DPMGibbsN_SeqPrior: Slice Sampling of Dirichlet Process Mixture of Gaussian distibutions

Description

Slice Sampling of Dirichlet Process Mixture of Gaussian distibutions

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

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.

number of MCMC iterations.

nbclust_init

number of clusters at initialisation. Default to 30 (or less if there are less than 30 observations).

add.vagueprior

logical flag indicating wether 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 wether 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 wether 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 wether 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 itertations
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, Thiebaut R, Sequential Dirichlet Process Mixtures of Multivariate Skew t-distributions for Model-based Clustering of Flow Cytometry Data, in preparation.

Examples

Run this code

rm(list=ls())
#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



# 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