi)) |
| 114 | |
| 115 | # update other local variables |
| 116 | Phi <- phi |
| 117 | ite <- ite + 1 |
| 118 | } |
| 119 | return(list(phi = phi, LLF = LLF)) |
| 120 | } |