Nothing
#' EMGrank
#'
#' Run an generalized EM algorithm developped for mixture of Gaussian regression
#' models with variable selection by an extension of the low rank estimator.
#' Reparametrization is done to ensure invariance by homothetic transformation.
#' It returns a collection of models, varying the number of clusters and the rank of the regression mean.
#'
#' @param Pi An initialization for pi
#' @param Rho An initialization for rho, the variance parameter
#' @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 vector of possible ranks
#' @param fast boolean to enable or not the C function call
#'
#' @return A list (corresponding to the model collection) defined by (phi,LLF):
#' phi : regression mean for each cluster, an array of size p*m*k
#' LLF : log likelihood with respect to the training set
#'
#' @export
EMGrank <- function(Pi, Rho, mini, maxi, X, Y, eps, rank, fast)
{
if (!fast)
{
# Function in R
return(.EMGrank_R(Pi, Rho, mini, maxi, X, Y, eps, rank))
}
# Function in C
.Call("EMGrank", Pi, Rho, mini, maxi, X, Y, eps, as.integer(rank), 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)))
X
}
# R version - slow but easy to read
.EMGrank_R <- function(Pi, Rho, mini, maxi, X, Y, eps, 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 > eps))
{
# 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
}
list(phi = phi, LLF = LLF)
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.