#'@keywords internal
#'@author Boris Hejblum
#'@importFrom stats rbeta rgamma runif
sliceSampler_N <- function(c, m, alpha, z, hyperG0, U_mu, U_Sigma, diagVar){
maxCl <- length(m) #maximum number of clusters
ind <- which(m!=0) # indexes of non empty clusters
# Sample the weights, i.e. the frequency of each existing cluster from a Dirichlet:
# temp_1 ~ Gamma(m_1,1), ... , temp_K ~ Gamma(m_K,1) # and sample the rest of the weigth for potential new clusters:
# temp_{K+1} ~ Gamma(alpha, 1)
# then renormalise temp
w <- numeric(maxCl)
temp <- stats::rgamma(n=(length(ind)+1), shape=c(m[ind], alpha), scale = 1)
temp_norm <- temp/sum(temp)
w[ind] <- temp_norm[-length(temp_norm)]
R <- temp_norm[length(temp_norm)]
#R is the rest, i.e. the weight for potential new clusters
# Sample the latent u
u <- stats::runif(length(c))*w[c]
u_star <- min(u)
# Sample the remaining weights that are needed with stick-breaking
# i.e. the new clusters
ind_new <- which(m==0) # potential new clusters
if(length(ind_new)>0){
t <- 0 # the number of new non empty clusters
while(R>u_star && (t<length(ind_new))){
# sum(w)<1-min(u) <=> R>min(u) car R=1-sum(w)
t <- t+1
beta_temp <- stats::rbeta(n=1, shape1=1, shape2=alpha)
# weight of the new cluster
w[ind_new[t]] <- R*beta_temp
R <- R * (1-beta_temp) # remaining weight
}
ind_new <- ind_new[1:t]
# Sample the centers and spread of each new cluster from prior
for (i in 1:t){
NiW <- rNiW(hyperG0, diagVar)
U_mu[, ind_new[i]] <- NiW[["mu"]]
U_Sigma[, , ind_new[i]] <- NiW[["S"]]
}
}
fullCl_ind <- which(w != 0)
# likelihood of belonging to each cluster computation
# sampling clusters
if(length(fullCl_ind)>1){
U_mu_full <- sapply(fullCl_ind, function(j) U_mu[, j])
U_Sigma_list <- lapply(fullCl_ind, function(j) U_Sigma[, ,j])
l <- mmvnpdfC(z, mean=U_mu_full, varcovM=U_Sigma_list, Log = TRUE)
u_mat <- t(sapply(w[fullCl_ind], function(x){as.numeric(u < x)}))
prob_mat_log <- log(u_mat) + l
#fast C++ code
c <- fullCl_ind[sampleClassC(probMat = prob_mat_log, Log = TRUE)]
# #slow C++ code
# c <- fullCl_ind[sampleClassC_bis(prob_mat)]
# #vectorized R code
# c <- fullCl_ind[apply(X= prob_mat, MARGIN=2, FUN=function(v){match(1,rmultinom(n=1, size=1, prob=v))})]
# #alternative implementation:
# prob_colsum <- colSums(prob_mat)
# prob_norm <- apply(X=prob_mat, MARGIN=1, FUN=function(r){r/prob_colsum})
# c <- fullCl_ind[apply(X=prob_norm, MARGIN=1, FUN=function(r){match(TRUE,stats::runif(1) <cumsum(r))})]
}else{
c <- rep(fullCl_ind, maxCl)
}
m_new <- numeric(maxCl) # number of observations in each cluster
m_new[unique(c)] <- table(c)[as.character(unique(c))]
# non vectorized code for cluster allocation:
# nb_fullCl <- nb_fullCl + t
# l <- numeric(length(fullCl_ind)) # likelihood of belonging to each cluster
# m_new <- numeric(maxCl) # number of observations in each cluster
# for(i in 1:maxCl){
# for (j in fullCl_ind){
# l[j] <- mvnpdf(x = matrix(z[,i], ncol= 1, nrow=length(z[,i])) ,
# mean = U_mu[, j],
# varcovM = U_Sigma[, , j])*w[j]
# }
# c[i] <- rmultinom(n=1, size=1, prob=l)
# m_new[c[i]] <- m_new[c[i]] + 1
# }
return(list("c"=c, "m"=m_new, "weights"=w,"U_mu"=U_mu,"U_Sigma"=U_Sigma))
}
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