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Posterior estimation for Dirichlet process mixture of multivariate (potentially skew) distributions models

Source: R/DPMpost.R
DPMpost.Rd

Partially collapse slice Gibbs sampling for Dirichlet process mixture of multivariate normal, skew normal or skew t distributions.

Usage

DPMpost(
  data,
  hyperG0,
  a = 1e-04,
  b = 1e-04,
  N,
  doPlot = TRUE,
  nbclust_init = 30,
  plotevery = floor(N/10),
  diagVar = TRUE,
  verbose = TRUE,
  distrib = c("gaussian", "skewnorm", "skewt"),
  ncores = 1,
  type_connec = "SOCK",
  informPrior = NULL,
  ...
)

Arguments

data

data matrix d x n with d dimensions in rows and n observations in columns.

hyperG0

prior mixing distribution.

a

shape hyperparameter of the Gamma prior on the concentration parameter of the Dirichlet Process. Default is 0.0001.

b

scale hyperparameter of the Gamma prior on the concentration parameter of the Dirichlet Process. Default is 0.0001. If 0, then the concentration is fixed set to a.

N

number of MCMC iterations.

doPlot

logical flag indicating whether to plot MCMC iteration or not. Default to TRUE.

nbclust_init

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

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.

distrib

the distribution used for the clustering. Current possibilities are "gaussian", "skewnorm" and "skewt".

ncores

number of cores to use.

type_connec

The type of connection between the processors. Supported cluster types are "SOCK", "FORK", "MPI", and "NWS". See also makeCluster.

informPrior

an optional informative prior such as the approximation computed by summary.DPMMclust.

...

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]]

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:

a list of length N containing the weights of each mixture component for each MCMC iterations

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

hyperG0:

the prior on the cluster location

Details

This function is a wrapper around the following functions: DPMGibbsN, DPMGibbsN_parallel, DPMGibbsN_SeqPrior, DPMGibbsSkewN, DPMGibbsSkewN_parallel, DPMGibbsSkewT, DPMGibbsSkewT_parallel, DPMGibbsSkewT_SeqPrior, DPMGibbsSkewT_SeqPrior_parallel.

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

See also

summary.DPMMclust

Author

Boris Hejblum

Examples

#rm(list=ls())
set.seed(123)

# Exemple in 2 dimensions with skew-t distributions

# Generate data:
n <- 2000 # number of data points
d <- 2 # dimensions
ncl <- 4 # number of true clusters
sdev <- array(dim=c(d,d,ncl))
xi <- matrix(nrow=d, ncol=ncl, c(-1.5, 1.5, 1.5, 1.5, 2, -2.5, -2.5, -3))
psi <- matrix(nrow=d, ncol=4, c(0.3, -0.7, -0.8, 0, 0.3, -0.7, 0.2, 0.9))
nu <- c(100,25,8,5)
proba <- c(0.15, 0.05, 0.5, 0.3) # cluster frequencies
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, 0, 0.2))
sdev[, ,4] <- .3*diag(2)
c <- rep(0,n)
w <- rep(1,n)
z <- matrix(0, nrow=d, ncol=n)
for(k in 1:n){
 c[k] = which(rmultinom(n=1, size=1, prob=proba)!=0)
 w[k] <- rgamma(1, shape=nu[c[k]]/2, rate=nu[c[k]]/2)
 z[,k] <- xi[, c[k]] + psi[, c[k]]*rtruncnorm(n=1, a=0, b=Inf, mean=0, sd=1/sqrt(w[k])) +
               (sdev[, , c[k]]/sqrt(w[k]))%*%matrix(rnorm(d, mean = 0, sd = 1), nrow=d, ncol=1)
}

# Define hyperprior
hyperG0 <- list()
hyperG0[["b_xi"]] <- rowMeans(z)
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(apply(z,MARGIN=1, FUN=var))/3


if(interactive()){
# Plot data
cytoScatter(z)

# Estimate posterior
MCMCsample_st <- DPMpost(data=z, hyperG0=hyperG0, N=2000,
   distrib="skewt",
   gg.add=list(ggplot2::theme_bw(),
      ggplot2::guides(shape=ggplot2::guide_legend(override.aes = list(fill="grey45"))))
 )
 s <- summary(MCMCsample_st, burnin = 1600, thin=5, lossFn = "Binder")
 s
 plot(s)
 #plot(s, hm=TRUE) # this can take a few sec...
 
 
 # more data plotting:
 library(ggplot2)
 p <- (ggplot(data.frame("X"=z[1,], "Y"=z[2,]), aes(x=X, y=Y))
       + geom_point()
       + ggtitle("Unsupervised data")
       + xlab("D1")
       + ylab("D2")
       + theme_bw()
 )
 p

 c2plot <- factor(c)
 levels(c2plot) <- c("4", "1", "3", "2")
 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("True clusters")
       + xlab("D1")
       + ylab("D2")
       + theme_bw()
       + scale_colour_discrete(guide=guide_legend(override.aes = list(size = 6, shape=22)))
 )
 pp
}




# Exemple in 2 dimensions with Gaussian distributions

set.seed(1234)

# Generate data 
n <- 2000 # number of data points
d <- 2 # dimensions
ncl <- 4 # number of true clusters
m <- matrix(nrow=2, ncol=4, c(-1, 1, 1.5, 2, 2, -2, -1.5, -2)) # cluster means
sdev <- array(dim=c(2, 2, 4)) # cluster standard-deviations
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)
proba <- c(0.15, 0.05, 0.5, 0.3) # cluster frequencies
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=proba)!=0)
 z[,k] <- m[, c[k]] + sdev[, , c[k]]%*%matrix(rnorm(2, mean = 0, sd = 1), nrow=2, ncol=1)
}

# Define hyperprior
hyperG0 <- list()
hyperG0[["mu"]] <- rep(0,d)
hyperG0[["kappa"]] <- 0.001
hyperG0[["nu"]] <- d+2
hyperG0[["lambda"]] <- diag(d)


if(interactive()){
# Plot data
cytoScatter(z)

# Estimate posterior
MCMCsample_n <- DPMpost(data=z, hyperG0=hyperG0, N=2000,
   distrib="gaussian", diagVar=FALSE,
   gg.add=list(ggplot2::theme_bw(),
      ggplot2::guides(shape=ggplot2::guide_legend(override.aes = list(fill="grey45"))))
 )
 s <- summary(MCMCsample_n, burnin = 1500, thin=5, lossFn = "Binder")
 s
 plot(s)
 #plot(s, hm=TRUE) # this can take a few sec...
 
 
 # more data plotting:
 library(ggplot2)
 p <- (ggplot(data.frame("X"=z[1,], "Y"=z[2,]), aes(x=X, y=Y))
       + geom_point()
       + ggtitle("Unsupervised data")
       + xlab("D1")
       + ylab("D2")
       + theme_bw()
 )
 p

 c2plot <- factor(c)
 levels(c2plot) <- c("4", "1", "3", "2")
 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)))
       + ggtitle("True clusters")
 )
 pp
}