#' @export
EMGLLF <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
X, Y, eps, fast = TRUE)
- {
+{
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
# R version - slow but easy to read
.EMGLLF_R <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
X2, Y, eps)
- {
+{
# Matrix dimensions
n <- dim(Y)[1]
- if (length(dim(phiInit)) == 2)
- {
+ if (length(dim(phiInit)) == 2) {
p <- 1
m <- dim(phiInit)[1]
k <- dim(phiInit)[2]
- } else
- {
+ } 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
+
# Outputs
phi <- array(NA, dim = c(p, m, k))
phi[1:p, , ] <- phiInit
pi <- piInit
llh <- -Inf
S <- array(0, dim = c(p, m, k))
-
+
# Algorithm variables
gam <- gamInit
Gram2 <- array(0, dim = c(p, p, 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
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) <
+ -sum(gam2 * log(pi2))/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#
-
+
# 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)
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]
+ 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]
+ }
}
- gam <- gam1/rowSums(gam1)
+ gam <- gam1 / rowSums(gam1)
sumLogLLH <- sum(log(rowSums(gam)) - log((2 * base::pi)^(m/2)))
sumPen <- sum(pi^gamma * b)
last_llh <- llh
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)
}
projects / valse.git / blobdiff