tess19

#!/usr/bin/env Rscript
# tess19 v1.0. Copyright (c) 2019. Shufei Ge and Lloyd T. Elliott.

suppressMessages(library(optparse))

exit_quietly = function() {
opt <- options(show.error.messages = FALSE)
on.exit(options(opt))
sink(file="/dev/null", type = "output")
sink(file="/dev/null", type = "message")
blankMsg <- sprintf("\r%s\r", paste(rep(" ", getOption("width")-1L),
collapse=" "));
stop(simpleError(blankMsg));
}

print_license = function() {
cat(sprintf("tess19 v1.0. Copyright (c) 2019. Shufei Ge and Lloyd T. Elliott.      \n"))
cat(sprintf("                                                                      \n"))
cat(sprintf("Redistribution and use in source and binary forms, with or without    \n"))
cat(sprintf("modification, are permitted provided that the following conditions    \n"))
cat(sprintf("are met:                                                              \n"))
cat(sprintf("                                                                      \n"))
cat(sprintf("1. Redistributions of source code must retain the above copyright     \n"))
cat(sprintf("notice, this list of conditions and the following disclaimer.         \n"))
cat(sprintf("                                                                      \n"))
cat(sprintf("2. Redistributions in binary form must reproduce the above copyright  \n"))
cat(sprintf("notice, this list of conditions and the following disclaimer in the   \n"))
cat(sprintf("documentation and/or other materials provided with the distribution.  \n"))
cat(sprintf("                                                                      \n"))
cat(sprintf("THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS   \n"))
cat(sprintf("'AS IS' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT     \n"))
cat(sprintf("LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR \n"))
cat(sprintf("A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT  \n"))
cat(sprintf("HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,\n"))
cat(sprintf("SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT      \n"))
cat(sprintf("LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, \n"))
cat(sprintf("DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY \n"))
cat(sprintf("THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT   \n"))
cat(sprintf("(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE \n"))
cat(sprintf("OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.  \n\n\n"))
exit_quietly()
}

print_help = function() {
cat(sprintf("tess19 v1.0. Copyright (c) 2019. Shufei Ge and Lloyd T. Elliott.\n"))
cat(sprintf("\n"))
cat(sprintf("The tess19 software implements the Bayesian nonparametric methods    \n"))
cat(sprintf("described in Ge et al, 'Random Tessellation Forests', 2019. This     \n"))
cat(sprintf("software constructs a random forest for posterior prediction of      \n"))
cat(sprintf("categorical data based on real valued predictors. The trees of the   \n"))
cat(sprintf("random forest are found through SMC inference. This manual is for    \n"))
cat(sprintf("version v1.0. This software requires the following R packages:       \n"))
cat(sprintf("optparse, purrr. This software is released under the open source     \n"))
cat(sprintf("BSD 2-clause license. \n"))
cat(sprintf("\n"))
cat(sprintf("      BASIC USAGE\n"))
cat(sprintf("\n"))
cat(sprintf("  tess19 <IFILE.txt> <OFILE.txt>\n"))
cat(sprintf("\n"))
cat(sprintf("Predictions for the missing labels in the 'Levels' column of the    \n"))
cat(sprintf("file <IFILE.txt> are made using the predictors in the file          \n"))
cat(sprintf("<IFILE.txt> and the uRTF model, with 100 trees, with the            \n"))
cat(sprintf("prespecified budget tau = infinity, and with the hyperparameter     \n"))
cat(sprintf("settings alpha_k = n_k/1000. The predictions are saved in the       \n"))
cat(sprintf("'Levels' column of the file <OFILE.txt>. \n"))
cat(sprintf("\n"))
cat(sprintf("The format of the file <IFILE.txt> is as follows. The file is space \n"))
cat(sprintf("separated. The first line is a header line with one column name for \n"))
cat(sprintf("each of predictor (for example, 'V1 V2 ...'), followed by a column  \n"))
cat(sprintf("named 'Levels'. Subsequent lines are given with one line per data   \n"))
cat(sprintf("item, with the predictors for the data item followed by the items   \n"))
cat(sprintf("level. The predictors are real numbers and the levels must be       \n"))
cat(sprintf("positive integers in the set 1 ... K, where K is the number of      \n"))
cat(sprintf("levels. Both test and train data must be provided in <IFILE.txt>,   \n"))
cat(sprintf("and the test data items must have missing labels indicated by the   \n"))
cat(sprintf("string 'NaN'. The predictors may not have missing data.\n"))
cat(sprintf("\n"))
cat(sprintf("The format of the file <OFILE.txt> is as follows. The first line is \n"))
cat(sprintf("a header line naming the column 'Levels' (ie, one column).          \n"))
cat(sprintf("Subsequent lines are given with one line for data item. If the data \n"))
cat(sprintf("item is a training data item, then the value 'NaN' is recorded in   \n"))
cat(sprintf("the corresponding line. If the data item is a testing data item,    \n"))
cat(sprintf("then a predicted label is recorded.\n"))
cat(sprintf("\n"))
cat(sprintf("      ADVANCED USAGE\n"))
cat(sprintf("\n"))
cat(sprintf("  tess19 --usage\n"))
cat(sprintf("\n"))
cat(sprintf("  tess19 --license\n"))
cat(sprintf("\n"))
cat(sprintf("  tess19 --version\n"))
cat(sprintf("\n"))
cat(sprintf("  tess19 [--Mondrian] [--weights <WFILE.txt>] [--cuts <MAX-CUTS>] \n"))
cat(sprintf("         [--tau <PRESPECIFIED-BUDGET>] [--alpha <HYPER-PARAMETER>]\n"))
cat(sprintf("         [--ntrees <NUMBER-OF-TREES>] [--particles <PARTICLES>]   \n"))
cat(sprintf("         [--seed <SEED>] <IFILE.txt> <OFILE.txt>\n\n"))
cat(sprintf("    --usage. Prints this manual to the standard output.\n"))
cat(sprintf("\n"))
cat(sprintf("    --license. Prints the open source BSD 2-clause license for    \n"))
cat(sprintf("    this software.\n"))
cat(sprintf("\n"))
cat(sprintf("    --version. Prints the software version information.\n"))
cat(sprintf("\n"))
cat(sprintf("    --Mondrian. Instructs tess19 to conduct axis aligned cuts,    \n"))
cat(sprintf("    yielding the MRTF model, or (if --weights flag is provided)   \n"))
cat(sprintf("    the wMRTF model. By default, axis aligned cuts are not used.  \n"))
cat(sprintf("\n"))
cat(sprintf("    --weights <WFILE.txt>. Instructs tess19 to use a weighted     \n"))
cat(sprintf("    version of the uniform distribution for the measure lambda^{d-1},\n"))
cat(sprintf("    yielding the wuRTF or wMRTF mdoel. The weights are read from \n"))
cat(sprintf("    the file <WFILE.txt> which must contain d lines corresponding \n"))
cat(sprintf("    the prior weight for each predictor, with one real number per \n"))
cat(sprintf("    line.\n"))
cat(sprintf("\n"))
cat(sprintf("    --cuts <MAX-CUTS>. This flag sets a stopping condition wherein \n"))
cat(sprintf("    SMC particles will return after <MAX-CUTS> cuts, regardless of \n"))
cat(sprintf("    the budget. By default, <MAX-CUTS> is set to 100. This value   \n"))
cat(sprintf("    must be a positive integer. By the pausing condition, each cut \n"))
cat(sprintf("    separates a data item, and setting <MAX-CUTS> to a value larger\n"))
cat(sprintf("    than or equal to the number of data items is equivalent to     \n"))
cat(sprintf("    setting <MAX-CUTS> to infinity. \n"))
cat(sprintf("\n"))
cat(sprintf("    --tau <PRESPECIFIED-BUDGET>. This flag specifies the budget.   \n"))
cat(sprintf("    The budget tau must be a positive real number, or infinity. By \n"))
cat(sprintf("    default, tau is set to infinity.\n"))
cat(sprintf("\n"))
cat(sprintf("    --alpha <HYPER-PARAMETER>. This flag is a positive real number \n"))
cat(sprintf("    that sets the coefficient of the empirical label proportion in \n"))
cat(sprintf("    the Dirichlet/multinomial prior, so that the value of the      \n"))
cat(sprintf("    hyperparameter is alpha_k = <HYPER-PARAMETER> * n_k. The       \n"))
cat(sprintf("    default value is 1E-3.\n"))
cat(sprintf("\n"))
cat(sprintf("    --ntrees <NUMBER-OF-TREES>. This flag is a positive integer    \n"))
cat(sprintf("    that sets the number of trees to use in the random forest. By  \n"))
cat(sprintf("    default, <NUMBER-OF-TREES> is set to 100. A value of 1         \n"))
cat(sprintf("    specifies the uRTP/wuRTP/MRTP/wMRTP priors (i.e., no random    \n"))
cat(sprintf("    forest).\n"))
cat(sprintf("\n"))
cat(sprintf("    --particles <PARTICLES>. This flag sets the number of particles\n"))
cat(sprintf("    to use in the SMC approximations. The default value of         \n"))
cat(sprintf("    <PARTICLES> is 100. \n"))
cat(sprintf("\n"))
cat(sprintf("    --seed <SEED>. This flag sets the random seed to <SEED>. The  \n"))
cat(sprintf("    default is to use to use the system clock to set the random   \n"))
cat(sprintf("    seed. \n"))
exit_quietly()
}

print_version = function() {
cat(sprintf("                                                              \n"))
cat(sprintf("                   ▄▄█████▄▄                                  \n"))
cat(sprintf("                  ▐██████████▄   ▄▄▄     ▄▄▄▄▄  ▄▄███▄▄       \n"))
cat(sprintf("                  █████████████▐█████▄████████▄███████▀       \n"))
cat(sprintf("                   ██▀▀███▌▄▀███▀▀  ▄███████▀█▌███████        \n"))
cat(sprintf("                      ████▐███     ████████   ▐████ 19        \n"))
cat(sprintf("                     ████▌████▄    ▐██████▌    ███▄           \n"))
cat(sprintf("                    ▐████▐██        ██████▄     █████         \n"))
cat(sprintf("                    ▐████▌███   ▄██  ▀█████▌ ▄▄  ████▌        \n"))
cat(sprintf("                    ▐█████ ████████▄ █ ▀███▌▐██▄ ▄███         \n"))
cat(sprintf("                     ▀████▌ ▀███▀▀▀ ███▄███▀████████          \n"))
cat(sprintf("                      ▀███▀           ▀▀▀▀   ▀████▀           \n"))
cat(sprintf("                             tess19 v1.0                      \n"))
cat(sprintf("                                                              \n"))
cat(sprintf("           Copyright (c) 2019. Shufei Ge and Lloyd T. Elliott.\n"))
cat(sprintf("\n"))
cat(sprintf("  Use tess19 --usage for help.\n"))
cat(sprintf("  Use tess19 --license to print the software license.\n"))
cat(sprintf("  Use tess19 --version for this message.\n\n\n"))
exit_quietly()
}

print_error = function(message) {
cat(sprintf('tess19: %s.\n', message))
exit_quietly()
}

args = commandArgs(trailingOnly = TRUE)
if (length(args) == 0) {
print_version()
}

if (length(args) > 1) {
fname = args[length(args)-1]
gname = args[length(args)]
args = args[-c(length(args) - 1, length(args))]
}


option_list <- list(
make_option("--version", action = "store_true", default = FALSE), #
make_option("--usage", action = "store_true", default = FALSE),
make_option("--license", action = "store_true", default = FALSE), #
make_option("--Mondrian", action = "store_true", default = FALSE), #
make_option("--weights", default = FALSE), #
make_option("--cuts", default = 100), #
make_option("--tau", default = Inf), #
make_option("--alpha", default = 1e-3),
make_option("--ntrees", default = 100), #
make_option("--particles", default = 100), #
make_option("--seed", default = -1) #
)

opt = parse_args(OptionParser(option_list = option_list), args = args)

if (opt$version) {
if (length(args) > 1) {
print_error('Argument error (2)')
} else {
print_version()
}
}

if (opt$license) {
if (length(args) > 1) {
print_error('Argument error (3)')
} else {
print_license()
}
}

if (opt$usage) {
if (length(args) > 1) {
print_error('Argument error (4)')
} else {
print_help()
}
}

if (!file.exists(fname)) {
print_error('<IFILE.txt> does not exist')
}

if (opt$Mondrian) {
cut.type = 2
} else {
cut.type = 1
}

ALPHA = as.numeric(opt$alpha)
if (ALPHA < 0) {
print_error('Argument to --alpha must be positive')
}

cat(sprintf('tess19 v1.0. Copyright (c) 2019. Shufei Ge and Lloyd T. Elliott.\n\n'))
cat(sprintf('%s ', format(Sys.time(), "%a %b %d %X %Y")))
cat(sprintf('%s\n\n', getwd()))

l.max=as.numeric(opt$cuts) #100  #this would be same as setting tau=Inf if number of train data points <100.
# set l.max to a large number greater than or equal to # of obs, if setting tau=Inf;
# otherwise, the inference will terminate when either tau reaches the budget or
# number of cuts exceeds the l.max.
split.seed=as.numeric(opt$seed)
if (split.seed == -1) {
split.seed = as.integer((as.double(Sys.time())*1000+Sys.getpid()) %% 2^31)
set.seed(split.seed)
}
tau=as.numeric(opt$tau)
sample.type=1
accept.rate.min=0.05
N=as.numeric(opt$particles)
rep.max=as.numeric(opt$ntrees)

if (opt$weight) {
if (!file.exists(opt$weight)) {
print_error('Could not open weight file')
}
w.normal=scan(opt$weight, numeric(), quote = "")
w.normal <- w.normal/sum(w.normal)
} else {
w.normal = NULL
}

cat(sprintf('Arguments:\n'))
if (opt$Mondrian) {
cat(sprintf('  --method Mondrian\n')) }
if (opt$weights != FALSE) {
cat(sprintf("  --weights '%s'\n", opt$weights)) }
cat(sprintf('  --cuts %d\n', opt$cuts))
cat(sprintf('  --tau %g\n', opt$tau))
cat(sprintf("  --alpha %g\n", opt$alpha))
cat(sprintf("  --ntrees %d\n", opt$ntrees)) #
cat(sprintf("  --particles %d\n", opt$particles)) #
cat(sprintf("  --seed %d\n\n", split.seed)) #

cat(sprintf("  IFILE '%s'\n", fname)) #
cat(sprintf("  OFILE '%s'\n\n", gname)) #

cat(sprintf('Loading packages.\n'))
suppressMessages(library(purrr)    )

cat(sprintf('Loading data.\n'))
data  <-  read.table(fname, sep = ' ', row.names = NULL, header = TRUE)
d     <- dim(data)[2]-1
V.all <-  as.matrix(data[,1:d])

if(l.max==Inf){
l.max=dim(data)[1]
}

min <- matrix(apply(V.all,2,min),nrow=dim(V.all)[1],ncol=dim(V.all)[2],byrow=TRUE)
max <- matrix(apply(V.all,2,max),nrow=dim(V.all)[1],ncol=dim(V.all)[2],byrow=TRUE)
V.all <- (V.all-min)/(max-min)
rm("min","max")


V.label <- data[,(d+1)]
id.test <- which(is.nan(V.label))
V.label[id.test]<- NA #set the unknow labels as NA; otherwise, they will be grouped as a new group.
group <- as.factor(V.label)

group.level <- levels(group)
group.len <- length(group.level)

Cut_plane_standard <- function(V,V.ID,V.label,sample.type,cut.type,accept.rate.min,dist.max=NA,w.normal=NULL){
d <- dim(V)[2]
P.u <- rep(NA,d)
theta <- rep(NA,(d-1))
mu <- c(NA)
len.projection <- c(NA)
normal.v <- rep(NA,d)
sample.cut.count <- 1
V.left.ID <-NULL
V.right.ID <- NULL
if(is.null(w.normal)){
w.normal <- rep(1/d,d)
}

if(sum(!is.na(V.label))>0){
V.unique <- unique(V[!is.na(V.label),])
d1 <- dim(V.unique)[1]
if(is.na(dist.max)){
if(d1==1){
dist.max <- 0
}else{
dist.max <- max(dist(V.unique))
}
}
#skip the cut if all obs are from the same group(pausing condition)
# or if labled vertices are same
skip.index <- (sum(table(V.label)!=0)==1) | dist.max==0
}else{
skip.index =1 # skip if all vertices are unlabled
}


if(!skip.index){
if(sample.type==1){
# use the largest distance between vertices as upper bound instead of the diameter of the
# smallest d-sphere, since
# length(projection.line.segment(Vertices))<= max{dist between Vertices}
#                                         <= the diameter of the smallest sphere
# dist.max would be the smallest boundary of the rejection sampling
run.index <- 1
if(cut.type==1){
while(run.index){


normal.v <- rnorm(d,sd=0.1)
normal.v <- w.normal*normal.v
normal.v <- normal.v/sqrt(sum(normal.v^2))

t.scale <-  V%*%matrix(normal.v,nrow=d,ncol=1)/sum(normal.v^2)
t.scale.train <- t.scale[!is.na(V.label)]
t.scale.ends <- range(t.scale.train,na.rm = TRUE)
V.projection.ends <-rbind(t.scale.ends[1]*normal.v,t.scale.ends[2]*normal.v)
len.projection <- diff(t.scale.ends)*sqrt(sum(normal.v^2))

mu <- runif(1,min=0,max=dist.max)
mu <- mu/len.projection
if(mu<1){
t.scale.mu <- (1-mu)*t.scale.ends[1]+mu*t.scale.ends[2]
#if(any(t.scale<t.scale.mu) && any(t.scale>t.scale.mu)){
if(any(t.scale.train<=t.scale.mu) && any(t.scale.train>t.scale.mu)){
run.index <- 0
P.u <- (1-mu)*V.projection.ends[1,]+mu*V.projection.ends[2,]
V.left.ID <- which(t.scale<=t.scale.mu)
V.right.ID <- which(t.scale>t.scale.mu)
}
}else{
sample.cut.count <- sample.cut.count+1
run.index <- (1/sample.cut.count>accept.rate.min)*1
skip.index <- 1-run.index
}
}
}else{
while(run.index){

normal.v<- c(rmultinom(1,size=1,prob=w.normal))


t.scale <-  V%*%matrix(normal.v,nrow=d,ncol=1)/sum(normal.v^2)
t.scale.train <- t.scale[!is.na(V.label)]
t.scale.ends <- range(t.scale.train,na.rm = TRUE)
V.projection.ends <-rbind(t.scale.ends[1]*normal.v,t.scale.ends[2]*normal.v)
len.projection <- diff(t.scale.ends)*sqrt(sum(normal.v^2))


mu <- runif(1,min=0,max=dist.max)
mu <- mu/len.projection

if(mu<1){
t.scale.mu<-(1-mu)*t.scale.ends[1]+mu*t.scale.ends[2]
if(any(t.scale.train<=t.scale.mu) && any(t.scale.train>t.scale.mu)){
run.index <- 0
P.u <- (1-mu)*V.projection.ends[1,]+mu*V.projection.ends[2,]
V.left.ID <- which(t.scale<=t.scale.mu)
V.right.ID <- which(t.scale>t.scale.mu)
}

}else{
sample.cut.count <- sample.cut.count+1
run.index <- (1/sample.cut.count>accept.rate.min)*1
skip.index <- 1-run.index
}
}
}
}else{
run.index <- 1
while(run.index){

if(cut.type==1){
normal.v <- rnorm(d,sd=0.1)
normal.v <- w.normal*normal.v
normal.v <- normal.v/sqrt(sum(normal.v^2))


}else{
normal.v<- c(rmultinom(1,size=1,prob=w.normal))

}

t.scale <-  V%*%matrix(normal.v,nrow=d,ncol=1)/sum(normal.v^2)
t.scale.train <- t.scale[!is.na(V.label)]
t.scale.ends <- range(t.scale.train,na.rm = TRUE)
V.projection.ends <-rbind(t.scale.ends[1]*normal.v,t.scale.ends[2]*normal.v)
len.projection <- diff(t.scale.ends)*sqrt(sum(normal.v^2))

mu <- runif(1,0,1)
t.scale.mu<-(1-mu)*t.scale.ends[1]+mu*t.scale.ends[2]

if(any(t.scale.train<=t.scale.mu) && any(t.scale.train>t.scale.mu)){
run.index <- 0
P.u <- (1-mu)*V.projection.ends[1,]+mu*V.projection.ends[2,]
V.left.ID <- which(t.scale<=t.scale.mu)
V.right.ID <- which(t.scale>t.scale.mu)
}else{
sample.cut.count <- sample.cut.count+1
run.index <- (sample.cut.count<11)*1
skip.index <- 1-run.index
}

}

}
}
return(list(N_vec= normal.v,Pu=P.u,
Len.projection=len.projection,dist.max=dist.max,
sample.cut.count=sample.cut.count,
skip.index=skip.index,
V.left.ID=V.left.ID,
V.right.ID=V.right.ID
))
}





#app_qhull <- function(V,d){
#  V.unique <- unique(V)
#  if(dim(V.unique)[1]==1){
#    Lambda <- 0
#    radius.V<-0
#  }else{
#    radius.V <- max(dist(V.unique))/2
#    Lambda   <- radius.V
#  }
#  return(c(Lambda, radius.V*2))
#}






Generative_Process <- function(partition,V.all,V.label,tau,group.level,group.len,sample.type,cut.type,accept.rate.min,w.normal){
l <- length(partition$Polytopes)
d <- dim(V.all)[2]
tau.v <- partition$tau
result <- c(0,0,0)
Cut <- list()
cut.idx <- 0
skip.all <- 0  #only set it to 1 when  (1) neither cond1 or cond2 is  true OR (2) cost exceeds the budget .
group.level2 <- as.factor(group.level)

if(tau.v[l]>=tau){
skip.all <- 1
}else{
Lambdas <- sapply(partition$Polytopes, "[[", 2)

##shrink the candidate space, only choose from polytopes whose
#  (i) Lambda>0
#       AND
#  (ii) obs are not from same group (the obs with known labels)
cond1 <- (Lambdas>0)
cond2 <- (apply(is.infinite(sapply(partition$Polytopes,"[[",3)/0),2,sum)>1)
cond12 <- sum(cond1&cond2)
if(cond12==0){
skip.all <- 1
}else{
sample.space <- which(cond1&cond2)
if(length(sample.space)==1){
j <- sample.space
}else{
j <- sample(x=c(sample.space),size=1,prob = Lambdas[sample.space])
}

V.temp.ID <- partition$Polytopes[[j]]$V.ID
V.temp <- V.all[V.temp.ID,]
V.temp.label <- V.label[V.temp.ID]
dist.max <- partition$Polytopes[[j]]$dist.max
Cut <- Cut_plane_standard(V.temp,V.tempID,V.temp.label,sample.type,cut.type,accept.rate.min,dist.max,w.normal)

if(Cut$skip.index!=1){
index.left <- Cut$V.left.ID
index.right <- Cut$V.right.ID

if(length(index.left)==1){
V.temp.left <- t(as.matrix(V.temp[index.left,]))
}else{
V.temp.left <- V.temp[index.left,]
}

if(length(index.right)==1){
V.temp.right <- t(as.matrix(V.temp[index.right,]))
}else{
V.temp.right <- V.temp[index.right,]
}

V.temp.ID.left <- V.temp.ID[index.left]
V.temp.ID.right <- V.temp.ID[index.right]

cut.idx <- 1
l <- l+1

#out.left <- app_qhull(V.temp.left,d)
#out.right <- app_qhull(V.temp.right,d)
#Lambda.left <- out.left[1]
#Lambda.right <- out.right[1]
#dist.max.left <- out.left[2]
#dist.max.right <- out.right[2]

dist.max.left <- max(dist.all[V.temp.ID.left,V.temp.ID.left])
dist.max.right <-  max(dist.all[V.temp.ID.right,V.temp.ID.right])
Lambda.left <- dist.max.left/2
Lambda.right <- dist.max.right/2



countbygroup.left <- as.numeric(table(c(V.label[V.temp.ID.left],group.level2))-1)
countbygroup.right <- as.numeric(table(c(V.label[V.temp.ID.right],group.level2))-1)
partition$Polytopes[[j]] <- list(V.ID=V.temp.ID.left,Lambda=Lambda.left,CountByGroup=countbygroup.left,dist.max=dist.max.left)
partition$Polytopes[[l]] <- list(V.ID=V.temp.ID.right,Lambda=Lambda.right,CountByGroup=countbygroup.right,dist.max=dist.max.right)


Lambdas <- sapply(partition$Polytopes, "[[", 2)
tau.v.plus1 <- rexp(n=1,sum(Lambdas))+tau.v[l-1]
tau.v <- c(tau.v,tau.v.plus1)
partition$tau <- tau.v
}
}

}
return(list(partition=partition,
cut.indx=cut.idx,
Cut=Cut,skip.all=skip.all))
}



partition_initial <- function(group.level,group.len,V.all,V.label,l.max,tau,sample.type,cut.type,accept.rate.min){
group.level2 <- as.factor(group.level)
n <- length(V.label)
V.temp.ID <- c(1:n)
V.temp <- V.all[V.temp.ID,]
d <- dim(V.all)[2]
Polytopes <- list()
#countbygroup <- rep(NA,group.len)
dist.all <- as.matrix(dist(V.all))



countbygroup <- as.numeric(table(c(V.label,group.level2))-1)

#out.temp <- app_qhull(V.temp,d)
#Polytopes[[1]] <- list(V.ID=V.temp.ID,  Lambda=out.temp[1], CountByGroup=countbygroup,dist.max=out.temp[2])
#rm("out.temp")
dist.max <- max(dist.all)
Polytopes[[1]] <- list(V.ID=V.temp.ID,  Lambda=dist.max/2, CountByGroup=countbygroup,dist.max=dist.max)


Partition.Inital <- list(Polytopes=Polytopes,tau=rexp(1,rate=Polytopes[[1]]$Lambda))

output <- list(Partition.Inital=Partition.Inital,dist.all=dist.all)
return(output)
}

getmode <- function(v) {
uniqv <- unique(v)
uniqv[which.max(tabulate(match(v, uniqv)))]
}


#----inference -----start from here--------



#------------------Partition versus no. cuts (No. of cuts =l.max or tau=Inf)------------------
alpha0 <- matrix((round(table(group)/table(group)[1],2))*ALPHA,ncol=1) #try math paramter
t0 <- proc.time()
table.out <- c()

cat(sprintf("\nEstimated runtime: ?\n"))
pb <- txtProgressBar(min = 0, max = N*rep.max, style = 3)

set.seed(split.seed)

part_init <- partition_initial(group.level,group.len,V.all,V.label,l.max,tau,sample.type,cut.type,accept.rate.min)

Partition.Inital <- part_init$Partition.Inital
dist.all <- part_init$dist.all


Partition.t0 <- list()
Lambda0 <- Partition.Inital$Polytopes[[1]]$Lambda
for(i in 1:N){
tau.temp <- rexp(1,rate=Lambda0)
Partition.t0[[i]] <- list(Polytopes=Partition.Inital$Polytopes,tau=tau.temp)
}

cbg0 <- sapply(Partition.Inital$Polytopes, "[[", 3)
multi.beta.0 <- apply(cbg0,2, (function(x){x+alpha0}))
logl.tminus0 <- rep(sum(lgamma(multi.beta.0))-sum(lgamma(apply(multi.beta.0,2,sum)))-dim(cbg0)[2]*(sum(lgamma(alpha0))-lgamma(sum(alpha0))),N)

Wt0 <- rep(1/N,N)   # Weights vector for N particles at time t=0
logWt0 <- log(Wt0)   # log Weights vector for N particles at time t=0

label.predict.all <- NULL
for(rep in 1:rep.max){
setTxtProgressBar(pb, ((rep-1)*N))

Partition.t <- Partition.t0
Wt <- Wt0        # Weights vector for N particles at time t
logWt <- logWt0  # log Weights vector for N particles at time t
logl.tminus1 <- logl.tminus0 #log likelihood for N particles at time t-1
logl.t <- logl.tminus1 #log likelihood for N particles at time t
# create progress bar
tau.li <- Partition.Inital$tau

end.cond <- FALSE

skip.index.N <- rep(0,N)

t <- 1  # here t is the number of cuts; we use vector tau to denote the cost at each cut.
t.idx <- rep(0,l.max)
while(tau.li<tau){
Cut <- vector(mode="list",length=N)
#resampling-------------start
if(t>1){

jC <- sample(x=1:N,size=N,prob =Wt,replace = TRUE )


Partition.t.new <- list()
for(i in 1:N){
Partition.t.new[[i]] <- Partition.t[[jC[i]]]
}


Wt[1:N] <- 1/N


logWt <- log(Wt)
logl.t <- logl.t[jC]
logl.tminus1 <- logl.tminus1[jC]
skip.index.N <- skip.index.N[jC]
Partition.t <- Partition.t.new
rm("Partition.t.new")
}
#resampling-------------end


for (i in 1:N){
if(!skip.index.N[i]){
partition.temp <- Partition.t[[i]]
Out.temp <- Generative_Process(partition.temp,V.all,V.label,tau,group.level,group.len,sample.type,cut.type,accept.rate.min,w.normal)
Cut[[i]] <- Out.temp$Cut
if(Out.temp$cut.indx){
cbg.new <- sapply(Out.temp$partition$Polytopes, "[[", 3) # count by group for the new partion
multi.beta.a <- apply(cbg.new,2, (function(x){x+alpha0}))
logl.t[i] <- sum(lgamma(multi.beta.a))-sum(lgamma(apply(multi.beta.a,2,sum)))-dim(cbg.new)[2]*(sum(lgamma(alpha0))-lgamma(sum(alpha0)))
logWt[i] <- logWt[i]+logl.t[i]-logl.tminus1[i]
logl.tminus1[i] <- logl.t[i]
Partition.t[[i]] <- Out.temp$partition
}else{
skip.index.N[i] <- Out.temp$skip.all
i.rep <- 0
if(!skip.index.N[i]){
while(i.rep<10){
Out.temp <- Generative_Process(partition.temp,V.all,V.label,tau,group.level,group.len,sample.type,cut.type,accept.rate.min,w.normal)
Cut[[i]] <- Out.temp$Cut
i.rep <- i.rep+1
if(Out.temp$cut.indx){
cbg.new <- sapply(Out.temp$partition$Polytopes, "[[", 3) # count by group for the new partion
multi.beta.a <- apply(cbg.new,2, (function(x){x+alpha0}))
logl.t[i] <- sum(lgamma(multi.beta.a))-sum(lgamma(apply(multi.beta.a,2,sum)))-dim(cbg.new)[2]*(sum(lgamma(alpha0))-lgamma(sum(alpha0)))
logWt[i] <- logWt[i]+logl.t[i]-logl.tminus1[i]
logl.tminus1[i] <- logl.t[i]
Partition.t[[i]] <- Out.temp$partition
i.rep <- Inf
}else{
skip.index.N[i] <- Out.temp$skip.all
}
}
}
}
}

}


Wt <- exp((logWt-max(logWt)))/sum(exp((logWt-max(logWt))))

t <- max(length(Partition.t[[which.max(Wt)]]$tau)-1,1)

tau.li <- min(map_dbl(Partition.t,~rev(.$tau)[1]))
end.cond <- min(skip.index.N)

t.idx[t] <- t.idx[t]+1

# to avoid endless while-loop
if(end.cond | (t+1)>l.max | tau.li>tau|(t.idx[t]>100) ){
tau.li <- Inf
}

if(tau.li==Inf){
#---correct%
count.by.group.temp <- sapply(Partition.t[[which.max(Wt)]]$Polytopes, "[[", 3)
count.by.group.temp.idx <- apply(count.by.group.temp,2,which.max)

ID.temp <- sapply(Partition.t[[which.max(Wt)]]$Polytopes, "[[", 1)
label.predic <- rep(NA,length(V.label))
for(id.j in 1:length(ID.temp)){
label.predic[ID.temp[[id.j]]] <- as.numeric(group.level[count.by.group.temp.idx[id.j]])
}
pred.t <- label.predic[id.test]
label.predict.all<- cbind(label.predict.all,pred.t)
}
}


if(rep==1){
zz = round((proc.time()-t0)[3]/60/60*rep.max,4)
if (zz < 1) {
zz = round(zz * 60)
if (zz <= 1) {
zz = "1 minute"
} else {
zz = sprintf("%d minutes", zz)
}
} else if (zz > 24) {
zz = round(zz/24)
if (zz <= 1) {
zz = "1 day"
} else {
zz = sprintf("%d days", zz)
}
} else {
zz = round(zz)
if (zz <= 1) {
zz = "1 hour"
} else {
zz = sprintf("%d hours", zz)
}
}

cat(sprintf("\r\033[K\033[1A\r\033[K\r%s\n", paste("Estimated runtime: ", zz, sep="" )))
}
}
label.predict.all <- as.matrix(t(na.omit(t(label.predict.all))))
label.predict.RF  <- apply(label.predict.all,1,getmode)
group.test <- data.frame(Level=data$Level)
group.test[-id.test, ] <- NaN
group.test[id.test, ] <- label.predict.RF
write.table(group.test, file = gname, sep = ' ', row.names = FALSE, col.names = TRUE, quote = FALSE, na = "NaN")
cat(sprintf("\r\033[K\033[K\r\nDone.\n"))
# proc.time()-t0