Package 'NPflow' reference manual

Title:	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 preprocessing applications. Method is detailed in: Hejblum, Alkhassimn, Gottardo, Caron & Thiebaut (2019) <doi: 10.1214/18-AOAS1209>.
Authors:	Boris P Hejblum [aut, cre], Chariff Alkhassim [aut], Francois Caron [aut]
Maintainer:	Boris P Hejblum <[email protected]>
License:	LGPL-3 \| file LICENSE
Version:	0.13.5
Built:	2024-11-11 05:15:22 UTC
Source:	https://github.com/sistm/npflow

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

Package:	NPflow
Type:	Package
Version:	0.13.5
Date:	2024-01-13
License:	LGPL-3

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

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

Arguments

`x`	a `DPMMclust` object.
`burnin`	the number of MCMC iterations to burn (default is `0`).
`thin`	the spacing at which MCMC iterations are kept. Default is `1`, i.e. no thining.

Value

a DPMMclust object minus the burnt iterations

Author(s)

Boris Hejblum

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)
cluster_est_binder(c, logposterior)

Arguments

`c`	a list of vector of length `n`. `c[[j]][i]` is the cluster allocation of observation `i=1...n` at iteration `j=1...N`.
`logposterior`	vector of logposterior corresponding to each partition from `c` used to break ties when minimizing the cost function

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.

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)
cluster_est_Fmeasure(c, logposterior)

Arguments

`c`	a list of vector of length `n`. `c[[j]][i]` is the cluster allocation of observation `i=1...n` at iteration `j=1...N`.
`logposterior`	a vector of logposterior corresponding to each partition from `c` used to break ties when minimizing the cost function

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

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

Arguments

`c`	a list of vector of length `n`. `c[[j]][i]` is the cluster allocation of observation `i=1...n` at iteration `j=1...N`.
`Mu`	is a list of length `n` composed of `p x l` matrices. Where `l` is the maximum number of components per partition.
`Sigma`	is list of length `n` composed of arrays containing a maximum of `l` `p x p` covariance matrices.
`lambda`	is a nonnegative tunning parameter allowing further control over the distance function. Default is 0.
`a`	nonnegative constant seen as the unit cost for pairwise misclassification. Default is 1.
`b`	nonnegative constant seen as the unit cost for the other kind of pairwise misclassification. Default is 1.
`logposterior`	vector of logposterior corresponding to each partition from `c` used to break ties when minimizing the cost function

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:

`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)

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.

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)
cluster_est_pear(c)

Arguments

`c`	a list of vector of length `n`. `c[[j]][i]` is the cluster allocation of observation `i=1...n` at iteration `j=1...N`.

Value

a list:

`c_est:`	a vector of length `n`. Point estimate of the partition
`pear:`	a vector of length `N`. `pear[j]` is the posterior expected adjusted Rand index 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)

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)

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

Arguments

`cytomatrix`	a `p x n` data matrix, of `n` cell observations measured over `p` markers.
`dims2plot`	a vector of length at least 2, indicating of the dimensions to be plotted. Default is `c(1, 2)`.
`gating`	an optional vector of length `n` indicating a known gating of the cells to be displayed. Default is `NULL` in which case no gating is displayed.
`scale_log`	a logical Flag indicating whether the data should be plotted on the log scale. Default is `FALSE`.
`xlim`	a vector of length 2 to specify the x-axis limits. Only used if `dims2plot` is of length 2Default is the data range.
`ylim`	a vector of length 2 to specify the y-axis limits. Only used if `dims2plot` is of length 2. Default is the data range.
`gg.add`	A list of instructions to add to the `ggplot2` instruction (see `gg-add`). Default is `list(theme())`, which adds nothing. to the plot.

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)

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)

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,
  ...
)
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

`z`	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).
`use_variance_hyperprior`	logical flag indicating whether a hyperprior is added for the variance parameter. Default is `TRUE` which decrease the impact of the variance prior on the posterior. `FALSE` is useful for using an informative prior.
`verbose`	logical flag indicating whether partition info is written in the console at each MCMC iteration.
`...`	additional arguments to be passed to `plot_DPM`. Only used if `doPlot` is `TRUE`.

Value

a object of class DPMclust with the following attributes:

`mcmc_partitions:`	a list of length `N`. Each element `mcmc_partitions[n]` is a vector of length `n` giving the partition of the `n` observations.
`alpha:`	a vector of length `N`. `cost[j]` is the cost associated to partition `c[[j]]`
`listU_mu:`	a list of length `N` containing the matrices of mean vectors for all the mixture components at each MCMC iteration
`listU_Sigma:`	a list of length `N` containing the arrays of covariances matrices for all the mixture components at each MCMC iteration
`U_SS_list:`	a list of length `N` containing the lists of sufficient statistics for all the mixture components at each MCMC iteration
`weights_list:`	a list of length `N` containing the logposterior values at 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 - `"gaussian"`
`hyperG0:`	the prior on the cluster location

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




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 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 = "",
  ...
)
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

`Ncpus`	the number of processors available
`type_connec`	The type of connection between the processors. Supported cluster types are `"SOCK"`, `"FORK"`, `"MPI"`, and `"NWS"`. See also `makeCluster`.
`z`	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).
`use_variance_hyperprior`	logical flag indicating whether a hyperprior is added for the variance parameter. Default is `TRUE` which decrease the impact of the variance prior on the posterior. `FALSE` is useful for using an informative prior.
`verbose`	logical flag indicating whether partition info is written in the console at each MCMC iteration.
`monitorfile`	a writable connections or a character string naming a file to write into, to monitor the progress of the analysis. Default is `""` which is no monitoring. See Details.
`...`	additional arguments to be passed to `plot_DPM`. Only used if `doPlot` is `TRUE`.

Value

a object of class DPMclust with the following attributes:

`mcmc_partitions:`	a list of length `N`. Each element `mcmc_partitions[n]` is a vector of length `n` giving the partition of the `n` observations.
`alpha:`	a vector of length `N`. `cost[j]` is the cost associated to partition `c[[j]]`
`listU_mu:`	a list of length `N` containing the matrices of mean vectors for all the mixture components at each MCMC iteration
`listU_Sigma:`	a list of length `N` containing the arrays of covariances matrices for all the mixture components at each MCMC iteration
`U_SS_list:`	a list of length `N` containing the lists of sufficient statistics for all the mixture components at each MCMC iteration
`weights_list:`	a list of length `N` containing the logposterior values at 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 - `"gaussian"`
`hyperG0:`	the prior on the cluster location

Author(s)

Boris Hejblum

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)
}


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

Arguments

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

Value

a object of class DPMclust with the following attributes:

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

Author(s)

Boris Hejblum, Chariff Alkhassim

References

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
}
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 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,
  ...
)
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

`z`	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 a cluster is a diagonal matrix. Default is `FALSE` (full matrix).
`use_variance_hyperprior`	logical flag indicating whether a hyperprior is added for the variance parameter. Default is `TRUE` which decrease the impact of the variance prior on the posterior. `FALSE` is useful for using an informative prior.
`verbose`	logical flag indicating whether partition info is written in the console at each MCMC iteration.
`...`	additional arguments to be passed to `plot_DPMsn`. 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:`
`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 - `"skewnorm"`
`hyperG0:`	the prior on the cluster location

Author(s)

Boris Hejblum

References

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)

}

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 = "",
  ...
)
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

`Ncpus`	the number of processors available
`type_connec`	The type of connection between the processors. Supported cluster types are `"SOCK"`, `"FORK"`, `"MPI"`, and `"NWS"`. See also `makeCluster`.
`z`	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).
`use_variance_hyperprior`	logical flag indicating whether a hyperprior is added for the variance parameter. Default is `TRUE` which decrease the impact of the variance prior on the posterior. `FALSE` is useful for using an informative prior.
`verbose`	logical flag indicating whether partition info is written in the console at each MCMC iteration.
`monitorfile`	a writable connections or a character string naming a file to write into, to monitor the progress of the analysis. Default is `""` which is no monitoring. See Details.
`...`	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:`
`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 - `"skewnorm"`
`hyperG0:`	the prior on the cluster location

Author(s)

Boris Hejblum

References

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)
 }




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,
  ...
)
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

`z`	data matrix `d x n` with `d` dimensions in rows and `n` observations in columns.
`hyperG0`	parameters of the prior mixing distribution in a `list` with the following named components: `"b_xi"`: a vector of length `d` with the mean location prior parameter. Can be set as the empirical mean of the data in an Empirical Bayes fashion. `"b_psi"`: a vector of length `d` with the skewness location prior parameter. Can be set as 0 a priori. `"kappa"`: a strictly positive number part of the inverse-Wishart component of the prior on the variance matrix. Can be set as very small (e.g. 0.001) a priori. `"D_xi"`: hyperprior controlling the information in $\xi$ (the larger the less information is carried). 100 is a reasonable value, based on Fruhwirth-Schnatter et al., Biostatistics, 2010. `"D_psi"`: hyperprior controlling the information in $\psi$ (the larger the less information is carried). 100 is a reasonable value, based on Fruhwirth-Schnatter et al., Biostatistics, 2010 `"nu"`: a prior number on the degrees of freedom of the $t$ component that must be strictly greater than `d`. Can be set as `d + 1` for instance. `"lambda"`: a `d x d` symmetric definitive positive matrix part of the inverse-Wishart component of the prior on the variance matrix. Can be set as the diagonal of empirical variance of the data in an Empircal Bayes fashion divided by a factor 3 according to Fruhwirth-Schnatter et al., Biostatistics, 2010.
`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).
`use_variance_hyperprior`	logical flag indicating whether a hyperprior is added for the variance parameter. Default is `TRUE` which decrease the impact of the variance prior on the posterior. `FALSE` is useful for using an informative prior.
`verbose`	logical flag indicating whether partition info is written in the console at each MCMC iteration.
`...`	additional arguments to be passed to `plot_DPMst`. 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 - `"skewt"`
`hyperG0:`	the prior on the cluster location

Author(s)

Boris Hejblum

References

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])
}

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_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 = "",
  ...
)
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

`Ncpus`	the number of processors available
`type_connec`	The type of connection between the processors. Supported cluster types are `"PSOCK"`, `"FORK"`, `"SOCK"`, `"MPI"`, and `"NWS"`. See also `makeCluster`.
`z`	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).
`use_variance_hyperprior`	logical flag indicating whether a hyperprior is added for the variance parameter. Default is `TRUE` which decrease the impact of the variance prior on the posterior. `FALSE` is useful for using an informative prior.
`verbose`	logical flag indicating whether partition info is written in the console at each MCMC iteration.
`monitorfile`	a writable connections or a character string naming a file to write into, to monitor the progress of the analysis. Default is `""` which is no monitoring. See Details.
`...`	additional arguments to be passed to `plot_DPMst`. 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 - `"skewt"`
`hyperG0:`	the prior on the cluster location

Author(s)

Boris Hejblum

References

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])
}



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])
}

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

Arguments

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

Value

a object of class DPMclust with the following attributes:

`mcmc_partitions:`	a list of length `N`. Each element `mcmc_partitions[n]` is a vector of length `n` giving the partition of the `n` observations.
`alpha:`	a vector of length `N`. `cost[j]` is the cost associated to partition `c[[j]]`
`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 - `"skewt"`
`hyperG0:`	the prior on the cluster location

Author(s)

Boris Hejblum

References

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"))))
}


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 = "",
  ...
)
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

`Ncpus`	the number of processors available
`type_connec`	The type of connection between the processors. Supported cluster types are `"SOCK"`, `"FORK"`, `"MPI"`, and `"NWS"`. See also `makeCluster`.
`z`	data matrix `d x n` with `d` dimensions in rows and `n` observations in columns.
`prior_inform`	an informative prior such as the approximation computed by `summary.DPMMclust`.
`hyperG0`	prior mixing distribution.
`N`	number of MCMC iterations.
`nbclust_init`	number of clusters at initialization. Default to 30 (or less if there are less than 30 observations).
`add.vagueprior`	logical flag indicating whether a non informative component should be added to the informative prior. Default is `TRUE`.
`weightnoninfo`	a real between 0 and 1 giving the weights of the non informative component in the prior.
`doPlot`	logical flag indicating whether to plot MCMC iteration or not. Default to `TRUE`.
`plotevery`	an integer indicating the interval between plotted iterations when `doPlot` is `TRUE`.
`diagVar`	logical flag indicating whether the variance of each cluster is estimated as a diagonal matrix, or as a full matrix. Default is `TRUE` (diagonal variance).
`verbose`	logical flag indicating whether partition info is written in the console at each MCMC iteration.
`monitorfile`	a writable connections or a character string naming a file to write into, to monitor the progress of the analysis. Default is `""` which is no monitoring. See Details.
`...`	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 logposterior values at 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 - `"skewt"`
`hyperG0:`	the prior on the cluster location

Author(s)

Boris Hejblum

References

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)
}


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)
}

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,
  ...
)
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`.

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:

`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

Author(s)

Boris Hejblum

References

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
}


#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
}

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

Arguments

`c`	vector of length `n` containing the estimated partition of the `n` observations.
`gs`	vector of length `n` containing the gold standard partition of the `n` observations.
`lossFn`	character string specifying the loss function to be used. Either "F-measure" or "Binder" (see Details). Default is "F-measure".
`a`	only relevant if `lossFn` is "Binder". Penalty for wrong co-clustering in `c` compared to `gs`. Defaults is 1.
`b`	only relevant if `lossFn` is "Binder". Penalty for missed co-clustering in `c` compared to `gs`. Defaults is 1.

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.

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)
Flimited(n_small_clst, pred, ref)

Arguments

`n_small_clst`	an integer for limit size of the small cluster
`pred`	vector of a predicted partition
`ref`	vector of a reference partition

References

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)

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)

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)
Fmeasure_costC(c)

Arguments

`c`	a matrix where each column is one MCMC partition

Value

a list with the following elements:

`Fmeas:`	TODO
`cost:`	TODO

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, "["))
}

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, "["))
}

C++ implementation of the F-measure computation

Description

C++ implementation of the F-measure computation

Usage

FmeasureC(pred, ref)
FmeasureC(pred, ref)

Arguments

`pred`	vector of a predicted partition
`ref`	vector of a reference partition

Examples

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

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)
FmeasureC_no0(pred, ref)

Arguments

`pred`	vector of a predicted partition
`ref`	vector of a reference partition

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)

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)

Multivariate log gamma function

Description

Multivariate log gamma function

Usage

lgamma_mv(x, p)
lgamma_mv(x, p)

Arguments

`x`	strictly positive real number
`p`	integer

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
)
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

`xi_list`	a list of length `n`, each element is a vector of size `d` containing the argument `xi` of the corresponding allocated cluster.
`psi_list`	a list of length `n`, each element is a vector of size `d` containing the argument `psi` of the corresponding allocated cluster.
`S_list`	a list of length `n`, each element is a matrix of size `d x d` containing the argument `S` of the corresponding allocated cluster.
`hyperG0`	prior mixing distribution used if `init` is `NULL`.
`init`	a list for initializing the algorithm with the following elements: `b_xi`, `b_psi`, `lambda`, `B`, `nu`. Default is `NULL` in which case the initialization of the algorithm is random.
`K`	integer giving the number of mixture components.
`maxit`	integer giving the maximum number of iteration for the EM algorithm. Default is `100`.
`tol`	real number giving the tolerance for the stopping of the EM algorithm. Default is `0.1`.
`doPlot`	a logical flag indicating whether the algorithm progression should be plotted. Default is `TRUE`.
`verbose`	logical flag indicating whether plot should be drawn. Default is `TRUE`.
`obsweight_list`	a list of length `n` where each element is a vector of weights for each sampled cluster at each MCMC iterations.

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)

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)

MLE for Gamma distribution

Description

Maximum likelihood estimation of Gamma distributed observations distribution parameters

Usage

MLE_gamma(g)
MLE_gamma(g)

Arguments

`g`	a list of Gamma distributed observation.

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

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

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

Arguments

`mu_list`	a list of length `N` whose elements are observed vectors of length `d` of the mean parameters.
`S_list`	a list of length `N` whose elements are observed variance-covariance matrices of dimension `d x d`.
`hyperG0`	prior mixing distribution used for randomly initializing the algorithm.
`K`	integer giving the number of mixture components.
`maxit`	integer giving the maximum number of iteration for the EM algorithm. Default is `100`.
`tol`	real number giving the tolerance for the stopping of the EM algorithm. Default is `0.1`.
`doPlot`	a logical flag indicating whether the algorithm progression should be plotted. Default is `TRUE`.

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
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 sNiW distributed observations

Description

Maximum likelihood estimation of Normal inverse Wishart distributed observations

Usage

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

Arguments

`xi_list`	a list of length `N` whose elements are observed vectors of length `d` of the mean parameters xi.
`psi_list`	a list of length `N` whose elements are observed vectors of length `d` of the skew parameters psi.
`S_list`	a list of length `N` whose elements are observed variance-covariance matrices of dimension `d x d`.
`doPlot`	a logical flag indicating whether the algorithm progression should be plotted. Default is `TRUE`.

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

Arguments

`xi_list`	a list of length `N` whose elements are observed vectors of length `d` of the mean parameters xi.
`psi_list`	a list of length `N` whose elements are observed vectors of length `d` of the skew parameters psi.
`S_list`	a list of length `N` whose elements are observed variance-covariance matrices of dimension `d x d`.
`hyperG0`	prior mixing distribution used if `init` is `NULL`.
`K`	integer giving the number of mixture components.
`init`	a list for initializing the algorithm with the following elements: `b_xi`, `b_psi`, `lambda`, `B`, `nu`. Default is `NULL` in which case the initialization of the algorithm is random.
`maxit`	integer giving the maximum number of iteration for the EM algorithm. Default is `100`.
`tol`	real number giving the tolerance for the stopping of the EM algorithm. Default is `0.1`.
`doPlot`	a logical flag indicating whether the algorithm progression should be plotted. Default is `TRUE`.
`verbose`	logical flag indicating whether plot should be drawn. Default is `TRUE`.

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)

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)

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

Arguments

`mu`	data matrix of dimension `p x n`, `p` being the dimension of the data and n the number of data points, where each column is an observed mean vector.
`Sigma`	list of length `n` of observed variance-covariance matrices, each of dimensions `p x p`.
`U_mu0`	mean vectors matrix of dimension `p x K`, `K` being the number of distributions for which the density probability has to be evaluated
`U_kappa0`	vector of length `K` of scale parameters.
`U_nu0`	vector of length `K` of degree of freedom parameters.
`U_lambda0`	list of length `K` of variance-covariance matrices, each of dimensions `p x p`.
`Log`	logical flag for returning the log of the probability density function. Defaults is `TRUE`.

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

Arguments

`Mu`	data matrix of dimension `p x n`, `p` being the dimension of the data and n the number of data points, where each column is an observed mean vector.
`Sigma`	list of length `n` of observed variance-covariance matrices, each of dimensions `p x p`.
`U_Mu0`	mean vectors matrix of dimension `p x K`, `K` being the number of distributions for which the density probability has to be evaluated
`U_Kappa0`	vector of length `K` of scale parameters.
`U_Nu0`	vector of length `K` of degree of freedom parameters.
`U_Sigma0`	list of length `K` of variance-covariance matrices, each of dimensions `p x p`.
`Log`	logical flag for returning the log of the probability density function. Defaults is `TRUE`.

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

Arguments

`U_xi`	a list of length n of observed mean vectors, each of dimension p
`U_psi`	a list of length n of observed skew vectors of dimension p
`U_Sigma`	a list of length n of observed covariance matrices, each of dimension p x p
`U_xi0`	a list of length K of mean vector parameters for sNiW, each of dimension p
`U_psi0`	a list of length K of mean vector parameters for sNiW, each of dimension p
`U_B0`	a list of length K of structuring matrix parameters for sNiW, each of dimension 2 x 2
`U_Sigma0`	a list of length K of covariance matrix parameters for sNiW, each of dimension p x p
`U_df0`	a list of length K of degrees of freedom parameters for sNiW, each of dimension p x p

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))

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

Arguments

`xi`	data matrix of dimensions `p x n` where columns contain the observed mean vectors.
`psi`	data matrix of dimensions `p x n` where columns contain the observed skew parameter vectors.
`Sigma`	list of length `n` of observed variance-covariance matrices, each of dimensions `p x p`.
`U_xi0`	mean vectors matrix of dimension `p x K`, `K` being the number of distributions for which the density probability has to be evaluated.
`U_psi0`	skew parameter vectors matrix of dimension `p x K`.
`U_B0`	list of length `K` of structured scale matrices, each of dimensions `p x p`.
`U_Sigma0`	list of length `K` of variance-covariance matrices, each of dimensions `p x p`.
`U_df0`	vector of length `K` of degree of freedom parameters.
`Log`	logical flag for returning the log of the probability density function. Defaults is `TRUE`.

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

Arguments

`x`	data matrix of dimension `p x n`, `p` being the dimension of the data and n the number of data points.
`mean`	mean vectors matrix of dimension `p x K`, `K` being the number of distributions for which the density probability has to be evaluated.
`varcovM`	list of length `K` of variance-covariance matrices, each of dimensions `p x p`.
`Log`	logical flag for returning the log of the probability density function. Defaults is `TRUE`.

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

Arguments

`x`	data matrix of dimension `p x n`, `p` being the dimension of the data and n the number of data points.
`xi`	mean vectors matrix of dimension `p x K`, `K` being the number of distributions for which the density probability has to be evaluated.
`psi`	skew parameter vectors matrix of dimension `p x K`.
`sigma`	list of length K of variance-covariance matrices, each of dimensions `p x p`.
`Log`	logical flag for returning the log of the probability density function. Default is `TRUE`.

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

Arguments

`x`	data matrix of dimension `p x n`, `p` being the dimension of the data and n the number of data points.
`xi`	mean vectors matrix of dimension `p x K`, `K` being the number of distributions for which the density probability has to be evaluated.
`psi`	skew parameter vectors matrix of dimension `p x K`.
`sigma`	list of length `K` of variance-covariance matrices, each of dimensions `p x p`.
`df`	vector of length K of degree of freedom parameters.
`Log`	logical flag for returning the log of the probability density function. Defaults is `TRUE`.

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

Arguments

`x`	data matrix of dimension `p x n`, `p` being the dimension of the data and n the number of data points.
`mean`	mean vectors matrix of dimension `p x K`, `K` being the number of distributions for which the density probability has to be evaluated.
`varcovM`	list of length `K` of variance-covariance matrices, each of dimensions `p x p`.
`df`	vector of length `K` of degree of freedom parameters.
`Log`	logical flag for returning the log of the probability density function. Defaults is `TRUE`.

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

Arguments

`x`	data matrix of dimension p x n, p being the dimension of the data and n the number of data points
`c`	integer vector of cluster allocations with values from 1 to K
`clustval`	vector of unique values from c in the order corresponding to the storage of cluster parameters in `xi`, `psi`, and `varcovM`
`mu`	mean vectors matrix of dimension p x K, K being the number of clusters
`sigma`	list of length `K` of variance-covariance matrices, each of dimensions `p x p`.
`loglik`	logical flag or returning the log-likelihood instead of the likelihood. Default is `TRUE`.

Value

a list:

`"indiv":`	vector of likelihood of length n;
`"clust":`	vector of likelihood of length K;
`"total":`	total (log)-likelihood;

Author(s)

Boris Hejblum

multivariate-Normal probability density function

Description

multivariate-Normal probability density function

Usage

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

Arguments

`x`	p x n data matrix with n the number of observations and p the number of dimensions
`mean`	mean vector or list of mean vectors (either a vector, a matrix or a list)
`varcovM`	variance-covariance matrix or list of variance-covariance matrices (either a matrix or a list)
`Log`	logical flag for returning the log of the probability density function. Defaults is `TRUE`.

Author(s)

Boris P. Hejblum

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
)

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

Arguments

`x`	data matrix
`mean`	mean vector
`varcovM`	variance covariance matrix
`Log`	logical flag for returning the log of the probability density function. Default is `TRUE`

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")
}

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

Arguments

`x`	data matrix of dimension p x n, p being the dimension of the data and n the number of data points
`c`	integer vector of cluster allocations with values from 1 to K
`clustval`	vector of unique values from c in the order corresponding to the storage of cluster parameters in `xi`, `psi`, and `sigma`
`xi`	mean vectors matrix of dimension p x K, K being the number of clusters
`psi`	skew parameter vectors matrix of dimension `p x K`
`sigma`	list of length `K` of variance-covariance matrices, each of dimensions `p x p`.
`loglik`	logical flag or returning the log-likelihood instead of the likelihood. Default is `TRUE`.

Value

a list:

`"indiv":`	vector of likelihood of length n;
`"clust":`	vector of likelihood of length K;
`"total":`	total (log)-likelihood;

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

Arguments

`x`	p x n data matrix with n the number of observations and p the number of dimensions
`xi`	mean vector or list of mean vectors (either a vector, a matrix or a list)
`sigma`	variance-covariance matrix or list of variance-covariance matrices (either a matrix or a list)
`psi`	skew parameter vector or list of skew parameter vectors (either a vector, a matrix or a list)
`Log`	logical flag for returning the log of the probability density function. Defaults is `TRUE`.

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()


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

Arguments

`x`	data matrix of dimension p x n, p being the dimension of the data and n the number of data points
`c`	integer vector of cluster allocations with values from 1 to K
`clustval`	vector of unique values from c in the order corresponding to the storage of cluster parameters in `xi`, `psi`, and `sigma`
`xi`	mean vectors matrix of dimension p x K, K being the number of clusters
`psi`	skew parameter vectors matrix of dimension `p x K`
`sigma`	list of length `K` of variance-covariance matrices, each of dimensions `p x p`.
`df`	vector of length `K` of degree of freedom parameters.
`loglik`	logical flag or returning the log-likelihood instead of the likelihood. Default is `TRUE`.

Value

a list:

`"indiv":`	vector of likelihood of length n;
`"clust":`	vector of likelihood of length K;
`"total":`	total (log)-likelihood;

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

Arguments

`x`	`p x n` data matrix with `n` the number of observations and `p` the number of dimensions
`xi`	mean vector or list of mean vectors (either a vector, a matrix or a list)
`sigma`	variance-covariance matrix or list of variance-covariance matrices (either a matrix or a list)
`psi`	skew parameter vector or list of skew parameter vectors (either a vector, a matrix or a list)
`df`	a numeric vector or a list of the degrees of freedom (either a vector or a list)
`Log`	logical flag for returning the log of the probability density function. Defaults is `TRUE`.

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)
)


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

Arguments

`x`	`p x n` data matrix with `n` the number of observations and `p` the number of dimensions
`mean`	mean vector or list of mean vectors (either a vector, a matrix or a list)
`varcovM`	variance-covariance matrix or list of variance-covariance matrices (either a matrix or a list)
`df`	a numeric vector or a list of the degrees of freedom (either a vector or a list)
`Log`	logical flag for returning the log of the probability density function. Defaults is `TRUE`.

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
)

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
)

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)
NuMatParC(c, d)

Arguments

`c`	an MCMC partitions of length `n`.
`d`	a symmetric `n x n` matrix containing distances between each group distributions.

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)


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

Convergence diagnostic plots

Description

Convergence diagnostic plots

Usage

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

Arguments

`MCMCsample`	a `DPMMclust` or `summaryDPMMclust` object.
`from`	the MCMC iteration from which the plot should start. Default is `1`.
`to`	the MCMC iteration up until which the plot should stop. Default is `1`.
`shift`	a number of initial iterations not to be displayed. Default is `0`.
`thin`	integer giving the spacing at which MCMC iterations are kept. Default is `1`, i.e. no thining.
`...`	further arguments passed to or from other methods

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())
)
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

`z`	data matrix `d x n` with `d` dimensions in rows and `n` observations in columns.
`U_mu`	either a list or a matrix containing the current estimates of mean vectors of length `d` for each cluster. Default is `NULL` in which case `U_SS` has to be provided.
`U_Sigma`	either a list or an array containing the `d x d` current estimates for covariance matrix of each cluster. Default is `NULL` in which case `U_SS` has to be provided.
`m`	vector of length `n` containing the number of observations currently assigned to each clusters.
`c`	allocation vector of length `n` indicating which observation belongs to which clusters.
`i`	current MCMC iteration number.
`alpha`	current value of the DP concentration parameter.
`U_SS`	a list containing `"mu"` and `"S"`. Default is `NULL` in which case `U_mu` and `U_Sigma` have to be provided.
`dims2plot`	index vector, subset of `1:d` indicating which dimensions should be drawn. Default is all of them.
`ellipses`	a logical flag indicating whether ellipses should be drawn around clusters. Default is `TRUE` if only 2 dimensions are plotted, `FALSE` otherwise.
`gg.add`	a list of instructions to add to the `ggplot2` instruction (see `gg-add`). Default is `list(theme())`, which adds nothing to the plot.

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
)
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

`z`	data matrix `d x n` with `d` dimensions in rows and `n` observations in columns.
`c`	allocation vector of length `n` indicating which observation belongs to which clusters.
`i`	current MCMC iteration number.
`alpha`	current value of the DP concentration parameter.
`U_SS`	a list containing `"xi"`, `"psi"`, `"S"`, and `"df"`.
`dims2plot`	index vector, subset of `1:d` indicating which dimensions should be drawn. Default is all of them.
`ellipses`	a logical flag indicating whether ellipses should be drawn around clusters. Default is `TRUE` if only 2 dimensions are plotted, `FALSE` otherwise.
`gg.add`	A list of instructions to add to the `ggplot2` instruction (see `gg-add`). Default is `list(theme())`, which adds nothing to the plot.
`nbsim_dens`	number of simulated points used for computing clusters density contours in 2D plots. Default is `1000` points.

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
)
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

`z`	data matrix `d x n` with `d` dimensions in rows and `n` observations in columns.
`c`	allocation vector of length `n` indicating which observation belongs to which clusters.
`i`	current MCMC iteration number.
`alpha`	current value of the DP concentration parameter.
`U_SS`	a list containing `"xi"`, `"psi"`, `"S"`, and `"df"`.
`dims2plot`	index vector, subset of `1:d` indicating which dimensions should be drawn. Default is all of them.
`ellipses`	a logical flag indicating whether ellipses should be drawn around clusters. Default is `TRUE` if only 2 dimensions are plotted, `FALSE` otherwise.
`gg.add`	A list of instructions to add to the `ggplot2` instruction (see `gg-add`). Default is `list(theme())`, which adds nothing to the plot.
`nbsim_dens`	number of simulated points used for computing clusters density contours in 2D plots. Default is `1000` points.
`nice`	logical flag changing the plot looks. Default is `FALSE`.

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

Arguments

`x`	a `DPMMclust` object.
`burnin`	integer giving the number of MCMC iterations to burn (defaults is half)
`thin`	integer giving the spacing at which MCMC iterations are kept. Default is `1`, i.e. no thining.
`gs`	optional vector of length `n` containing the gold standard partition of the `n` observations to compare to the point estimate.
`lossFn`	character string specifying the loss function to be used. Either "F-measure" or "Binder" (see Details). Default is "F-measure".
`K`	integer giving the number of mixture components. Default is `10`.
`...`	further arguments passed to or from other methods

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:

`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
`point_estim:`
`loss:`
`index_estim:`

Author(s)

Boris Hejblum

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()),
  ...
)
## 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

`x`	a `summaryDPMMclust` object.
`...`	further arguments passed to or from other methods
`hm`	logical flag to plot the heatmap of the similarity matrix. Default is `FALSE`.
`nbsim_densities`	the number of simulated observations to be used to plot the density lines of the clusters in the point estimate partition plot
`hm_subsample`	a integer designating the number of observations to use when plotting the heatmap. Used only if `hm` is `TRUE`. #'Default is `NULL` in which no subsampling is done and all observations are plotted.
`hm_order_by_clust`	logical flag indicating whether observations should be ordered according to the point estimate first. Used only if `hm` is `TRUE`. Default is `TRUE`.
`gg.add`	a list of instructions to add to the `ggplot2` instruction (see `gg-add`). Default is `list(theme())`, which adds nothing to the plot.

Author(s)

Boris Hejblum

Construction of an Empirical based prior

Description

Construction of an Empirical based prior

Usage

priormix(sDPMclust, nu0add = 5)
priormix(sDPMclust, nu0add = 5)

Arguments

`sDPMclust`	an object of class `summary.DPMMclust`
`nu0add`	an additional value integer added to hyperprior parameter nu (increase to avoid non positive definite matrix sampling)

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)
}

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

Arguments

`n`	number of observations
`alpha`	concentration parameter
`hyperG0`	base distribution hyperparameter
`verbose`	logical flag indicating whether info is written in the console.

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)
}

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)
}

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

Arguments

`alpha_old`	the current value of alpha
`n`	the number of data points
`K`	current number of cluster
`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 and this function returns `a`.

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






#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)
similarityMat(c, step = 1)

Arguments

`c`	a list of vector of length `n`. `c[[j]][i]` is the cluster allocation of observation `i=1...n` at iteration `j=1...N`.
`step`	provide co-clustering every `step` iterations. Default is 1.

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

similarityMat_nocostC(cc)
similarityMat_nocostC(cc)

Arguments

`cc`	a matrix whose columns each represents a ()MCMC) partition

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")
}
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")
}

C++ implementation

Description

C++ implementation

Usage

similarityMatC(cc)
similarityMatC(cc)

Arguments

`cc`	a matrix whose columns each represents a (MCMC) partition

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 <- 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, "["))

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

Arguments

`object`	a `DPMMclust` object.
`burnin`	integer giving the number of MCMC iterations to burn (defaults is half)
`thin`	integer giving the spacing at which MCMC iterations are kept. Default is `1`, i.e. no thining.
`gs`	optional vector of length `n` containing the gold standard partition of the `n` observations to compare to the point estimate
`lossFn`	character string specifying the loss function to be used. Either "F-measure" or "Binder" (see Details). Default is "Binder".
`posterior_approx`	logical flag whether a parametric approximation of the posterior should be computed. Default is `FALSE`
`...`	further arguments passed to or from other methods

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

C++ implementation

Description

C++ implementation

Usage

vclust2mcoclustC(c)
vclust2mcoclustC(c)

Arguments

`c`	is an MCMC partition

Author(s)

Chariff Alkhassim

Examples

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


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

Package 'NPflow'

Help Index

Bayesian Nonparametrics for Automatic Gating of Flow Cytometry data

Description

Details

Author(s)

References

See Also

Burning MCMC iterations from a Dirichlet Process Mixture Model.

Description

Usage

Arguments

Value

Author(s)

See Also

Point estimate of the partition for the Binder loss function

Description

Usage

Arguments

Value

Author(s)

References

See Also

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

Description

Usage

Arguments

Value

Author(s)

See Also

Point estimate of the partition using a modified Binder loss function

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

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

Description

Usage

Arguments

Value

Author(s)

References

See Also

Scatterplot of flow cytometry data

Description

Usage

Arguments

Examples

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

Description

Usage

Arguments

Value

Author(s)

Examples

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

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Slice Sampling of Dirichlet Process Mixture of Gaussian distributions

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Slice Sampling of Dirichlet Process Mixture of skew normal distributions

Description

Usage

Arguments