R/DPMGibbsSkewT_parallel.R

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

#'Slice Sampling of Dirichlet Process Mixture of skew Student's t-distributions
#'
#'@param Ncpus the number of processors available
#'
#'@param type_connec The type of connection between the processors. Supported
#'cluster types are \code{"PSOCK"}, \code{"FORK"}, \code{"SOCK"}, \code{"MPI"}, and
#'\code{"NWS"}. See also \code{\link[parallel:makeCluster]{makeCluster}}.
#'
#'@param z data matrix \code{d x n} with \code{d} dimensions in rows
#'and \code{n} observations in columns.
#'
#'@param hyperG0 prior mixing distribution.
#'
#'@param a shape hyperparameter of the Gamma prior
#'on the concentration parameter of the Dirichlet Process. Default is \code{0.0001}.
#'
#'@param b scale hyperparameter of the Gamma prior
#'on the concentration parameter of the Dirichlet Process. Default is \code{0.0001}. If \code{0}, 
#'then the concentration is fixed set to \code{a}.
#'
#'@param N number of MCMC iterations.
#'
#'@param doPlot logical flag indicating whether to plot MCMC iteration or not.
#'Default to \code{TRUE}.
#'
#'@param plotevery an integer indicating the interval between plotted iterations when \code{doPlot}
#'is \code{TRUE}.
#'
#'@param nbclust_init number of clusters at initialization.
#'Default to 30 (or less if there are less than 30 observations).
#'
#'@param diagVar logical flag indicating whether the variance of each cluster is
#'estimated as a diagonal matrix, or as a full matrix.
#'Default is \code{TRUE} (diagonal variance).
#'
#'@param use_variance_hyperprior logical flag indicating whether a hyperprior is added 
#'for the variance parameter. Default is \code{TRUE} which decrease the impact of the variance prior
#'on the posterior. \code{FALSE} is useful for using an informative prior.
#'
#'@param verbose logical flag indicating whether partition info is
#'written in the console at each MCMC iteration.
#'
#'@param monitorfile
#'a writable \link{connections} or a character string naming a file to write into,
#'to monitor the progress of the analysis.
#'Default is \code{""} which is no monitoring. See Details.
#'
#'@param ... additional arguments to be passed to \code{\link{plot_DPMst}}.
#'Only used if \code{doPlot} is \code{TRUE}.
#'
#'@return a object of class \code{DPMclust} with the following attributes:
#'  \itemize{
#'      \item{\code{mcmc_partitions}:}{a list of length \code{N}. Each
#'       element \code{mcmc_partitions[n]} is a vector of length
#'       \code{n} giving the partition of the \code{n} observations.}
#'      \item{\code{alpha}:}{a vector of length \code{N}. \code{cost[j]} is the cost
#' associated to partition \code{c[[j]]}}
#'       \item{\code{U_SS_list}:}{a list of length \code{N} containing the lists of
#'       sufficient statistics for all the mixture components at each MCMC iteration}
#'      \item{\code{weights_list}:}{a list of length \code{N} containing the weights of each
#'      mixture component for each MCMC iterations}
#'      \item{\code{logposterior_list}:}{a list of length \code{N} containing the logposterior values
#'       at each MCMC iterations}
#'      \item{\code{data}:}{the data matrix \code{d x n} with \code{d} dimensions in rows
#'and \code{n} observations in columns}
#'      \item{\code{nb_mcmcit}:}{the number of MCMC iterations}
#'      \item{\code{clust_distrib}:}{the parametric distribution of the mixture component - \code{"skewt"}}
#'      \item{\code{hyperG0}:}{the prior on the cluster location}
#'  }
#'
#'@author Boris Hejblum
#'
#'@references Hejblum BP, Alkhassim C, Gottardo R, Caron F and Thiebaut R (2019) 
#'Sequential Dirichlet Process Mixtures of Multivariate Skew t-distributions for 
#'Model-based Clustering of Flow Cytometry Data. The Annals of Applied Statistics, 
#'13(1): 638-660. <doi: 10.1214/18-AOAS1209> <arXiv: 1702.04407> 
#'\url{https://arxiv.org/abs/1702.04407} \url{https://doi.org/10.1214/18-AOAS1209}
#'
#'@export
#'
#'@examples
#' rm(list=ls())
#'
#' #Number of data
#' n <- 2000
#' set.seed(123)
#' #set.seed(4321)
#'
#'
#' d <- 2
#' ncl <- 4
#'
#' # Sample data
#'
#' sdev <- array(dim=c(d,d,ncl))
#'
#' xi <- matrix(nrow=d, ncol=ncl, c(-1.5, 1, 1.5, 1, 1.5, -2, -2, -2))
#' psi <- matrix(nrow=d, ncol=4, c(0.4, -0.6, 0.8, 0, 0.3, -0.7, -0.3, -0.8))
#' p <- c(0.2, 0.1, 0.4, 0.3) # frequence des clusters
#' sdev[, ,1] <- matrix(nrow=d, ncol=d, c(0.3, 0, 0, 0.3))
#' sdev[, ,2] <- matrix(nrow=d, ncol=d, c(0.1, 0, 0, 0.3))
#' sdev[, ,3] <- matrix(nrow=d, ncol=d, c(0.3, 0.15, 0.15, 0.3))
#' sdev[, ,4] <- .3*diag(2)
#'
#'
#' c <- rep(0,n)
#' z <- matrix(0, nrow=d, ncol=n)
#' for(k in 1:n){
#'  c[k] = which(rmultinom(n=1, size=1, prob=p)!=0)
#'  z[,k] <- (xi[, c[k]]
#'           + psi[, c[k]]*abs(rnorm(1))
#'           + sdev[, , c[k]]%*%matrix(rnorm(d, mean = 0, sd = 1), nrow=d, ncol=1))
#'  #cat(k, "/", n, " observations simulated\n", sep="")
#' }
#'
#' # Set parameters of G0
#' hyperG0 <- list()
#' hyperG0[["b_xi"]] <- rep(0,d)
#' hyperG0[["b_psi"]] <- rep(0,d)
#' hyperG0[["kappa"]] <- 0.001
#' hyperG0[["D_xi"]] <- 100
#' hyperG0[["D_psi"]] <- 100
#' hyperG0[["nu"]] <- d + 1
#' hyperG0[["lambda"]] <- diag(d)
#'
#'  # hyperprior on the Scale parameter of DPM
#'  a <- 0.0001
#'  b <- 0.0001
#'
#'  # do some plots
#'  doPlot <- TRUE
#'  nbclust_init <- 30
#'
#'
#'
#'  ## Data
#'  ########
#' library(ggplot2)
#'  p <- (ggplot(data.frame("X"=z[1,], "Y"=z[2,]), aes(x=X, y=Y))
#'        + geom_point()
#'        + ggtitle("Simple example in 2d data")
#'        +xlab("D1")
#'        +ylab("D2")
#'        +theme_bw())
#'  p
#'
#'  c2plot <- factor(c)
#'  levels(c2plot) <- c("3", "2", "4", "1")
#'  pp <- (ggplot(data.frame("X"=z[1,], "Y"=z[2,], "Cluster"=as.character(c2plot)))
#'        + geom_point(aes(x=X, y=Y, colour=Cluster, fill=Cluster))
#'        + ggtitle("Slightly overlapping skew-normal simulation\n")
#'        + xlab("D1")
#'        + ylab("D2")
#'        + theme_bw()
#'        + scale_colour_discrete(guide=guide_legend(override.aes = list(size = 6, shape=22))))
#'  pp
#'
#'
#'  ## alpha priors plots
#'  #####################
#'  prioralpha <- data.frame("alpha"=rgamma(n=5000, shape=a, scale=1/b),
#'                          "distribution" =factor(rep("prior",5000),
#'                          levels=c("prior", "posterior")))
#'  p <- (ggplot(prioralpha, aes(x=alpha))
#'        + geom_histogram(aes(y=..density..),
#'                         colour="black", fill="white")
#'        + geom_density(alpha=.2, fill="red")
#'        + ggtitle(paste("Prior distribution on alpha: Gamma(", a,
#'                  ",", b, ")\n", sep=""))
#'       )
#'  p
#'
#'
#'if(interactive()){
#'  # Gibbs sampler for Dirichlet Process Mixtures
#'  ##############################################
#'  MCMCsample_st <- DPMGibbsSkewT(z, hyperG0, a, b, N=2000,
#'                                 doPlot, nbclust_init, plotevery=100, gg.add=list(theme_bw(),
#'                                  guides(shape=guide_legend(override.aes = list(fill="grey45")))),
#'                                 diagVar=FALSE)
#'  s <- summary(MCMCsample_st, burnin = 350)
#'  print(s)
#'  plot(s)
#'  plot_ConvDPM(MCMCsample_st, from=2)
#'  cluster_est_binder(MCMCsample_st$mcmc_partitions[1500:2000])
#'}
#'
#'
#'
DPMGibbsSkewT_parallel <- function (Ncpus, type_connec,
                                    z, hyperG0, a=0.0001, b=0.0001, N, doPlot=FALSE,
                                    nbclust_init=30, plotevery=N/10,
                                    diagVar=TRUE, use_variance_hyperprior=TRUE, verbose=FALSE,
                                    monitorfile="",
                                    ...){

  dpmclus <- NULL

  if(!requireNamespace("itertools", quietly=TRUE)){
    stop("Package 'itertools' is not available.\n  -> Try running 'install.packages(\"itertools\")'\n   or use non parallel version of the function: 'DPMGibbsN'")
  }else{
    requireNamespace("itertools", quietly=TRUE)
  }
  
  if(!requireNamespace("doParallel", quietly=TRUE)){
    stop("Package 'doParallel' is not available.\n  -> Try running 'install.packages(\"doParallel\")'\n   or use non parallel version of the function: 'DPMGibbsN'")
  }else{
    requireNamespace("doParallel", quietly=TRUE)

    # declare the cores
    cl <- parallel::makeCluster(Ncpus, type = type_connec, outfile=monitorfile)
    doParallel::registerDoParallel(cl)

    if(doPlot){requireNamespace("ggplot2", quietly=TRUE)}

    p <- dim(z)[1]
    n <- dim(z)[2]
    U_xi <- matrix(0, nrow=p, ncol=n)
    U_psi <- matrix(0, nrow=p, ncol=n)
    U_Sigma = array(0, dim=c(p, p, n))
    U_df = rep(10,n)
    U_B = array(0, dim=c(2, 2, n))
    U_nu <- rep(p,n)
    
    if(Ncpus<2){
        warning("Only 1 core specified\n=> non-parallel version of the algorithm would be more efficient")
    }

    # U_SS is a list where each U_SS[[k]] contains the sufficient
    # statistics associated to cluster k
    U_SS <- list()

    #store U_SS :
    U_SS_list <- list()
    #store clustering :
    c_list <- list()
    #store sliced weights
    weights_list <- list()

    #store log posterior probability
    logposterior_list <- list()

    m <- numeric(n) # number of obs in each clusters
    c <- numeric(n) # cluster label of ech observation
    ltn <- rtruncnorm(n, a=0, b=Inf, mean=0, sd=1) # latent truncated normal
    sc <- rep(1,n)

    # Initialization----
    # each observation is assigned to a different cluster
    # or to 1 of the 50 initial clusters if there are more than
    # 50 observations

    i <- 1

    if(ncol(z)<nbclust_init){
        for (k in 1:n){
            c[k] <- k
            #cat("cluster ", k, ":\n")
            U_SS[[k]] <- update_SSst(z=z[, k], S=hyperG0, ltn=ltn[k], scale=sc[obs_k], df=U_df[k])
            NNiW <- rNNiW(U_SS[[k]], diagVar)
            U_xi[, k] <- NNiW[["xi"]]
            U_SS[[k]][["xi"]] <- NNiW[["xi"]]
            U_psi[, k] <- NNiW[["psi"]]
            U_SS[[k]][["psi"]] <- NNiW[["psi"]]
            U_Sigma[, , k] <- NNiW[["S"]]
            U_SS[[k]][["S"]] <- NNiW[["S"]]
            U_B[, ,k] <- U_SS[[k]][["B"]]
            m[k] <- m[k]+1
        }
    } else{
        c <- sample(x=1:nbclust_init, size=n, replace=TRUE)
        for (k in unique(c)){
            obs_k <- which(c==k)
            U_SS[[k]] <- update_SSst(z=z[, obs_k], S=hyperG0, ltn=ltn[obs_k], scale=sc[obs_k], df=U_df[k])
            NNiW <- rNNiW(U_SS[[k]], diagVar)
            U_xi[, k] <- NNiW[["xi"]]
            U_SS[[k]][["xi"]] <- NNiW[["xi"]]
            U_psi[, k] <- NNiW[["psi"]]
            U_SS[[k]][["psi"]] <- NNiW[["psi"]]
            U_Sigma[, , k] <- NNiW[["S"]]
            U_SS[[k]][["S"]] <- NNiW[["S"]]
            U_B[, ,k] <- U_SS[[k]][["B"]]
            m[k] <- length(obs_k)
        }
    }


    alpha <- c(log(n))


    U_SS_list[[i]] <- U_SS
    c_list[[i]] <- c
    weights_list[[1]] <- numeric(length(m))
    weights_list[[1]][unique(c)] <- table(c)/length(c)

    logposterior_list[[i]] <- logposterior_DPMST(z, xi=U_xi, psi=U_psi, Sigma=U_Sigma, df=U_df, B=U_B,
                                                 hyper=hyperG0, c=c, m=m, alpha=alpha[i], n=n, a=a, b=b, diagVar)

    if(doPlot){
        plot_DPMst(z=z, c=c, i=i, alpha=alpha[i], U_SS=U_SS_list[[i]], ellipses=TRUE, ...)
    }
    if(verbose){
        cat(i, "/", N, " samplings:\n", sep="",
            file=monitorfile, append = TRUE)
        cat("  logposterior = ", sum(logposterior_list[[i]]), "\n", sep="",
            file=monitorfile, append = TRUE)
        cl2print <- unique(c)
        cat(length(cl2print), "clusters:", cl2print[order(cl2print)], "\n\n",
            file=monitorfile, append = TRUE)
    }


    if(N>1){
        for(i in 2:N){
            nbClust <- length(unique(c))

            alpha <- c(alpha,
                       sample_alpha(alpha_old=alpha[i-1], n=n,
                                    K=nbClust, a=a, b=b)
            )

            slice <- sliceSampler_skewT_parallel(Ncpus=Ncpus,
                                                 c=c, m=m,
                                                 alpha=alpha[i],
                                                 z=z, hyperG0=hyperG0,
                                                 U_xi=U_xi,
                                                 U_psi=U_psi,
                                                 U_Sigma=U_Sigma,
                                                 U_df=U_df,
                                                 scale=sc, diagVar)
            m <- slice[["m"]]
            c <- slice[["c"]]
            weights_list[[i]] <- slice[["weights"]]
            ltn <- slice[["latentTrunc"]]
            U_xi <- slice[["xi"]]
            U_psi <- slice[["psi"]]
            U_Sigma <- slice[["Sigma"]]
            U_df <- slice[["df"]]

            # Update cluster locations
            fullCl <- which(m!=0)
            fullCl_nb <- length(fullCl)
            for(k in 1:fullCl_nb){
                j <- fullCl[k]
                obs_j <- which(c==j)
                #cat("cluster ", j, ":\n")
                if(use_variance_hyperprior){
                  U_SS[[j]] <- update_SSst(z=z[, obs_j, drop=FALSE], S=hyperG0,
                                           ltn=ltn[obs_j], scale=sc[obs_j],
                                           df=U_df[j],
                                           hyperprior = list("Sigma"=U_Sigma[,,j])
                  )
                }else{
                  U_SS[[j]] <- update_SSst(z=z[, obs_j, drop=FALSE], S=hyperG0,
                                           ltn=ltn[obs_j], scale=sc[obs_j],
                                           df=U_df[j]
                  )
                }

                U_nu[j] <- U_SS[[j]][["nu"]]
                NNiW <- rNNiW(U_SS[[j]], diagVar)
                U_xi[, j] <- NNiW[["xi"]]
                U_SS[[j]][["xi"]] <- NNiW[["xi"]]
                U_psi[, j] <- NNiW[["psi"]]
                U_SS[[j]][["psi"]] <- NNiW[["psi"]]
                U_Sigma[, , j] <- NNiW[["S"]]
                U_SS[[j]][["S"]] <- NNiW[["S"]]
                U_B[, ,j] <- U_SS[[j]][["B"]]
            }

            update_scale <- sample_scale(c=c, m=m, z=z, U_xi=U_xi,
                                         U_psi=U_psi, U_Sigma=U_Sigma,
                                         U_df=U_df, ltn=ltn,
                                         weights=weights_list[[i]],
                                         scale=sc)
            U_df_full <- update_scale[["df"]]
            sc <- update_scale[["scale"]]

            for(k in 1:fullCl_nb){
                j <- fullCl[k]
                U_df[j] <- U_df_full[k]
                U_SS[[j]][["df"]] <- U_df[j]
            }

            U_SS_list[[i]] <- U_SS[which(m!=0)]
            c_list[[i]] <- c

            logposterior_list[[i]] <- logposterior_DPMST(z, xi=U_xi, psi=U_psi, Sigma=U_Sigma, df=U_df, B=U_B,
                                                         hyper=hyperG0, c=c, m=m, alpha=alpha[i], n=n, a=a, b=b, diagVar)

            if(doPlot && i/plotevery==floor(i/plotevery)){
                plot_DPMst(z=z, c=c, i=i, alpha=alpha[i], U_SS=U_SS_list[[i]], ellipses=TRUE, ...)
            }
            if(verbose){
                cat(i, "/", N, " samplings:\n", sep="",
                    file=monitorfile, append = TRUE)
                cat("  logposterior = ", sum(logposterior_list[[i]]), "\n", sep="",
                    file=monitorfile, append = TRUE)
                cl2print <- unique(c)
                cat(length(cl2print), "clusters:", cl2print[order(cl2print)], "\n\n",
                    file=monitorfile, append = TRUE)
            }
        }
    }



    parallel::stopCluster(cl)

    dpmclus <- list("mcmc_partitions" = c_list,
                    "alpha"=alpha,
                    "U_SS_list"=U_SS_list,
                    "weights_list"=weights_list,
                    "logposterior_list"=logposterior_list,
                    "data"=z,
                    "nb_mcmcit"=N,
                    "clust_distrib"="skewt",
                    "hyperG0"=hyperG0)
    class(dpmclus) <- "DPMMclust"

  }
    return(dpmclus)
}