Bayesian Nonparametrics for Automatic Gating of Flow Cytometry data

Description

Dirichlet process mixture of multivariate normal, skew normal or skew t-distributions modeling oriented towards flow-cytometry data pre-processing applications.

Details

The main function in this package is DPMpost.

Author(s)

Boris P. Hejblum, Chariff Alkhassim, Francois Caron — Maintainer: Boris P. 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> https://arxiv.org/abs/1702.04407 doi:10.1214/18-AOAS1209

See Also

Useful links:

• http://sistm.github.io/NPflow/

• Report bugs at https://github.com/sistm/NPflow/issues

Slice Sampling of the Dirichlet Process Mixture Model with a prior on alpha

Description

Slice Sampling of the Dirichlet Process Mixture Model with a prior on alpha

Usage

DPMGibbsN(
  z,
  hyperG0,
  a = 1e-04,
  b = 1e-04,
  N,
  doPlot = TRUE,
  nbclust_init = 30,
  plotevery = N/10,
  diagVar = TRUE,
  use_variance_hyperprior = TRUE,
  verbose = TRUE,
  ...
)

Arguments

Value

a object of class DPMclust with the following attributes:

Author(s)

Boris Hejblum

Examples

rm(list=ls())
#Number of data
n <- 500
d <- 4
#n <- 2000
set.seed(1234)
#set.seed(123)
#set.seed(4321)

# Sample data
m <- matrix(nrow=d, ncol=4, c(-1, 1, 1.5, 2, 2, -2, -1.5, -2))
p <- c(0.2, 0.1, 0.4, 0.3) # frequence des clusters

sdev <- array(dim=c(d,d,4))
sdev[, ,1] <- 0.3*diag(d)
sdev[, ,2] <- c(0.1, 0.3)*diag(d)
sdev[, ,3] <- matrix(nrow=d, ncol=d, 0.15)
diag(sdev[, ,3]) <- 0.3
sdev[, ,4] <- 0.3*diag(d)
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] <- m[, c[k]] + 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[["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 <- 30



 ## 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


 ## 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", bins=30)
       + geom_density(alpha=.6, fill="red", color=NA)
       + ggtitle(paste("Prior distribution on alpha: Gamma(", a,
                 ",", b, ")\n", sep=""))
       + theme_bw()
      )
 p


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

 MCMCsample <- DPMGibbsN(z, hyperG0, a, b, N=500, doPlot, nbclust_init, plotevery=100,
                         gg.add=list(theme_bw(),
                                 guides(shape=guide_legend(override.aes = list(fill="grey45")))),
                         diagVar=FALSE)

 plot_ConvDPM(MCMCsample, from=2)

 s <- summary(MCMCsample, burnin = 200, thin=2, posterior_approx=FALSE,
 lossFn = "MBinderN")

 F <- FmeasureC(pred=s$point_estim$c_est, ref=c)

 postalpha <- data.frame("alpha"=MCMCsample$alpha[50:500],
                         "distribution" = factor(rep("posterior",500-49),
                         levels=c("prior", "posterior")))
 p <- (ggplot(postalpha, aes(x=alpha))
       + geom_histogram(aes(y=..density..), binwidth=.1,
                        colour="black", fill="white")
       + geom_density(alpha=.2, fill="blue")
       + ggtitle("Posterior distribution of alpha\n")
       # Ignore NA values for mean
       # Overlay with transparent density plot
       + geom_vline(aes(xintercept=mean(alpha, na.rm=TRUE)),
                    color="red", linetype="dashed", size=1)
     )
 p

 p <- (ggplot(drop=FALSE, alpha=.6)
       + geom_density(aes(x=alpha, fill=distribution),
                      color=NA, alpha=.6,
                      data=prioralpha)
       #+ geom_density(aes(x=alpha, fill=distribution),
       #               color=NA, alpha=.6,
       #               data=postalpha)
       + ggtitle("Prior and posterior distributions of alpha\n")
       + scale_fill_discrete(drop=FALSE)
       + theme_bw()
       +xlim(0,10)
       +ylim(0, 1.3)
     )
 p

}

# k-means comparison
####################

 plot(x=z[1,], y=z[2,], col=kmeans(t(z), centers=4)$cluster,
      xlab = "d = 1", ylab= "d = 2", main="k-means with K=4 clusters")

 KM <- kmeans(t(z), centers=4)
 dataKM <- data.frame("X"=z[1,], "Y"=z[2,],
                    "Cluster"=as.character(KM$cluster))
 dataCenters <- data.frame("X"=KM$centers[,1],
                           "Y"=KM$centers[,2],
                           "Cluster"=rownames(KM$centers))

 p <- (ggplot(dataKM)
       + geom_point(aes(x=X, y=Y, col=Cluster))
       + geom_point(aes(x=X, y=Y, fill=Cluster, order=Cluster),
                    data=dataCenters, shape=22, size=5)
       + scale_colour_discrete(name="Cluster")
       + ggtitle("K-means with K=4 clusters\n"))
 p

Slice Sampling of Dirichlet Process Mixture of Gaussian distributions

Description

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

Value

a object of class DPMclust with the following attributes:

Author(s)

Boris Hejblum, Chariff Alkhassim

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

postProcess.DPMMclust DPMGibbsN

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
}

Slice Sampling of the Dirichlet Process Mixture Model with a prior on alpha

Description

Slice Sampling of the Dirichlet Process Mixture Model with a prior on alpha

Usage

DPMGibbsN_parallel(
  Ncpus,
  type_connec,
  z,
  hyperG0,
  a = 1e-04,
  b = 1e-04,
  N,
  doPlot = TRUE,
  nbclust_init = 30,
  plotevery = N/10,
  diagVar = TRUE,
  use_variance_hyperprior = TRUE,
  verbose = TRUE,
  monitorfile = "",
  ...
)

Arguments

Value

a object of class DPMclust with the following attributes:

Author(s)

Boris Hejblum

See Also

DPMGibbsN

Examples

# Scaling up: ----
rm(list=ls())
#Number of data
n <- 2000
set.seed(1234)

# Sample data
d <- 3
nclust <- 5
m <- matrix(nrow=d, ncol=nclust, runif(d*nclust)*8)
# p: cluster probabilities
p <- runif(nclust)
p <- p/sum(p)

# Covariance matrix of the clusters
sdev <- array(dim=c(d, d, nclust))
for (j in 1:nclust){
    sdev[, ,j] <- matrix(NA, nrow=d, ncol=d)
    diag(sdev[, ,j]) <- abs(rnorm(n=d, mean=0.3, sd=0.1))
    sdev[, ,j][lower.tri(sdev[, ,j], diag = FALSE)] <- rnorm(n=d*(d-1)/2,
    mean=0, sd=0.05)
    sdev[, ,j][upper.tri(sdev[, ,j], diag = FALSE)] <- (sdev[, ,j][
                                                        lower.tri(sdev[, ,j], diag = FALSE)])
}
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] <- m[, c[k]] + sdev[, , c[k]]%*%matrix(rnorm(d, mean = 0, sd = 1), nrow=d, ncol=1)
    #cat(k, "/", n, " observations simulated\n", sep="")
}

# hyperprior on the Scale parameter of DPM
a <- 0.001
b <- 0.001

# Number of iterations
N <- 25

# do some plots
doPlot <- TRUE

# Set parameters of G0
hyperG0 <- list()
hyperG0[["mu"]] <- rep(0, d)
hyperG0[["kappa"]] <- 0.01
hyperG0[["nu"]] <- d + 2
hyperG0[["lambda"]] <- diag(d)/10


nbclust_init <- 30

if(interactive()){
 library(doParallel)
 MCMCsample <- DPMGibbsN_parallel(Ncpus=2, type_connec="FORK", z, hyperG0, a, b, 
                                  N=1000, doPlot=FALSE, nbclust_init=30, 
                                  plotevery=100, gg.add=list(ggplot2::theme_bw(),
                                  ggplot2::guides(shape = 
                                    ggplot2::guide_legend(override.aes = list(fill="grey45")))),
                                  diagVar=FALSE)
}

Slice Sampling of Dirichlet Process Mixture of skew normal distributions

Description

Slice Sampling of Dirichlet Process Mixture of skew normal distributions

Usage

DPMGibbsSkewN(
  z,
  hyperG0,
  a = 1e-04,
  b = 1e-04,
  N,
  doPlot = TRUE,
  nbclust_init = 30,
  plotevery = N/10,
  diagVar = TRUE,
  use_variance_hyperprior = TRUE,
  verbose = TRUE,
  ...
)

Arguments

Value

a object of class DPMclust with the following attributes:

Author(s)

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

Examples

rm(list=ls())

#Number of data
n <- 1000
set.seed(123)

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))
xi <- matrix(nrow=d, ncol=ncl, c(-0.5, 0, 0.5, 0, 0.5, -1, -1, 1))
##xi <- matrix(nrow=d, ncol=ncl, c(-0.3, 0, 0.5, 0.5, 0.5, -1.2, -1, 1))
psi <- matrix(nrow=d, ncol=4, c(0.4, -0.6, 0.8, 0, 0.3, -0.7, -0.3, -1.2))
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"]] <- 0.0001
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_sn <- DPMGibbsSkewN(z, hyperG0, a, b, N=2500,
                                doPlot, nbclust_init, plotevery=200,
                                gg.add=list(theme_bw(),
                                 guides(shape=guide_legend(override.aes = list(fill="grey45")))),
                               diagVar=FALSE)

 s <- summary(MCMCsample_sn, burnin = 2000, thin=10)
 #cluster_est_binder(MCMCsample_sn$mcmc_partitions[1000:1500])
 print(s)
 plot(s)
 #plot_ConvDPM(MCMCsample_sn, from=2)






 # k-means

 plot(x=z[1,], y=z[2,], col=kmeans(t(z), centers=4)$cluster,
      xlab = "d = 1", ylab= "d = 2", main="k-means with K=4 clusters")

 KM <- kmeans(t(z), centers=4)
 KMclust <- factor(KM$cluster)
 levels(KMclust) <- c("2", "4", "1", "3")
 dataKM <- data.frame("X"=z[1,], "Y"=z[2,],
                    "Cluster"=as.character(KMclust))
 dataCenters <- data.frame("X"=KM$centers[,1],
                           "Y"=KM$centers[,2],
                           "Cluster"=c("2", "4", "1", "3"))


 p <- (ggplot(dataKM)
       + geom_point(aes(x=X, y=Y, col=Cluster))
       + geom_point(aes(x=X, y=Y, fill=Cluster, order=Cluster),
                    data=dataCenters, shape=22, size=5)
       + scale_colour_discrete(name="Cluster",
                               guide=guide_legend(override.aes=list(size=6, shape=22)))
       + ggtitle("K-means with K=4 clusters\n")
       + theme_bw()
 )
 p

 postalpha <- data.frame("alpha"=MCMCsample_sn$alpha[501:1000],
                         "distribution" = factor(rep("posterior",1000-500),
                         levels=c("prior", "posterior")))

 postK <- data.frame("K"=sapply(lapply(postalpha$alpha, "["),
                                function(x){sum(x/(x+0:(1000-1)))}))

 p <- (ggplot(postalpha, aes(x=alpha))
       + geom_histogram(aes(y=..density..), binwidth=.1,
                        colour="black", fill="white")
       + geom_density(alpha=.2, fill="blue")
       + ggtitle("Posterior distribution of alpha\n")
       # Ignore NA values for mean
       # Overlay with transparent density plot
       + geom_vline(aes(xintercept=mean(alpha, na.rm=T)),
                    color="red", linetype="dashed", size=1)
     )
 p

 p <- (ggplot(postK, aes(x=K))
       + geom_histogram(aes(y=..density..),
                        colour="black", fill="white")
       + geom_density(alpha=.2, fill="blue")
       + ggtitle("Posterior distribution of predicted K\n")
       # Ignore NA values for mean
       # Overlay with transparent density plot
       + geom_vline(aes(xintercept=mean(K, na.rm=T)),
                    color="red", linetype="dashed", size=1)
       #+ scale_x_continuous(breaks=c(0:6)*2, minor_breaks=c(0:6)*2+1)
       + scale_x_continuous(breaks=c(1:12))
     )
 p

 p <- (ggplot(drop=FALSE, alpha=.6)
       + geom_density(aes(x=alpha, fill=distribution),
                      color=NA, alpha=.6,
                      data=postalpha)
       + geom_density(aes(x=alpha, fill=distribution),
                      color=NA, alpha=.6,
                      data=prioralpha)
       + ggtitle("Prior and posterior distributions of alpha\n")
       + scale_fill_discrete(drop=FALSE)
       + theme_bw()
       + xlim(0,100)
     )
 p

#Skew Normal
n=100000
xi <- 0
d <- 0.995
alpha <- d/sqrt(1-d^2)
z <- rtruncnorm(n,a=0, b=Inf)
e <- rnorm(n, mean = 0, sd = 1)
x <- d*z + sqrt(1-d^2)*e
o <- 1
y <- xi+o*x
nu=1.3
w <- rgamma(n,scale=nu/2, shape=nu/2)
yy <- xi+o*x/w
snd <- data.frame("Y"=y,"YY"=yy)
p <- (ggplot(snd)+geom_density(aes(x=Y), fill="blue", alpha=.2)
     + theme_bw()
     + ylab("Density")
     + ggtitle("Y~SN(0,1,10)\n")
     + xlim(-1,6)
     + ylim(0,0.8)
     )
p

p <- (ggplot(snd)+geom_density(aes(x=YY), fill="blue", alpha=.2)
     + theme_bw()
     + ylab("Density")
     + ggtitle("Y~ST(0,1,10,1.3)\n")
     + xlim(-2,40)
     + ylim(0,0.8)
     )
p

p <- (ggplot(snd)
     + geom_density(aes(x=Y, fill="blue"), alpha=.2)
     + geom_density(aes(x=YY, fill="red"), alpha=.2)
     + theme_bw()
     +theme(legend.text = element_text(size = 13), legend.position="bottom")
     + ylab("Density")
     + xlim(-2,40)
     + ylim(0,0.8)
     + scale_fill_manual(name="", labels=c("Y~SN(0,1,10)       ", "Y~ST(0,1,10,1.3)"),
     guide="legend", values=c("blue", "red"))
     )
p

#Variations
n=100000
xi <- -1
d <- 0.995
alpha <- d/sqrt(1-d^2)
z <- rtruncnorm(n,a=0, b=Inf)
e <- rnorm(n, mean = 0, sd = 1)
x <- d*z + sqrt(1-d^2)*e
snd <- data.frame("X"=x)
p <- (ggplot(snd)+geom_density(aes(x=X), fill="blue", alpha=.2)
     + theme_bw()
     + ylab("Density")
     + ggtitle("X~SN(10)\n")
     + xlim(-1.5,4)
     + ylim(0,1.6)
     )
p

o <- 0.5
y <- xi+o*x
snd <- data.frame("Y"=y)
p <- (ggplot(snd)+geom_density(aes(x=Y), fill="blue", alpha=.2)
     + theme_bw()
     + ylab("Density")
     + ggtitle("Y~SN(-1,1,10)\n")
     + xlim(-1.5,4)
     + ylim(0,1.6)
     )
p




#Simple toy example
###################

n <- 500
set.seed(12345)


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, -1.2))
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)

#' # Set parameters of G0
hyperG0 <- list()
hyperG0[["b_xi"]] <- rep(0,d)
hyperG0[["b_psi"]] <- rep(0,d)
hyperG0[["kappa"]] <- 0.0001
hyperG0[["D_xi"]] <- 100
hyperG0[["D_psi"]] <- 100
hyperG0[["nu"]] <- d + 1
hyperG0[["lambda"]] <- diag(d)


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="")
}

 MCMCsample_sn_sep <- DPMGibbsSkewN(z, hyperG0, a, b, N=600,
                                    doPlot, nbclust_init, plotevery=100,
                                    gg.add=list(theme_bw(),
                               guides(shape=guide_legend(override.aes = list(fill="grey45")))),
                                    diagVar=TRUE)

 s <- summary(MCMCsample_sn, burnin = 400)

}

Parallel Implementation of Slice Sampling of Dirichlet Process Mixture of skew normal distributions

Description

If the monitorfile argument is a character string naming a file to write into, in the case of a new file that does not exist yet, such a new file will be created. A line is written at each MCMC iteration.

Usage

DPMGibbsSkewN_parallel(
  Ncpus,
  type_connec,
  z,
  hyperG0,
  a = 1e-04,
  b = 1e-04,
  N,
  doPlot = FALSE,
  nbclust_init = 30,
  plotevery = N/10,
  diagVar = TRUE,
  use_variance_hyperprior = TRUE,
  verbose = FALSE,
  monitorfile = "",
  ...
)

Arguments

Value

a object of class DPMclust with the following attributes:

Author(s)

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

Examples

rm(list=ls())
#Number of data
n <- 2000
set.seed(1234)

d <- 4
ncl <- 5

# Sample data

sdev <- array(dim=c(d,d,ncl))

xi <- matrix(nrow=d, ncol=ncl, c(runif(n=d*ncl,min=0,max=3)))
psi <- matrix(nrow=d, ncol=ncl, c(runif(n=d*ncl,min=-1,max=1)))
p <- runif(n=ncl)
p <- p/sum(p)
sdev0 <- diag(runif(n=d, min=0.05, max=0.6))
for (j in 1:ncl){
     sdev[, ,j] <- invwishrnd(n = d+2, lambda = sdev0)
}


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)/10

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

 # do some plots
 doPlot <- TRUE
 nbclust_init <- 30


 z <- z*200
 ## 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


 ## 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



 # Gibbs sampler for Dirichlet Process Mixtures
 ##############################################
 if(interactive()){
  MCMCsample_sn_par <- DPMGibbsSkewN_parallel(Ncpus=parallel::detectCores()-1,
                                              type_connec="SOCK", z, hyperG0,
                                              a, b, N=5000, doPlot, nbclust_init,
                                              plotevery=25, gg.add=list(theme_bw(),
                                guides(shape=guide_legend(override.aes = list(fill="grey45")))))
  plot_ConvDPM(MCMCsample_sn_par, from=2)
 }

Slice Sampling of Dirichlet Process Mixture of skew Student's t-distributions

Description

Slice Sampling of Dirichlet Process Mixture of skew Student's t-distributions

Usage

DPMGibbsSkewT(
  z,
  hyperG0,
  a = 1e-04,
  b = 1e-04,
  N,
  doPlot = TRUE,
  nbclust_init = 30,
  plotevery = N/10,
  diagVar = TRUE,
  use_variance_hyperprior = TRUE,
  verbose = TRUE,
  ...
)

Arguments

Value

a object of class DPMclust with the following attributes:

Author(s)

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

Fruhwirth-Schnatter S, Pyne S, Bayesian inference for finite mixtures of univariate and multivariate skew-normal and skew-t distributions, Biostatistics, 2010.

Examples

rm(list=ls())

#Number of data
n <- 2000
set.seed(4321)


d <- 2
ncl <- 4

# Sample data
library(truncnorm)

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))
#xi <- matrix(nrow=d, ncol=ncl, c(-0.5, 0, 0.5, 0, 0.5, -1, -1, 1))
xi <- matrix(nrow=d, ncol=ncl, c(-0.2, 0.5, 2.4, 0.4, 0.6, -1.3, -0.9, -2.7))
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)
p <- c(0.15, 0.05, 0.5, 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)
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=p)!=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)
 #cat(k, "/", n, " observations simulated\n", sep="")
}

# Set parameters of G0
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

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



 ## 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 #pdf(height=8.5, width=8.5)

 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))))
 pp #pdf(height=7, width=7.5)


 ## 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=1500,
                                doPlot=TRUE, nbclust_init=30, plotevery=100,
                               diagVar=FALSE)
 s <- summary(MCMCsample_st, burnin = 1000, thin=10, lossFn = "Binder")
 print(s)
 plot(s, hm=TRUE) #pdf(height=8.5, width=10.5) #png(height=700, width=720)
 plot_ConvDPM(MCMCsample_st, from=2)
 #cluster_est_binder(MCMCsample_st$mcmc_partitions[900:1000])
}

Slice Sampling of Dirichlet Process Mixture of skew Student's t-distributions

Description

Slice Sampling of Dirichlet Process Mixture of skew Student's t-distributions

Usage

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

Arguments

Value

a object of class DPMclust with the following attributes:

Author(s)

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

Examples

rm(list=ls())

#Number of data
n <- 2000
set.seed(123)


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))
nu <- c(100,15,8,5)
p <- c(0.15, 0.05, 0.5, 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)
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=p)!=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)
 #cat(k, "/", n, " observations simulated\n", sep="")
}

# Set parameters of G0
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

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

 # do some plots
 nbclust_init <- 30

 ## Plot Data
 library(ggplot2)
 q <- (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())
 q

if(interactive()){
 MCMCsample_st <- DPMGibbsSkewT(z, hyperG0, a, b, N=2000,
                                doPlot=TRUE, plotevery=250,
                                nbclust_init, diagVar=FALSE,
                                gg.add=list(theme_bw(),
                                 guides(shape=guide_legend(override.aes = list(fill="grey45")))))
 s <- summary(MCMCsample_st, burnin = 1500, thin=2, posterior_approx=TRUE)
 F <- FmeasureC(pred=s$point_estim$c_est, ref=c)

for(k in 1:n){
 c[k] = which(rmultinom(n=1, size=1, prob=p)!=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)
 cat(k, "/", n, " observations simulated\n", sep="")
}
 MCMCsample_st2 <- DPMGibbsSkewT_SeqPrior(z, prior=s$param_posterior,
                                          hyperG0, N=2000,
                                          doPlot=TRUE, plotevery=100,
                                          nbclust_init, diagVar=FALSE,
                                          gg.add=list(theme_bw(),
                                 guides(shape=guide_legend(override.aes = list(fill="grey45")))))
s2 <- summary(MCMCsample_st2, burnin = 1500, thin=5)
F2 <- FmeasureC(pred=s2$point_estim$c_est, ref=c)

# MCMCsample_st2_par <- DPMGibbsSkewT_SeqPrior_parallel(Ncpus= 2, type_connec="SOCK",
#                                                       z, prior_inform=s$param_posterior,
#                                                       hyperG0, N=2000,
#                                                       doPlot=TRUE, plotevery=50,
#                                                       nbclust_init, diagVar=FALSE,
#                                                       gg.add=list(theme_bw(),
#                                  guides(shape=guide_legend(override.aes = list(fill="grey45"))))
}

Slice Sampling of Dirichlet Process Mixture of skew Student's t-distributions

Description

Slice Sampling of Dirichlet Process Mixture of skew Student's t-distributions

Usage

DPMGibbsSkewT_SeqPrior_parallel(
  Ncpus,
  type_connec,
  z,
  prior_inform,
  hyperG0,
  N,
  nbclust_init,
  add.vagueprior = TRUE,
  weightnoninfo = NULL,
  doPlot = FALSE,
  plotevery = N/10,
  diagVar = TRUE,
  verbose = TRUE,
  monitorfile = "",
  ...
)

Arguments

Value

a object of class DPMclust with the following attributes:

Author(s)

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

Examples

rm(list=ls())

#Number of data
n <- 2000
set.seed(123)


d <- 2
ncl <- 4

# Sample data

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(0.4, -0.6, 0.8, 0, 0.3, -0.7, -0.3, -0.8))
xi <- matrix(nrow=d, ncol=ncl, c(-0.2, 0.5, 2.4, 0.4, 0.6, -1.3, -0.9, -2.7))
psi <- matrix(nrow=d, ncol=4, c(0.3, -0.7, -0.8, 0, 0.3, -0.7, 0.2, 0.9))
nu <- c(100,15,8,5)
p <- c(0.15, 0.05, 0.5, 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)
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=p)!=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)
 #cat(k, "/", n, " observations simulated\n", sep="")
}

# Set parameters of G0
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

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

 # do some plots
 nbclust_init <- 30

 ## Plot Data
 library(ggplot2)
 q <- (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())
 q

if(interactive()){
 MCMCsample_st <- DPMGibbsSkewT(z, hyperG0, a, b, N=2000,
                                doPlot=TRUE, plotevery=250,
                                nbclust_init,
                                gg.add=list(theme_bw(),
                                 guides(shape=guide_legend(override.aes = list(fill="grey45")))),
                                diagVar=FALSE)
 s <- summary(MCMCsample_st, burnin = 1500, thin=5, posterior_approx=TRUE)
 F <- FmeasureC(pred=s$point_estim$c_est, ref=c)

for(k in 1:n){
 c[k] = which(rmultinom(n=1, size=1, prob=p)!=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)
 #cat(k, "/", n, " observations simulated\n", sep="")
}
MCMCsample_st2 <- DPMGibbsSkewT_SeqPrior_parallel(Ncpus=2, type_connec="SOCK",
                                                  z, prior_inform=s$param_posterior,
                                                  hyperG0, N=3000,
                                                  doPlot=TRUE, plotevery=100,
                                                  nbclust_init, diagVar=FALSE, verbose=FALSE,
                                                  gg.add=list(theme_bw(),
                                 guides(shape=guide_legend(override.aes = list(fill="grey45")))))
s2 <- summary(MCMCsample_st2, burnin = 2000, thin=5)
F2 <- FmeasureC(pred=s2$point_estim$c_est, ref=c)
}

Slice Sampling of Dirichlet Process Mixture of skew Student's t-distributions

Description

Slice Sampling of Dirichlet Process Mixture of skew Student's t-distributions

Usage

DPMGibbsSkewT_parallel(
  Ncpus,
  type_connec,
  z,
  hyperG0,
  a = 1e-04,
  b = 1e-04,
  N,
  doPlot = FALSE,
  nbclust_init = 30,
  plotevery = N/10,
  diagVar = TRUE,
  use_variance_hyperprior = TRUE,
  verbose = FALSE,
  monitorfile = "",
  ...
)

Arguments

Value

a object of class DPMclust with the following attributes:

Author(s)

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

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])
}

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

Description

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

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.

Value

a object of class DPMclust with the following attributes:

Author(s)

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

See Also

summary.DPMMclust

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
}

Compute a limited F-measure

Description

A limited version of F-measure that only takes into account small clusters

Usage

Flimited(n_small_clst, pred, ref)

Arguments

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

Examples

pred <- c(rep(1, 5),rep(2, 8),rep(3,10))
ref <- c(rep(1, 5),rep(c(2,3), 4),rep(c(3,2),5))
FmeasureC(pred, ref)
Flimited(6, pred, ref)

C++ implementation of the F-measure computation

Description

C++ implementation of the F-measure computation

Usage

FmeasureC(pred, ref)

Arguments

Examples

pred <- c(1,1,2,3,2,3)
ref <- c(2,2,1,1,1,3)
FmeasureC(pred, ref)

C++ implementation of the F-measure computation without the reference class 0

Description

Aghaeepour in FlowCAP 1 ignore the reference class labeled "0"

Usage

FmeasureC_no0(pred, ref)

Arguments

References

N Aghaeepour, G Finak, H Hoos, TR Mosmann, RR Brinkman, R Gottardo, RH Scheuermann, Critical assessment of automated flow cytometry data analysis techniques, Nature Methods, 10(3):228-38, 2013.

Examples

library(NPflow)
pred <- c(1,1,2,3,2,3)
ref <- c(2,2,0,0,0,3)
FmeasureC(pred, ref)
FmeasureC_no0(pred, ref)

Multiple cost computations with the F-measure as the loss function

Description

C++ implementation of multiple cost computations with the F-measure as the loss function using the Armadillo library

Usage

Fmeasure_costC(c)

Arguments

Value

a list with the following elements:

Examples

library(NPflow)
c <- list(c(1,1,2,3,2,3), c(1,1,1,2,3,3),c(2,2,1,1,1,1))
#Fmeasure_costC(sapply(c, "["))

if(interactive()){
c2 <- list()
for(i in 1:100){
    c2 <- c(c2, list(rmultinom(n=1, size=2000, prob=rexp(n=2000))))
}
Fmeasure_costC(sapply(c2, "["))
}

EM MAP for mixture of sNiW

Description

Maximum A Posteriori (MAP) estimation of mixture of Normal inverse Wishart distributed observations with an EM algorithm

Usage

MAP_sNiW_mmEM(
  xi_list,
  psi_list,
  S_list,
  hyperG0,
  init = NULL,
  K,
  maxit = 100,
  tol = 0.1,
  doPlot = TRUE,
  verbose = TRUE
)

MAP_sNiW_mmEM_weighted(
  xi_list,
  psi_list,
  S_list,
  obsweight_list,
  hyperG0,
  K,
  maxit = 100,
  tol = 0.1,
  doPlot = TRUE,
  verbose = TRUE
)

MAP_sNiW_mmEM_vague(
  xi_list,
  psi_list,
  S_list,
  hyperG0,
  K = 10,
  maxit = 100,
  tol = 0.1,
  doPlot = TRUE,
  verbose = TRUE
)

Arguments

Details

MAP_sNiW_mmEM provides an estimation for the MAP of mixtures of Normal inverse Wishart distributed observations. MAP_sNiW_mmEM_vague provides an estimates incorporating a vague component in the mixture. MAP_sNiW_mmEM_weighted provides a weighted version of the algorithm.

Author(s)

Boris Hejblum, Chariff Alkhassim

Examples

set.seed(1234)
hyperG0 <- list()
hyperG0$b_xi <- c(0.3, -1.5)
hyperG0$b_psi <- c(0, 0)
hyperG0$kappa <- 0.001
hyperG0$D_xi <- 100
hyperG0$D_psi <- 100
hyperG0$nu <- 20
hyperG0$lambda <- diag(c(0.25,0.35))

hyperG0 <- list()
hyperG0$b_xi <- c(1, -1.5)
hyperG0$b_psi <- c(0, 0)
hyperG0$kappa <- 0.1
hyperG0$D_xi <- 1
hyperG0$D_psi <- 1
hyperG0$nu <- 2
hyperG0$lambda <- diag(c(0.25,0.35))

xi_list <- list()
psi_list <- list()
S_list <- list()
w_list <- list()

for(k in 1:200){
 NNiW <- rNNiW(hyperG0, diagVar=FALSE)
 xi_list[[k]] <- NNiW[["xi"]]
 psi_list[[k]] <- NNiW[["psi"]]
 S_list[[k]] <- NNiW[["S"]]
 w_list [[k]] <- 0.75
}


hyperG02 <- list()
hyperG02$b_xi <- c(-1, 2)
hyperG02$b_psi <- c(-0.1, 0.5)
hyperG02$kappa <- 0.1
hyperG02$D_xi <- 1
hyperG02$D_psi <- 1
hyperG02$nu <- 4
hyperG02$lambda <- 0.5*diag(2)

for(k in 201:400){
 NNiW <- rNNiW(hyperG02, diagVar=FALSE)
 xi_list[[k]] <- NNiW[["xi"]]
 psi_list[[k]] <- NNiW[["psi"]]
 S_list[[k]] <- NNiW[["S"]]
 w_list [[k]] <- 0.25

}

map <- MAP_sNiW_mmEM(xi_list, psi_list, S_list, hyperG0, K=2, tol=0.1)

EM MLE for mixture of NiW

Description

Maximum likelihood estimation of mixture of Normal inverse Wishart distributed observations with an EM algorithm

Usage

MLE_NiW_mmEM(
  mu_list,
  S_list,
  hyperG0,
  K,
  maxit = 100,
  tol = 0.1,
  doPlot = TRUE
)

Arguments

Examples

set.seed(123)
U_mu <- list()
U_Sigma <- list()
U_nu<-list()
U_kappa<-list()

d <- 2
hyperG0 <- list()
hyperG0[["mu"]] <- rep(1,d)
hyperG0[["kappa"]] <- 0.01
hyperG0[["nu"]] <- d+1
hyperG0[["lambda"]] <- diag(d)

for(k in 1:200){

  NiW <- rNiW(hyperG0, diagVar=FALSE)
  U_mu[[k]] <-NiW[["mu"]]
  U_Sigma[[k]] <-NiW[["S"]]
}


hyperG02 <- list()
hyperG02[["mu"]] <- rep(2,d)
hyperG02[["kappa"]] <- 1
hyperG02[["nu"]] <- d+10
hyperG02[["lambda"]] <- diag(d)/10

for(k in 201:400){

  NiW <- rNiW(hyperG02, diagVar=FALSE)
  U_mu[[k]] <-NiW[["mu"]]
  U_Sigma[[k]] <-NiW[["S"]]
}


mle <- MLE_NiW_mmEM( U_mu, U_Sigma, hyperG0, K=2)

hyperG0[["mu"]]
hyperG02[["mu"]]
mle$U_mu

hyperG0[["lambda"]]
hyperG02[["lambda"]]
mle$U_lambda

hyperG0[["nu"]]
hyperG02[["nu"]]
mle$U_nu

hyperG0[["kappa"]]
hyperG02[["kappa"]]
mle$U_kappa

MLE for Gamma distribution

Description

Maximum likelihood estimation of Gamma distributed observations distribution parameters

Usage

MLE_gamma(g)

Arguments

Examples

g_list <- list()
for(i in 1:1000){
 g_list <- c(g_list, rgamma(1, shape=100, rate=5))
}

mle <- MLE_gamma(g_list)
mle

MLE for sNiW distributed observations

Description

Maximum likelihood estimation of Normal inverse Wishart distributed observations

Usage

MLE_sNiW(xi_list, psi_list, S_list, doPlot = TRUE)

Arguments

Author(s)

Boris Hejblum, Chariff Alkhassim

Examples

hyperG0 <- list()
hyperG0$b_xi <- c(0.3, -1.5)
hyperG0$b_psi <- c(0, 0)
hyperG0$kappa <- 0.001
hyperG0$D_xi <- 100
hyperG0$D_psi <- 100
hyperG0$nu <- 35
hyperG0$lambda <- diag(c(0.25,0.35))

xi_list <- list()
psi_list <- list()
S_list <- list()
for(k in 1:1000){
 NNiW <- rNNiW(hyperG0, diagVar=FALSE)
 xi_list[[k]] <- NNiW[["xi"]]
 psi_list[[k]] <- NNiW[["psi"]]
 S_list[[k]] <- NNiW[["S"]]
}

mle <- MLE_sNiW(xi_list, psi_list, S_list)
mle

EM MLE for mixture of sNiW

Description

Maximum likelihood estimation of mixture of Normal inverse Wishart distributed observations with an EM algorithm

Usage

MLE_sNiW_mmEM(
  xi_list,
  psi_list,
  S_list,
  hyperG0,
  K,
  init = NULL,
  maxit = 100,
  tol = 0.1,
  doPlot = TRUE,
  verbose = TRUE
)

Arguments

Author(s)

Boris Hejblum, Chariff Alkhassim

Examples

set.seed(1234)
hyperG0 <- list()
hyperG0$b_xi <- c(0.3, -1.5)
hyperG0$b_psi <- c(0, 0)
hyperG0$kappa <- 0.001
hyperG0$D_xi <- 100
hyperG0$D_psi <- 100
hyperG0$nu <- 3
hyperG0$lambda <- diag(c(0.25,0.35))

xi_list <- list()
psi_list <- list()
S_list <- list()
for(k in 1:200){
 NNiW <- rNNiW(hyperG0, diagVar=FALSE)
 xi_list[[k]] <- NNiW[["xi"]]
 psi_list[[k]] <- NNiW[["psi"]]
 S_list[[k]] <- NNiW[["S"]]
}

hyperG02 <- list()
hyperG02$b_xi <- c(-1, 2)
hyperG02$b_psi <- c(-0.1, 0.5)
hyperG02$kappa <- 0.001
hyperG02$D_xi <- 10
hyperG02$D_psi <- 10
hyperG02$nu <- 3
hyperG02$lambda <- 0.5*diag(2)

for(k in 201:400){
 NNiW <- rNNiW(hyperG02, diagVar=FALSE)
 xi_list[[k]] <- NNiW[["xi"]]
 psi_list[[k]] <- NNiW[["psi"]]
 S_list[[k]] <- NNiW[["S"]]
}

mle <- MLE_sNiW_mmEM(xi_list, psi_list, S_list, hyperG0, K=2)

C++ implementation of similarity matrix computation using pre-computed distances

Description

C++ implementation of similarity matrix computation using pre-computed distances

Usage

NuMatParC(c, d)

Arguments

Author(s)

Boris Hejblum, Chariff Alkhassim

Examples

c <- c(1,1,2,3,2,3)
d <- matrix(runif(length(c)^2),length(c))
NuMatParC(c,d)

Burning MCMC iterations from a Dirichlet Process Mixture Model.

Description

Utility function for burning MCMC iteration from a DPMMclust object.

Usage

burn.DPMMclust(x, burnin = 0, thin = 1)

Arguments

Value

a DPMMclust object minus the burnt iterations

Author(s)

Boris Hejblum

See Also

summary.DPMMclust

Point estimate of the partition using the F-measure as the cost function.

Description

Get a point estimate of the partition using the F-measure as the cost function.

Usage

cluster_est_Fmeasure(c, logposterior)

Arguments

Value

a list:

Author(s)

Francois Caron, Boris Hejblum

See Also

similarityMat

Point estimate of the partition using a modified Binder loss function

Description

Get a point estimate of the partition using a modified Binder loss function for Gaussian components

Usage

cluster_est_Mbinder_norm(c, Mu, Sigma, lambda = 0, a = 1, b = a, logposterior)

Arguments

Details

Note that he current implementation only allows Gaussian components.

The modified Binder loss function takes into account the distance between mixture components using #'the Bhattacharyya distance.

Value

a list:

Author(s)

Chariff Alkhassim

References

JW Lau, PJ Green, Bayesian Model-Based Clustering Procedures, Journal of Computational and Graphical Statistics, 16(3):526-558, 2007.

DA Binder, Bayesian cluster analysis, Biometrika 65(1):31-38, 1978.

See Also

similarityMat similarityMatC similarityMat_nocostC

Point estimate of the partition for the Binder loss function

Description

Get a point estimate of the partition using the Binder loss function.

Usage

cluster_est_binder(c, logposterior)

Arguments

Value

a list:

c_est:

a vector of length n. Point estimate of the partition

cost:

a vector of length N. cost[j] is the cost associated to partition c[[j]]

similarity:

matrix of size n x n. Similarity matrix (see similarityMat)

opt_ind:

the index of the optimal partition among the MCMC iterations.

Author(s)

Francois Caron, Boris Hejblum

References

F Caron, YW Teh, TB Murphy, Bayesian nonparametric Plackett-Luce models for the analysis of preferences for college degree programmes, Annals of Applied Statistics, 8(2):1145-1181, 2014.

DB Dahl, Model-Based Clustering for Expression Data via a Dirichlet Process Mixture Model, Bayesian Inference for Gene Expression and Proteomics, K-A Do, P Muller, M Vannucci (Eds.), Cambridge University Press, 2006.

See Also

similarityMat similarityMatC

Gets a point estimate of the partition using posterior expected adjusted Rand index (PEAR)

Description

Gets a point estimate of the partition using posterior expected adjusted Rand index (PEAR)

Usage

cluster_est_pear(c)

Arguments

Value

a list:

Author(s)

Chariff Alkhassim

References

A. Fritsch, K. Ickstadt. Improved Criteria for Clustering Based on the Posterior Similarity Matrix, in Bayesian Analysis, Vol.4 : p.367-392 (2009)

See Also

similarityMat similarityMatC

Scatterplot of flow cytometry data

Description

Scatterplot of flow cytometry data

Usage

cytoScatter(
  cytomatrix,
  dims2plot = c(1, 2),
  gating = NULL,
  scale_log = FALSE,
  xlim = NULL,
  ylim = NULL,
  gg.add = list(theme())
)

Arguments

Examples

rm(list=ls())
#Number of data
n <- 500
#n <- 2000
set.seed(1234)
#set.seed(123)
#set.seed(4321)

# Sample data
m <- matrix(nrow=2, ncol=4, c(-1, 1, 1.5, 2, 2, -2, -1.5, -2))
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="")
}

cytoScatter(z)

ELoss of a partition point estimate compared to a gold standard

Description

Evaluate the loss of a point estimate of the partition compared to a gold standard according to a given loss function

Usage

evalClustLoss(c, gs, lossFn = "F-measure", a = 1, b = 1)

Arguments

Details

The cost of a point estimate partition is calculated using either a pairwise coincidence loss function (Binder), or 1-Fmeasure (F-measure).

Value

the cost of the point estimate c in regard of the gold standard gs for a given loss function.

Author(s)

Boris Hejblum

References

J.W. Lau & P.J. Green. Bayesian Model-Based Clustering Procedures, Journal of Computational and Graphical Statistics, 16(3): 526-558, 2007.

D. B. Dahl. Model-Based Clustering for Expression Data via a Dirichlet Process Mixture Model, in Bayesian Inference for Gene Expression and Proteomics, K.-A. Do, P. Muller, M. Vannucci (Eds.), Cambridge University Press, 2006.

See Also

similarityMat, cluster_est_binder

Sample from a inverse-Wishart distribution

Description

For internal use only.

Usage

invwishrnd(n, lambda)

Arguments

Multivariate log gamma function

Description

Multivariate log gamma function

Usage

lgamma_mv(x, p)

Arguments

multivariate Normal inverse Wishart probability density function for multiple inputs

Description

multivariate Normal inverse Wishart probability density function for multiple inputs

Usage

mmNiWpdf(mu, Sigma, U_mu0, U_kappa0, U_nu0, U_lambda0, Log = TRUE)

Arguments

Value

matrix of densities of dimension K x n

C++ implementation of multivariate Normal inverse Wishart probability density function for multiple inputs

Description

C++ implementation of multivariate Normal inverse Wishart probability density function for multiple inputs

Usage

mmNiWpdfC(Mu, Sigma, U_Mu0, U_Kappa0, U_Nu0, U_Sigma0, Log = TRUE)

Arguments

Value

matrix of densities of dimension K x n

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

Probability density function of multiple structured Normal inverse Wishart

Description

Probability density function of structured Normal inverse Wishart (sNiW) for multiple inputs, on the log scale.

Usage

mmsNiWlogpdf(U_xi, U_psi, U_Sigma, U_xi0, U_psi0, U_B0, U_Sigma0, U_df0)

Arguments

Examples

hyperG0 <- list()
hyperG0$b_xi <- c(-1.6983129, -0.4819131)
hyperG0$b_psi <- c(-0.0641866, -0.7606068)
hyperG0$kappa <- 0.001
hyperG0$D_xi <- 16.951313
hyperG0$D_psi <- 1.255192
hyperG0$nu <- 27.67656
hyperG0$lambda <- matrix(c(2.3397761, -0.3975259,-0.3975259, 1.9601773), ncol=2)

xi_list <- list()
psi_list <- list()
S_list <- list()
for(k in 1:1000){
 NNiW <- rNNiW(hyperG0, diagVar=FALSE)
 xi_list[[k]] <- NNiW[["xi"]]
 psi_list[[k]] <- NNiW[["psi"]]
 S_list[[k]] <- NNiW[["S"]]
}
mmsNiWlogpdf(U_xi=xi_list, U_psi=psi_list, U_Sigma=S_list,
            U_xi0=list(hyperG0$b_xi), U_psi0=list(hyperG0$b_psi) ,
            U_B0=list(diag(c(hyperG0$D_xi, hyperG0$D_psi))) ,
            U_Sigma0=list(hyperG0$lambda), U_df0=list(hyperG0$nu))


hyperG0 <- list()
hyperG0$b_xi <- c(-1.6983129)
hyperG0$b_psi <- c(-0.0641866)
hyperG0$kappa <- 0.001
hyperG0$D_xi <- 16.951313
hyperG0$D_psi <- 1.255192
hyperG0$nu <- 27.67656
hyperG0$lambda <- matrix(c(2.3397761), ncol=1)
#'xi_list <- list()
psi_list <- list()
S_list <- list()
for(k in 1:1000){
 NNiW <- rNNiW(hyperG0, diagVar=FALSE)
 xi_list[[k]] <- NNiW[["xi"]]
 psi_list[[k]] <- NNiW[["psi"]]
 S_list[[k]] <- NNiW[["S"]]
}

mmsNiWlogpdf(U_xi=xi_list, U_psi=psi_list, U_Sigma=S_list,
            U_xi0=list(hyperG0$b_xi), U_psi0=list(hyperG0$b_psi) ,
            U_B0=list(diag(c(hyperG0$D_xi, hyperG0$D_psi))) ,
            U_Sigma0=list(hyperG0$lambda), U_df0=list(hyperG0$nu))

C++ implementation of multivariate structured Normal inverse Wishart probability density function for multiple inputs

Description

C++ implementation of multivariate structured Normal inverse Wishart probability density function for multiple inputs

Usage

mmsNiWpdfC(xi, psi, Sigma, U_xi0, U_psi0, U_B0, U_Sigma0, U_df0, Log = TRUE)

Arguments

Value

matrix of densities of dimension K x n

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

C++ implementation of multivariate Normal probability density function for multiple inputs

Description

C++ implementation of multivariate Normal probability density function for multiple inputs

Usage

mmvnpdfC(x, mean, varcovM, Log = TRUE)

Arguments

Value

matrix of densities of dimension K x n.

Examples

if(require(microbenchmark)){
library(microbenchmark)
microbenchmark(mvnpdf(x=matrix(1.96), mean=0, varcovM=diag(1), Log=FALSE),
               mvnpdfC(x=matrix(1.96), mean=0, varcovM=diag(1), Log=FALSE),
               mmvnpdfC(x=matrix(1.96), mean=matrix(0), varcovM=list(diag(1)), Log=FALSE),
               times=1000L)
microbenchmark(mvnpdf(x=matrix(rep(1.96,2), nrow=2, ncol=1), mean=c(-0.2, 0.3),
                      varcovM=matrix(c(2, 0.2, 0.2, 2), ncol=2), Log=FALSE),
               mvnpdfC(x=matrix(rep(1.96,2), nrow=2, ncol=1), mean=c(-0.2, 0.3),
                       varcovM=matrix(c(2, 0.2, 0.2, 2), ncol=2), Log=FALSE),
               mmvnpdfC(x=matrix(rep(1.96,2), nrow=2, ncol=1),
                        mean=matrix(c(-0.2, 0.3), nrow=2, ncol=1),
                        varcovM=list(matrix(c(2, 0.2, 0.2, 2), ncol=2)), Log=FALSE),
               times=1000L)
microbenchmark(mvnpdf(x=matrix(c(rep(1.96,2),rep(0,2)), nrow=2, ncol=2),
                      mean=list(c(0,0),c(-1,-1), c(1.5,1.5)),
                      varcovM=list(diag(2),10*diag(2), 20*diag(2)), Log=FALSE),
               mmvnpdfC(matrix(c(rep(1.96,2),rep(0,2)), nrow=2, ncol=2),
                        mean=matrix(c(0,0,-1,-1, 1.5,1.5), nrow=2, ncol=3),
                        varcovM=list(diag(2),10*diag(2), 20*diag(2)), Log=FALSE),
               times=1000L)
}else{
cat("package 'microbenchmark' not available\n")
}

C++ implementation of multivariate skew Normal probability density function for multiple inputs

Description

C++ implementation of multivariate skew Normal probability density function for multiple inputs

Usage

mmvsnpdfC(x, xi, psi, sigma, Log = TRUE)

Arguments

Value

matrix of densities of dimension K x n.

Author(s)

Boris Hejblum

Examples

mmvsnpdfC(x=matrix(rep(1.96,2), nrow=2, ncol=1),
         xi=matrix(c(0, 0)), psi=matrix(c(1, 1),ncol=1), sigma=list(diag(2)), Log=FALSE
         )
mmvsnpdfC(x=matrix(rep(1.96,2), nrow=2, ncol=1),
         xi=matrix(c(0, 0)), psi=matrix(c(1, 1),ncol=1), sigma=list(diag(2))
         )

if(require(microbenchmark)){
library(microbenchmark)
microbenchmark(mvsnpdf(x=matrix(rep(1.96,2), nrow=2, ncol=1), xi=c(0, 0), psi=c(1, 1),
                       sigma=diag(2), Log=FALSE),
               mmvsnpdfC(x=matrix(rep(1.96,2), nrow=2, ncol=1), xi=matrix(c(0, 0)),
                         psi=matrix(c(1, 1),ncol=1), sigma=list(diag(2)), Log=FALSE),
               times=1000L
             )
microbenchmark(mvsnpdf(x=matrix(c(rep(1.96,2),rep(0,2)), nrow=2, ncol=2),
                      xi=list(c(0,0),c(-1,-1), c(1.5,1.5)),
                      psi=list(c(0.1,0.1),c(-0.1,-1), c(0.5,-1.5)),
                      sigma=list(diag(2),10*diag(2), 20*diag(2)), Log=FALSE),
               mmvsnpdfC(matrix(c(rep(1.96,2),rep(0,2)), nrow=2, ncol=2),
                         xi=matrix(c(0,0,-1,-1, 1.5,1.5), nrow=2, ncol=3),
                         psi=matrix(c(0.1,0.1,-0.1,-1, 0.5,-1.5), nrow=2, ncol=3),
                         sigma=list(diag(2),10*diag(2), 20*diag(2)), Log=FALSE),
              times=1000L)
}else{
cat("package 'microbenchmark' not available\n")
}

C++ implementation of multivariate Normal probability density function for multiple inputs

Description

C++ implementation of multivariate Normal probability density function for multiple inputs

Usage

mmvstpdfC(x, xi, psi, sigma, df, Log = TRUE)

Arguments

Value

matrix of densities of dimension K x n.

Author(s)

Boris Hejblum

Examples

mmvstpdfC(x = matrix(c(3.399890,-5.936962), ncol=1), xi=matrix(c(0.2528859,-2.4234067)),
psi=matrix(c(11.20536,-12.51052), ncol=1),
sigma=list(matrix(c(0.2134011, -0.0382573, -0.0382573, 0.2660086), ncol=2)),
df=c(7.784106)
)
mvstpdf(x = matrix(c(3.399890,-5.936962), ncol=1), xi=c(0.2528859,-2.4234067),
psi=c(11.20536,-12.51052),
sigma=matrix(c(0.2134011, -0.0382573, -0.0382573, 0.2660086), ncol=2),
df=c(7.784106)
)

#skew-normal limit
mmvsnpdfC(x=matrix(rep(1.96,2), nrow=2, ncol=1),
         xi=matrix(c(0, 0)), psi=matrix(c(1, 1),ncol=1), sigma=list(diag(2))
         )
mvstpdf(x=matrix(rep(1.96,2), nrow=2, ncol=1),
       xi=c(0, 0), psi=c(1, 1), sigma=diag(2),
       df=100000000
       )
mmvstpdfC(x=matrix(rep(1.96,2), nrow=2, ncol=1),
         xi=matrix(c(0, 0)), psi=matrix(c(1, 1),ncol=1), sigma=list(diag(2)),
         df=100000000
         )

#non-skewed limit
mmvtpdfC(x=matrix(rep(1.96,2), nrow=2, ncol=1),
        mean=matrix(c(0, 0)), varcovM=list(diag(2)),
        df=10
        )
mmvstpdfC(x=matrix(rep(1.96,2), nrow=2, ncol=1),
         xi=matrix(c(0, 0)), psi=matrix(c(0, 0),ncol=1), sigma=list(diag(2)),
         df=10
         )

if(require(microbenchmark)){
library(microbenchmark)
microbenchmark(mvstpdf(x=matrix(rep(1.96,2), nrow=2, ncol=1),
                       xi=c(0, 0), psi=c(1, 1),
                       sigma=diag(2), df=10),
               mmvstpdfC(x=matrix(rep(1.96,2), nrow=2, ncol=1),
                         xi=matrix(c(0, 0)), psi=matrix(c(1, 1),ncol=1),
                         sigma=list(diag(2)), df=10),
               times=1000L)
}else{
cat("package 'microbenchmark' not available\n")
}

C++ implementation of multivariate Normal probability density function for multiple inputs

Description

C++ implementation of multivariate Normal probability density function for multiple inputs

Usage

mmvtpdfC(x, mean, varcovM, df, Log = TRUE)

Arguments

Value

matrix of densities of dimension K x n.

Author(s)

Boris Hejblum

Examples

mvnpdf(x=matrix(1.96), mean=0, varcovM=diag(1), Log=FALSE)
mvtpdf(x=matrix(1.96), mean=0, varcovM=diag(1), df=10000000, Log=FALSE)
mmvtpdfC(x=matrix(1.96), mean=matrix(0), varcovM=list(diag(1)), df=10000000, Log=FALSE)

mvnpdf(x=matrix(1.96), mean=0, varcovM=diag(1))
mvtpdf(x=matrix(1.96), mean=0, varcovM=diag(1), df=10000000)
mmvtpdfC(x=matrix(1.96), mean=matrix(0), varcovM=list(diag(1)), df=10000000)

mvtpdf(x=matrix(1.96), mean=0, varcovM=diag(1), df=10)
mmvtpdfC(x=matrix(1.96), mean=matrix(0), varcovM=list(diag(1)), df=10)


if(require(microbenchmark)){
library(microbenchmark)
microbenchmark(mvtpdf(x=matrix(1.96), mean=0, varcovM=diag(1), df=1, Log=FALSE),
               mmvtpdfC(x=matrix(1.96), mean=matrix(0), varcovM=list(diag(1)),
                        df=c(1), Log=FALSE),
               times=10000L)
}else{
cat("package 'microbenchmark' not available\n")
}

C++ implementation of multivariate Normal probability density function for multiple inputs

Description

C++ implementation of multivariate Normal probability density function for multiple inputs

Usage

mvnlikC(x, c, clustval, mu, sigma, loglik = TRUE)

Arguments

Value

a list:

Author(s)

Boris Hejblum

multivariate-Normal probability density function

Description

multivariate-Normal probability density function

Usage

mvnpdf(x, mean, varcovM, Log = TRUE)

Arguments

Author(s)

Boris P. Hejblum

See Also

mvnpdf, mmvnpdfC

Examples

mvnpdf(x=matrix(1.96), mean=0, varcovM=diag(1), Log=FALSE)
dnorm(1.96)

mvnpdf(x=matrix(rep(1.96,2), nrow=2, ncol=1),
      mean=c(0, 0), varcovM=diag(2), Log=FALSE
)

C++ implementation of multivariate normal probability density function for multiple inputs

Description

Based on the implementation from Nino Hardt and Dicko Ahmadou https://gallery.rcpp.org/articles/dmvnorm_arma/ (accessed in August 2014)

Usage

mvnpdfC(x, mean, varcovM, Log = TRUE)

Arguments

Value

vector of densities

Author(s)

Boris P. Hejblum

Examples

mvnpdf(x=matrix(1.96), mean=0, varcovM=diag(1), Log=FALSE)
mvnpdfC(x=matrix(1.96), mean=0, varcovM=diag(1), Log=FALSE)
mvnpdf(x=matrix(1.96), mean=0, varcovM=diag(1))
mvnpdfC(x=matrix(1.96), mean=0, varcovM=diag(1))

if(require(microbenchmark)){
library(microbenchmark)
microbenchmark(dnorm(1.96),
               mvnpdf(x=matrix(1.96), mean=0, varcovM=diag(1), Log=FALSE),
               mvnpdfC(x=matrix(1.96), mean=0, varcovM=diag(1), Log=FALSE),
               times=10000L)
}else{
cat("package 'microbenchmark' not available\n")
}

C++ implementation of multivariate skew normal likelihood function for multiple inputs

Description

C++ implementation of multivariate skew normal likelihood function for multiple inputs

Usage

mvsnlikC(x, c, clustval, xi, psi, sigma, loglik = TRUE)

Arguments

Value

a list:

Author(s)

Boris Hejblum

multivariate Skew-Normal probability density function

Description

multivariate Skew-Normal probability density function

Usage

mvsnpdf(x, xi, sigma, psi, Log = TRUE)

Arguments

See Also

mvnpdf, mmvsnpdfC

Examples

mvnpdf(x=matrix(1.96), mean=0, varcovM=diag(1), Log=FALSE)
dnorm(1.96)
mvsnpdf(x=matrix(rep(1.96,1), nrow=1, ncol=1),
      xi=c(0), psi=c(0), sigma=diag(1),
      Log=FALSE
)

mvsnpdf(x=matrix(rep(1.96,2), nrow=2, ncol=1),
      xi=c(0, 0), psi=c(1, 1), sigma=diag(2)
)

N=50000#00
Yn <- rnorm(n=N, mean=0, sd=1)

Z <- rtruncnorm(n=N, a=0, b=Inf, mean=0, sd=1)
eps <- rnorm(n=N, mean=0, sd=1)
psi <- 10
Ysn <- psi*Z + eps

nu <- 1.5
W <- rgamma(n=N, shape=nu/2, rate=nu/2)
Yst=Ysn/sqrt(W)

library(reshape2)
library(ggplot2)
data2plot <- melt(cbind.data.frame(Ysn, Yst))
#pdf(file="ExSNST.pdf", height=5, width=4)
p <- (ggplot(data=data2plot)
     + geom_density(aes(x=value, fill=variable, alpha=variable), col="black")#, lwd=1.1)
     + theme_bw()
     + xlim(-15,100)
     + theme(legend.position="bottom")
     + scale_fill_manual(values=alpha(c("#F8766D", "#00B0F6"),c(0.2,0.45)),
                         name =" ",
                         labels=c("Y~SN(0,1,10)      ", "Y~ST(0,1,10,1.5)")
     )
     + scale_alpha_manual(guide=FALSE, values=c(0.25, 0.45))
     + xlab("Y")
     + ylim(0,0.08)
     + ylab("Density")
     + guides(fill = guide_legend(override.aes = list(colour = NULL)))
     + theme(legend.key = element_rect(colour = "black"))
)
p
#dev.off()

C++ implementation of multivariate skew t likelihood function for multiple inputs

Description

C++ implementation of multivariate skew t likelihood function for multiple inputs

Usage

mvstlikC(x, c, clustval, xi, psi, sigma, df, loglik = TRUE)

Arguments

Value

a list:

Author(s)

Boris Hejblum

multivariate skew-t probability density function

Description

multivariate skew-t probability density function

Usage

mvstpdf(x, xi, sigma, psi, df, Log = TRUE)

Arguments

See Also

mvtpdf, mvsnpdf, mmvstpdfC, mvstlikC

Examples

mvstpdf(x=matrix(rep(1.96,2), nrow=2, ncol=1),
      xi=c(0, 0), psi=c(1, 1), sigma=diag(2),
      df=100000000, Log=FALSE
)
mvsnpdf(x=matrix(rep(1.96,2), nrow=2, ncol=1),
      xi=c(0, 0), psi=c(1, 1), sigma=diag(2),
      Log=FALSE
)
mvstpdf(x=matrix(rep(1.96,2), nrow=2, ncol=1),
      xi=c(0, 0), psi=c(1, 1), sigma=diag(2),
      df=100000000
)
mvsnpdf(x=matrix(rep(1.96,2), nrow=2, ncol=1),
      xi=c(0, 0), psi=c(1, 1), sigma=diag(2)
)

multivariate Student's t-distribution probability density function

Description

multivariate Student's t-distribution probability density function

Usage

mvtpdf(x, mean, varcovM, df, Log = TRUE)

Arguments

Examples

mvtpdf(x=matrix(1.96), mean=0, varcovM=diag(1), df=10000000)
mvnpdf(x=matrix(1.96), mean=0, varcovM=diag(1))

mvtpdf(x=matrix(1.96), mean=0, varcovM=diag(1), df=10)

mvtpdf(x=matrix(rep(1.96,2), nrow=2, ncol=1),
      mean=c(0, 0), varcovM=diag(2), df=10
)

Convergence diagnostic plots

Description

Convergence diagnostic plots

Usage

plot_ConvDPM(
  MCMCsample,
  from = 1,
  to = length(MCMCsample$logposterior_list),
  shift = 0,
  thin = 1,
  ...
)

Arguments

Plot of a Dirichlet process mixture of gaussian distribution partition

Description

Plot of a Dirichlet process mixture of gaussian distribution partition

Usage

plot_DPM(
  z,
  U_mu = NULL,
  U_Sigma = NULL,
  m,
  c,
  i,
  alpha = "?",
  U_SS = NULL,
  dims2plot = 1:nrow(z),
  ellipses = ifelse(length(dims2plot) < 3, TRUE, FALSE),
  gg.add = list(theme())
)

Arguments

Author(s)

Boris Hejblum

Plot of a Dirichlet process mixture of skew normal distribution partition

Description

Plot of a Dirichlet process mixture of skew normal distribution partition

Usage

plot_DPMsn(
  z,
  c,
  i = "",
  alpha = "?",
  U_SS,
  dims2plot = 1:nrow(z),
  ellipses = ifelse(length(dims2plot) < 3, TRUE, FALSE),
  gg.add = list(theme()),
  nbsim_dens = 1000
)

Arguments

Author(s)

Boris Hejblum

Plot of a Dirichlet process mixture of skew t-distribution partition

Description

Plot of a Dirichlet process mixture of skew t-distribution partition

Usage

plot_DPMst(
  z,
  c,
  i = "",
  alpha = "?",
  U_SS,
  dims2plot = 1:nrow(z),
  ellipses = ifelse(length(dims2plot) < 3, TRUE, FALSE),
  gg.add = list(theme()),
  nbsim_dens = 1000,
  nice = FALSE
)

Arguments

Author(s)

Boris Hejblum

Post-processing Dirichlet Process Mixture Models results to get a mixture distribution of the posterior locations

Description

Post-processing Dirichlet Process Mixture Models results to get a mixture distribution of the posterior locations

Usage

postProcess.DPMMclust(
  x,
  burnin = 0,
  thin = 1,
  gs = NULL,
  lossFn = "F-measure",
  K = 10,
  ...
)

Arguments

Details

The cost of a point estimate partition is calculated using either a pairwise coincidence loss function (Binder), or 1-Fmeasure (F-measure).

Value

a list:

Author(s)

Boris Hejblum

See Also

similarityMat summary.DPMMclust

Methods for a summary of a DPMMclust object

Description

Methods for a summary of a DPMMclust object

Usage

## S3 method for class 'summaryDPMMclust'
print(x, ...)

## S3 method for class 'summaryDPMMclust'
plot(
  x,
  hm = FALSE,
  nbsim_densities = 5000,
  hm_subsample = NULL,
  hm_order_by_clust = TRUE,
  gg.add = list(theme_bw()),
  ...
)

Arguments

Author(s)

Boris Hejblum

Construction of an Empirical based prior

Description

Construction of an Empirical based prior

Usage

priormix(sDPMclust, nu0add = 5)

Arguments

See Also

summary.DPMMclust

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, 1.5, 1.5, 1.5, 2, -2.5, -2.5, -3))
#xi <- matrix(nrow=d, ncol=ncl, c(-0.5, 0, 0.5, 0, 0.5, -1, -1, 1))
psi <- matrix(nrow=d, ncol=4, c(0.4, -0.6, 0.8, 0, 0.3, -0.7, -0.3, -0.8))
nu <- c(100,15,8,5)
p <- c(0.15, 0.05, 0.5, 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)
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=p)!=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)
 #cat(k, "/", n, " observations simulated\n", sep="")
}

# Set parameters of G0
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

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

 nbclust_init <- 30

if(interactive()){
 MCMCsample_st <- DPMGibbsSkewT(z, hyperG0, a, b, N=2000, doPlot=FALSE,
                                nbclust_init, diagVar=FALSE)
 s <- summary(MCMCsample_st, burnin = 1500, thin=5, posterior_approx=TRUE)
 pmix <- priormix(s)
}

Generating cluster data from the Chinese Restaurant Process

Description

Generating cluster data from the Chinese Restaurant Process

Usage

rCRP(n = 1000, alpha = 2, hyperG0, verbose = TRUE)

Arguments

Examples

rm(list=ls())

d=2
hyperG0 <- list()
hyperG0[["NNiW"]] <- list()
hyperG0[["NNiW"]][["b_xi"]] <- rep(0,d)
hyperG0[["NNiW"]][["b_psi"]] <- rep(0,d)
hyperG0[["NNiW"]][["D_xi"]] <- 100
hyperG0[["NNiW"]][["D_psi"]] <- 8
hyperG0[["NNiW"]][["nu"]] <- d+1
hyperG0[["NNiW"]][["lambda"]] <- diag(c(1,1))

hyperG0[["scale"]] <- list()

set.seed(4321)
N <- 200
alph <- runif(n=1,0.2,2)
GvHD_sims <- rCRP(n=2*N, alpha=alph, hyperG0=hyperG0)
library(ggplot2)
q <- (ggplot(data=cbind.data.frame("D1"=GvHD_sims$data[1,],
                                  "D2"=GvHD_sims$data[2,],
                                  "Cluster"=GvHD_sims$cluster),
             aes(x=D1, y=D2))
      + geom_point(aes(colour=Cluster), alpha=0.6)
      + theme_bw()
      )
q
#q + stat_density2d(alpha=0.15, geom="polygon")

if(interactive()){
MCMCy1 <- DPMGibbsSkewT(z=GvHD_sims$data[,1:N],
                        hyperG0$NNiW, a=0.0001, b=0.0001, N=5000,
                        doPlot=TRUE, nbclust_init=64, plotevery=500,
                        gg.add=list(theme_bw()), diagVar=FALSE)
 s1 <- summary(MCMCy1, burnin=4000, thin=5,
               posterior_approx=TRUE)
 F1 <- FmeasureC(ref=GvHD_sims$cluster[1:N], pred=s1$point_estim$c_est)

 # s <- summary(MCMCy1, burnin=4000, thin=5,
 #               posterior_approx=TRUE, K=1)
 # s2 <- summary(MCMCy1, burnin=4000, thin=5,
 #               posterior_approx=TRUE, K=2)
 # MCMCy2_seqPost<- DPMGibbsSkewT(z=GvHD_sims$data[,(N+1):(2*N)],
 #                                  hyperG0=s1$param_post$parameters,
 #                                  a=s1$param_post$alpha_param$shape,
 #                                  b=s1$param_post$alpha_param$rate,
 #                                  N=5000, doPlot=TRUE, nbclust_init=64, plotevery=500,
 #                                  gg.add=list(theme_bw()), diagVar=FALSE)

 MCMCy2_seqPost <- DPMGibbsSkewT_SeqPrior(z=GvHD_sims$data[,(N+1):(2*N)],
                                           prior=s1$param_post, hyperG0=hyperG0$NNiW, , N=1000,
                                           doPlot=TRUE, nbclust_init=10, plotevery=100,
                                           gg.add=list(theme_bw()), diagVar=FALSE)
 s2_seqPost <- summary(MCMCy2_seqPost, burnin=600, thin=2)
 F2_seqPost <- FmeasureC(ref=GvHD_sims$cluster[(N+1):(2*N)], pred=s2_seqPost$point_estim$c_est)

 MCMCy2 <- DPMGibbsSkewT(z=GvHD_sims$data[,(N+1):(2*N)],
                         hyperG0$NNiW, a=0.0001, b=0.0001, N=5000,
                         doPlot=TRUE, nbclust_init=64, plotevery=500,
                         gg.add=list(theme_bw()), diagVar=FALSE)
 s2 <- summary(MCMCy2, burnin=4000, thin=5)
 F2 <- FmeasureC(ref=GvHD_sims$cluster[(N+1):(2*N)], pred=s2$point_estim$c_est)

 MCMCtot <- DPMGibbsSkewT(z=GvHD_sims$data,
                          hyperG0$NNiW, a=0.0001, b=0.0001, N=5000,
                          doPlot=TRUE, nbclust_init=10, plotevery=500,
                          gg.add=list(theme_bw()), diagVar=FALSE)
 stot <- summary(MCMCtot, burnin=4000, thin=5)
 F2tot <- FmeasureC(ref=GvHD_sims$cluster[(N+1):(2*N)], pred=stot$point_estim$c_est[(N+1):(2*N)])

 c(F1, F2, F2_seqPost, F2tot)
}

Sample from a normal inverse Wishart distribution whose parameter are given by the structure SufStat

Description

For internal use only.

Usage

rNNiW(SufStat, diagVar)

Sample from a Normal inverse-Wishart distribution whose parameter are given by the structure hyper

Description

For internal use only.

Usage

rNiW(hyper, diagVar)

C++ implementation of the multinomial sampling from a matrix of column vectors, each containing the sampling probabilities for their respective draw

Description

C++ implementation of the multinomial sampling from a matrix of column vectors, each containing the sampling probabilities for their respective draw

Usage

sampleClassC(probMat, Log = FALSE)

Arguments

Value

a vector of integer of length n containing the multinomial draws for each observation, i.e. the class allocation.

Sampler for the concentration parameter of a Dirichlet process

Description

Sampler updating the concentration parameter of a Dirichlet process given the number of observations and a Gamma(a, b) prior, following the augmentation strategy of West, and of Escobar and West.

Usage

sample_alpha(alpha_old, n, K, a = 1e-04, b = 1e-04)

Arguments

Details

A Gamma prior is used.

References

M West, Hyperparameter estimation in Dirichlet process mixture models, Technical Report, Duke University, 1992.

MD Escobar, M West, Bayesian Density Estimation and Inference Using Mixtures Journal of the American Statistical Association, 90(430):577-588, 1995.

Examples

#Test with a fixed K
####################

alpha_init <- 1000
N <- 10000
#n=500
n=10000
K <- 80
a <- 0.0001
b <- a
alphas <- numeric(N)
alphas[1] <- alpha_init
for (i in 2:N){
 alphas[i] <- sample_alpha(alpha_old = alphas[i-1], n=n, K=K, a=a, b=b)
}

postalphas <- alphas[floor(N/2):N]
alphaMMSE <- mean(postalphas)
alphaMAP <- density(postalphas)$x[which.max(density(postalphas)$y)]

expK <- sum(alphaMMSE/(alphaMMSE+0:(n-1)))
round(expK)


 prioralpha <- data.frame("alpha"=rgamma(n=5000, a,1/b),
                         "distribution" =factor(rep("prior",5000),
                         levels=c("prior", "posterior")))

 library(ggplot2)
 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

postalpha.df <- data.frame("alpha"=postalphas,
                         "distribution" = factor(rep("posterior",length(postalphas)),
                         levels=c("prior", "posterior")))
 p <- (ggplot(postalpha.df, aes(x=alpha))
       + geom_histogram(aes(y=..density..), binwidth=.1,
                        colour="black", fill="white")
       + geom_density(alpha=.2, fill="blue")
       + ggtitle("Posterior distribution of alpha\n")
       # Ignore NA values for mean
       # Overlay with transparent density plot
       + geom_vline(aes(xintercept=mean(alpha, na.rm=TRUE)),
                    color="red", linetype="dashed", size=1)
     )
 p

Computes the co-clustering (or similarity) matrix

Description

Computes the co-clustering (or similarity) matrix

Usage

similarityMat(c, step = 1)

Arguments

Value

A matrix of size n x n whose term [i,j] is the proportion of MCMC iterations where observation i and observations j are allocated to the same cluster.

Author(s)

Boris Hejblum

C++ implementation

Description

C++ implementation

Usage

similarityMatC(cc)

Arguments

Examples

c <- list(c(1,1,2,3,2,3), c(1,1,1,2,3,3),c(2,2,1,1,1,1))
similarityMatC(sapply(c, "["))

c2 <- list()
for(i in 1:10){
    c2 <- c(c2, list(rmultinom(n=1, size=200, prob=rexp(n=200))))
}
similarityMatC(sapply(c2, "["))

C++ implementation

Description

C++ implementation

Usage

similarityMat_nocostC(cc)

Arguments

Examples

c <- list(c(1,1,2,3,2,3), c(1,1,1,2,3,3),c(2,2,1,1,1,1))
similarityMat_nocostC(sapply(c, "["))

c2 <- list()
for(i in 1:10){
    c2 <- c(c2, list(rmultinom(n=1, size=1000, prob=rexp(n=1000))))
}

c3 <- sapply(c2, "[")

if(require(microbenchmark)){
library(microbenchmark)
microbenchmark(similarityMat(c3), similarityMat_nocostC(c3), times=2L)
}else{
cat("package 'microbenchmark' not available\n")
}

Summarizing Dirichlet Process Mixture Models

Description

Summary methods for DPMMclust objects.

Usage

## S3 method for class 'DPMMclust'
summary(
  object,
  burnin = 0,
  thin = 1,
  gs = NULL,
  lossFn = "Binder",
  posterior_approx = FALSE,
  ...
)

Arguments

Details

The cost of a point estimate partition is calculated using either a pairwise coincidence loss function (Binder), or 1-Fmeasure (F-measure).

The number of retained sampled partitions is m = (N - burnin)/thin

Value

a list containing the following elements:

nb_mcmcit:

an integer giving the value of m, the number of retained sampled partitions, i.e. (N - burnin)/thin

burnin:

an integer passing along the burnin argument

thin:

an integer passing along the thin argument

lossFn:

a character string passing along the lossFn argument

clust_distrib:

a character string passing along the clust_distrib argument

point_estim:

a list containing:

c_est:

a vector of length ncontaining the point estimated clustering for each observations

cost:

a vector of length m containing the cost of each sampled partition

Fmeas:

if lossFn is 'F-measure', the m x m matrix of total F-measures for each pair of sampled partitions

opt_ind:

the index of the point estimate partition among the m sampled

loss:

the loss for the point estimate. NA if lossFn is not 'Binder'

param_posterior:

a list containing the parametric approximation of the posterior, suitable to be plugged in as prior for a new MCMC algorithm run

mcmc_partitions:

a list containing the m sampled partitions

alpha:

a vector of length m with the values of the alpha DP parameter

index_estim:

the index of the point estimate partition among the m sampled

hyperG0:

a list passing along the prior, i.e. the hyperG0 argument

logposterior_list:

a list of length m containing the logposterior and its decomposition, for each sampled partition

U_SS_list:

a list of length m containing the containing the lists of sufficient statistics for all the mixture components, for each sampled partition

data:

a d x n matrix containing the clustered data

Author(s)

Boris Hejblum

See Also

similarityMat similarityMatC

C++ implementation of residual trace computation step used when sampling the scale

Description

C++ implementation of residual trace computation step used when sampling the scale

Usage

traceEpsC(eps, sigma)

Arguments

Value

the computed trace

Return updated sufficient statistics S with new data matrix z

Description

For internal use only.

Usage

update_SS(z, S, hyperprior = NULL)

Arguments

Return updated sufficient statistics S with new data matrix z

Description

For internal use only.

Usage

update_SSsn(z, S, ltn, hyperprior = NULL)

Arguments

Return updated sufficient statistics S for skew t-distribution with data matrix z

Description

For internal use only.

Usage

update_SSst(z, S, ltn, scale, df, hyperprior = NULL)

Arguments

C++ implementation

Description

C++ implementation

Usage

vclust2mcoclustC(c)

Arguments

Author(s)

Chariff Alkhassim

Examples

cc <- c(1,1,2,3,2,3)
vclust2mcoclustC(cc)

Sample from a Wishart distribution

Description

For internal use only.

Usage

wishrnd(n, Sigma)

Arguments