R/sliceSampler_skewT_parallel.R

In borishejblum/NPflow: Bayesian Nonparametrics for Automatic Gating of Flow-Cytometry Data

#'@keywords internal
#'@author Boris Hejblum
#'@importFrom stats rbeta rgamma runif
sliceSampler_skewT_parallel <- function(Ncpus, c, m, alpha, z, hyperG0,
                                        U_xi, U_psi, U_Sigma,
                                        U_df, scale, 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){
            NNiW <- rNNiW(hyperG0, diagVar)
            U_xi[, ind_new[i]] <- NNiW[["xi"]]
            U_psi[, ind_new[i]] <- NNiW[["psi"]]
            U_Sigma[, , ind_new[i]] <- NNiW[["S"]]
            U_df[ind_new[i]] <- 10
        }
    }

    fullCl_ind <- which(w != 0)
    nb_fullCl_ind <- length(fullCl_ind)
    # likelihood of belonging to each cluster computation
    # sampling clusters
    U_xi_full <- sapply(fullCl_ind, function(j) U_xi[, j])
    U_psi_full <- sapply(fullCl_ind, function(j) U_psi[, j])
    U_Sigma_full <- lapply(fullCl_ind, function(j) U_Sigma[, ,j])
    U_df_full <- sapply(fullCl_ind, function(j) U_df[j])

    if(length(fullCl_ind)>1){
      
        iter <- itertools::isplitIndices(ncol(z), chunks=Ncpus)
        c <- foreach::"%dopar%"(foreach::foreach(i=iter, .combine='c'),
                                {
            l <- mmvstpdfC(x=z[, i, drop=FALSE], xi=U_xi_full, psi=U_psi_full, sigma=U_Sigma_full, df=U_df_full, Log=TRUE)
            u_mat <- t(sapply(w[fullCl_ind], function(x){as.numeric(u[i] < x)}))
            prob_mat_log <- log(u_mat) + l

            #fast C++ code
            fullCl_ind[sampleClassC(probMat = prob_mat_log, Log=TRUE)]

            #         #slow C++ code
            #         fullCl_ind[sampleClassC_bis(prob_mat)]
            #         #vectorized R code
            #         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})
            #         fullCl_ind[apply(X=prob_norm, MARGIN=1, FUN=function(r){match(TRUE,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))]

    ltn <- numeric(maxCl) # latent truncated normal variables
    for (k in which(m_new!=0)){
        obs_k <- which(c==k)
        siginv <- solve(U_Sigma[, , k])
        psi <- U_psi[,k, drop=FALSE]
        A_k <-  1/(1 + (crossprod(psi, siginv)%*%psi))
        a_ik <- (tcrossprod(A_k, psi)%*%siginv%*%(z[,obs_k, drop=FALSE]-U_xi[,k]))
        A_k <- c(A_k)/scale[obs_k]
        ltn[obs_k] <- rtruncnorm(length(obs_k), a=0, b=Inf, mean = a_ik, sd = sqrt(A_k))
    }

    return(list("c"=c, "m"=m_new, "weights"=w, "latentTrunc"=ltn,
                "xi"=U_xi, "psi"=U_psi, "Sigma"=U_Sigma, "df"=U_df))
}