Slice Sampling of Dirichlet Process Mixture of Gaussian distributions

Usage

DPMGibbsN_SeqPrior(
  z,
  prior_inform,
  hyperG0,
  N,
  nbclust_init,
  add.vagueprior = TRUE,
  weightnoninfo = NULL,
  doPlot = TRUE,
  plotevery = N/10,
  diagVar = TRUE,
  verbose = TRUE,
  ...
)

Arguments

z: data matrix d x n with d dimensions in rows and n observations in columns.
prior_inform: an informative prior such as the approximation computed by summary.DPMMclust.
hyperG0: a non informative prior component for the mixing distribution. Only used if add.vagueprior is TRUE.
N: number of MCMC iterations.
nbclust_init: number of clusters at initialization. Default to 30 (or less if there are less than 30 observations).
add.vagueprior: logical flag indicating whether a non informative component should be added to the informative prior. Default is TRUE.
weightnoninfo: a real between 0 and 1 giving the weights of the non informative component in the prior.
doPlot: logical flag indicating whether to plot MCMC iteration or not. Default to TRUE.
plotevery: an integer indicating the interval between plotted iterations when doPlot is TRUE.
diagVar: logical flag indicating whether the variance of each cluster is estimated as a diagonal matrix, or as a full matrix. Default is TRUE (diagonal variance).
verbose: logical flag indicating whether partition info is written in the console at each MCMC iteration.
...: additional arguments to be passed to plot_DPM. Only used if doPlot is TRUE.

Value

a object of class DPMclust with the following attributes:

mcmc_partitions:: a list of length N. Each element mcmc_partitions[n] is a vector of length n giving the partition of the n observations.
alpha:: a vector of length N. cost[j] is the cost associated to partition c[[j]]
listU_mu:: a list of length N containing the matrices of mean vectors for all the mixture components at each MCMC iteration
listU_Sigma:: a list of length N containing the arrays of covariances matrices for all the mixture components at each MCMC iteration
U_SS_list:: a list of length N containing the lists of sufficient statistics for all the mixture components at each MCMC iteration
weights_list:
logposterior_list:: a list of length N containing the logposterior values at each MCMC iterations
data:: the data matrix d x n with d dimensions in rows and n observations in columns.
nb_mcmcit:: the number of MCMC iterations
clust_distrib:: the parametric distribution of the mixture component - "gaussian"
hyperG0:: the prior on the cluster location

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> https://arxiv.org/abs/1702.04407 doi:10.1214/18-AOAS1209

Author

Boris Hejblum, Chariff Alkhassim

Examples


rm(list=ls())
library(NPflow)
#Number of data
n <- 1500
# Sample data
#m <- matrix(nrow=2, ncol=4, c(-1, 1, 1.5, 2, 2, -2, 0.5, -2))
m <- matrix(nrow=2, ncol=4, c(-.8, .7, .5, .7, .5, -.7, -.5, -.7))
p <- c(0.2, 0.1, 0.4, 0.3) # frequence des clusters

sdev <- array(dim=c(2,2,4))
sdev[, ,1] <- matrix(nrow=2, ncol=2, c(0.3, 0, 0, 0.3))
sdev[, ,2] <- matrix(nrow=2, ncol=2, c(0.1, 0, 0, 0.3))
sdev[, ,3] <- matrix(nrow=2, ncol=2, c(0.3, 0.15, 0.15, 0.3))
sdev[, ,4] <- .3*diag(2)
c <- rep(0,n)
z <- matrix(0, nrow=2, ncol=n)
for(k in 1:n){
 c[k] = which(rmultinom(n=1, size=1, prob=p)!=0)
 z[,k] <- m[, c[k]] + sdev[, , c[k]]%*%matrix(rnorm(2, mean = 0, sd = 1), nrow=2, ncol=1)
 #cat(k, "/", n, " observations simulated\n", sep="")
}

d<-2
# Set parameters of G0
hyperG0 <- list()
hyperG0[["mu"]] <- rep(0,d)
hyperG0[["kappa"]] <- 0.001
hyperG0[["nu"]] <- d+2
hyperG0[["lambda"]] <- diag(d)/10

# hyperprior on the Scale parameter of DPM
a <- 0.0001
b <- 0.0001

# Number of iterations
N <- 30

# do some plots
doPlot <- TRUE
nbclust_init <- 20



## Data
########
library(ggplot2)
p <- (ggplot(data.frame("X"=z[1,], "Y"=z[2,]), aes(x=X, y=Y))
      + geom_point()
      + ggtitle("Toy example Data"))
p



if(interactive()){
# Gibbs sampler for Dirichlet Process Mixtures
##############################################

MCMCsample <- DPMGibbsN(z, hyperG0, a, b, N=1500, doPlot, nbclust_init, plotevery=200,
                        gg.add=list(theme_bw(),
                                 guides(shape=guide_legend(override.aes = list(fill="grey45")))),
                        diagVar=FALSE)

s <- summary(MCMCsample, posterior_approx=TRUE, burnin = 1000, thin=5)
F1 <- FmeasureC(pred=s$point_estim$c_est, ref=c)
F1


MCMCsample2 <- DPMGibbsN_SeqPrior(z, prior_inform=s$param_posterior,
                                  hyperG0, N=1500,
                                  add.vagueprior = TRUE,
                                  doPlot=TRUE, plotevery=100,
                                  nbclust_init=nbclust_init,
                                  gg.add=list(theme_bw(),
                                 guides(shape=guide_legend(override.aes = list(fill="grey45")))),
                                  diagVar=FALSE)


s2 <- summary(MCMCsample2, burnin = 500, thin=5)
F2 <- FmeasureC(pred=s2$point_estim$c_est, ref=c)
F2
}