Nothing
#' A Reference Class which contains statistics of a NMoE model.
#'
#' StatNMoE contains all the statistics associated to a [NMoE][ParamNMoE] model.
#' It mainly includes the E-Step of the EM algorithm calculating the posterior
#' distribution of the hidden variables, as well as the calculation of the
#' log-likelhood.
#'
#' @field piik Matrix of size \eqn{(n, K)} representing the probabilities
#' \eqn{\pi_{k}(x_{i}; \boldsymbol{\Psi}) = P(z_{i} = k |
#' \boldsymbol{x}; \Psi)}{\pi_{k}(x_{i}; \Psi) = P(z_{i} = k | x; \Psi)} of
#' the latent variable \eqn{z_{i}, i = 1,\dots,n}.
#' @field z_ik Hard segmentation logical matrix of dimension \eqn{(n, K)}
#' obtained by the Maximum a posteriori (MAP) rule: \eqn{z\_ik = 1 \
#' \textrm{if} \ z\_ik = \textrm{arg} \ \textrm{max}_{s} \ \tau_{is};\ 0 \
#' \textrm{otherwise}}{z_ik = 1 if z_ik = arg max_s \tau_{is}; 0 otherwise},
#' \eqn{k = 1,\dots,K}.
#' @field klas Column matrix of the labels issued from `z_ik`. Its elements are
#' \eqn{klas(i) = k}, \eqn{k = 1,\dots,K}.
#' @field tik Matrix of size \eqn{(n, K)} giving the posterior probability
#' \eqn{\tau_{ik}}{\tauik} that the observation \eqn{y_{i}}{yi} originates
#' from the \eqn{k}-th expert.
#' @field Ey_k Matrix of dimension \emph{(n, K)} giving the estimated means of the experts.
#' @field Ey Column matrix of dimension \emph{n} giving the estimated mean of the NMoE.
#' @field Var_yk Column matrix of dimension \emph{K} giving the estimated means of the experts.
#' @field Vary Column matrix of dimension \emph{n} giving the estimated variance of the response.
#' @field loglik Numeric. Observed-data log-likelihood of the NMoE model.
#' @field com_loglik Numeric. Complete-data log-likelihood of the NMoE model.
#' @field stored_loglik Numeric vector. Stored values of the log-likelihood at
#' each EM iteration.
#' @field BIC Numeric. Value of BIC (Bayesian Information Criterion).
#' @field ICL Numeric. Value of ICL (Integrated Completed Likelihood).
#' @field AIC Numeric. Value of AIC (Akaike Information Criterion).
#' @field log_piik_fik Matrix of size \eqn{(n, K)} giving the values of the
#' logarithm of the joint probability \eqn{P(y_{i}, \ z_{i} = k |
#' \boldsymbol{x}, \boldsymbol{\Psi})}{P(y_{i}, z_{i} = k | x, \Psi)}, \eqn{i
#' = 1,\dots,n}.
#' @field log_sum_piik_fik Column matrix of size \emph{m} giving the values of
#' \eqn{\textrm{log} \sum_{k = 1}^{K} P(y_{i}, \ z_{i} = k | \boldsymbol{x},
#' \boldsymbol{\Psi})}{log \sum_{k = 1}^{K} P(y_{i}, z_{i} = k | x, \Psi)},
#' \eqn{i = 1,\dots,n}.
#' @seealso [ParamNMoE]
#' @export
StatNMoE <- setRefClass(
"StatNMoE",
fields = list(
piik = "matrix",
z_ik = "matrix",
klas = "matrix",
Ey_k = "matrix",
Ey = "matrix",
Var_yk = "matrix",
Vary = "matrix",
loglik = "numeric",
com_loglik = "numeric",
stored_loglik = "numeric",
BIC = "numeric",
ICL = "numeric",
AIC = "numeric",
log_piik_fik = "matrix",
log_sum_piik_fik = "matrix",
tik = "matrix"
),
methods = list(
initialize = function(paramNMoE = ParamNMoE()) {
piik <<- matrix(NA, paramNMoE$n, paramNMoE$K)
z_ik <<- matrix(NA, paramNMoE$n, paramNMoE$K)
klas <<- matrix(NA, paramNMoE$n, 1)
Ey_k <<- matrix(NA, paramNMoE$n, paramNMoE$K)
Ey <<- matrix(NA, paramNMoE$n, 1)
Var_yk <<- matrix(NA, 1, paramNMoE$K)
Vary <<- matrix(NA, paramNMoE$n, 1)
loglik <<- -Inf
com_loglik <<- -Inf
stored_loglik <<- numeric()
BIC <<- -Inf
ICL <<- -Inf
AIC <<- -Inf
log_piik_fik <<- matrix(0, paramNMoE$n, paramNMoE$K)
log_sum_piik_fik <<- matrix(NA, paramNMoE$n, 1)
tik <<- matrix(0, paramNMoE$n, paramNMoE$K)
},
MAP = function() {
"MAP calculates values of the fields \\code{z_ik} and \\code{klas}
by applying the Maximum A Posteriori Bayes allocation rule.
\\eqn{z_{ik} = 1 \\ \\textrm{if} \\ k = \\textrm{arg} \\ \\textrm{max}_{s}
\\ \\tau_{is};\\ 0 \\ \\textrm{otherwise}}{
z_{ik} = 1 if z_ik = arg max_{s} \\tau_{is}; 0 otherwise}"
N <- nrow(tik)
K <- ncol(tik)
ikmax <- max.col(tik)
ikmax <- matrix(ikmax, ncol = 1)
z_ik <<- ikmax %*% ones(1, K) == ones(N, 1) %*% (1:K) # partition_MAP
klas <<- ones(N, 1)
for (k in 1:K) {
klas[z_ik[, k] == 1] <<- k
}
},
computeLikelihood = function(reg_irls) {
"Method to compute the log-likelihood. \\code{reg_irls} is the value of
the regularization part in the IRLS algorithm."
loglik <<- sum(log_sum_piik_fik) + reg_irls
},
computeStats = function(paramNMoE) {
"Method used in the EM algorithm to compute statistics based on
parameters provided by the object \\code{paramNMoE} of class
\\link{ParamNMoE}."
# E[yi|xi,zi=k]
Ey_k <<- paramNMoE$phiBeta$XBeta[1:paramNMoE$n,] %*% paramNMoE$beta
# E[yi|xi]
Ey <<- matrix(apply(piik * Ey_k, 1, sum))
# Var[yi|xi,zi=k]
Var_yk <<- paramNMoE$sigma2
# Var[yi|xi]
Vary <<- apply(piik * (Ey_k ^ 2 + ones(paramNMoE$n, 1) %*% Var_yk), 1, sum) - Ey ^ 2
# BIC, AIC and ICL
BIC <<- loglik - (paramNMoE$df * log(paramNMoE$n) / 2)
AIC <<- loglik - paramNMoE$df
# CL(theta) : complete-data loglikelihood
zik_log_piik_fk <- z_ik * log_piik_fik
sum_zik_log_fik <- apply(zik_log_piik_fk, 1, sum)
com_loglik <<- sum(sum_zik_log_fik)
ICL <<- com_loglik - (paramNMoE$df * log(paramNMoE$n) / 2)
},
EStep = function(paramNMoE) {
"Method used in the EM algorithm to update statistics based on parameters
provided by the object \\code{paramNMoE} of class \\link{ParamNMoE}
(prior and posterior probabilities)."
piik <<- multinomialLogit(paramNMoE$alpha, paramNMoE$phiAlpha$XBeta, ones(paramNMoE$n, paramNMoE$K), ones(paramNMoE$n, 1))$piik
piik_fik <- zeros(paramNMoE$n, paramNMoE$K)
for (k in (1:paramNMoE$K)) {
muk <- paramNMoE$phiBeta$XBeta %*% paramNMoE$beta[, k]
sigma2k <- paramNMoE$sigma2[k]
log_piik_fik[, k] <<- log(piik[, k]) - 0.5 * log(2 * pi) - 0.5 * log(sigma2k) - 0.5 * ((paramNMoE$Y - muk) ^ 2) / sigma2k
}
log_sum_piik_fik <<- matrix(log(rowSums(exp(log_piik_fik))))
log_tik <- log_piik_fik - log_sum_piik_fik %*% ones(1, paramNMoE$K)
ttik <- exp(log_tik)
tik <<- ttik / (rowSums(ttik) %*% ones(1, paramNMoE$K))
}
)
)
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.