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Sec3.3_Prior_graphs.R
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####################
## Sally Paganin
## Nov 4 2021
####################
####################
library(CPLogit)
library(ggplot2)
library(grid)
library(gridExtra)
library(BNPmix)
####################
## Check CP process using normalized distance
####################
# Bell numbers - sequence A000110
bell_n = c(1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804)
####################
## Functions for the CP prior
####################
CPpenalization <- function(distance, psi, returnLog = FALSE) {
if(returnLog){
-psi*distance
} else {
exp(-psi*distance)
}
}
####################
## Dirichlet Process EPPF e
####################
dpEPPF <- function(partition, concentration, returnLog = FALSE){
nObs = length(partition)
nBlocks = length(unique(partition))
blockSizes = table(partition)
logProb = nBlocks*log(concentration) + sum(lgamma(blockSizes))
if(returnLog) {
logProb
} else {
exp(logProb)
}
}
###########################
## Finite Dirichlet EPPF
###########################
finiteDirichletEPPF = function(partition, concentration, nClusters, returnLog = FALSE){
nObs = length(partition)
nBlocks = length(unique(partition))
blockSizes = table(partition)
log_c = 0
if(nBlocks < nClusters) {log_c = - lgamma(nClusters - nBlocks +1)}
logProb = lgamma(nClusters +1) + log_c + sum(lgamma(concentration/nClusters + blockSizes) - lgamma(concentration/H))
## + lgamma(concentration) - lgamma(concentration + nObs) # (normalizaoitn constant)
if(returnLog) {
logProb
} else {
exp(logProb)
}
}
##############################
## Pitman-Yor process eppf
##############################
pyEPPF <- function(partition, concentration, discount, returnLog = FALSE){
n = length(partition)
nBlocks = length(unique(partition))
blockSizes = table(partition)
if(nBlocks == 1){
logProb = -
lgamma(n + concentration) + lgamma(concentration + 1) +
sum(lgamma(discount + blockSizes) - lgamma(1 - discount))
} else {
logProb = sum(log(concentration + 1:(nBlocks-1)*discount)) -
lgamma(n + concentration) + lgamma(concentration + 1) +
sum(lgamma(discount + blockSizes) - lgamma(1 - discount))
}
if(returnLog) {
logProb
} else {
exp(logProb)
}
}
##################
## Plotting
##################
## Set c0 partition color
col2 = "#00B0DA"
## Set a list of c0 partitions
c0_list = list(c(0,0,0,0,0),
c(0,0,0,1,1),
c(0,0,1,1,2),
c(0,0,1,2,3),
c(0,1,2,3,4))
##################
## UNIFORM EPPF
##################
## values of psi parameter (x-axis)
psiVal = c(0,0.5,1,1.5,2,2.5, 3)
for(i in 1:5){
c0 = c0_list[[i]]
## Compute distances from c0 and generate all possible partitions
dd = CPLogit::dist_from(c0, TRUE)
## Numerator of CP process
CPNum = sapply(psiVal, function(x) CPpenalization(dd$distances, psi = x))
## Compute probabilities (normalization)
CPProbs = apply(CPNum, 2, function(x) x/sum(x))
nBlocks = apply(dd$partition, 1, function(x) length(unique(x)))
biggestBlock = apply(dd$partition, 1, function(x) max(table(x)))
indBiggestBlock = order(as.numeric(paste(nBlocks, biggestBlock, sep = "")), decreasing = TRUE)
#
tmp = CPProbs[indBiggestBlock, ]
df = reshape2::melt(tmp) ## data frame Var1 = partition index Var2 psi index
## Find position of the c0 partition
c0Pos = which(apply(dd$partitions[indBiggestBlock, ], 1, function(x) all(x == c0)))
df$isC0 = as.numeric(df$Var1==c0Pos)
yTicks = c(0, cumsum(tmp[,1])[c(1,16, 41, 51, 52)])
p = ggplot(df, aes(x = Var2, y = value)) +
geom_area(aes(group = Var1, fill = factor(isC0)),col = "grey20" ) +
scale_fill_manual(values = c('grey90',col2))+
theme_minimal(18) +
scale_x_continuous(breaks = 1:7,labels = psiVal, limits = c(1, 7), expand = c(0, 0)) +
theme(legend.position = 'none',plot.margin=grid::unit(c(1,1,1,1), "cm")) +
scale_y_continuous(breaks= yTicks, limits = c(0, 1), expand = c(0, 0),
sec.axis = sec_axis(trans = ~., name = "Cumulative probability", breaks = c(0, 0.2, 0.4, 0.6, 0.8, 1),
labels = c("0.0", "0.2", "0.4", "0.6", "0.8", "1.0"))) +
theme(axis.title.y.left = element_blank(), axis.text.y.left = element_blank(),
axis.ticks.y.left = element_line(size = 0.6, colour = "grey20", linetype = "dotted"),
axis.ticks.length.y.left = unit(2, "cm"),
axis.ticks.length.x.bottom = unit(2, "cm"),
axis.text.y.right = element_text( size = rel(1.6)),
axis.ticks.x = element_blank(),
axis.text.x = element_text(margin = margin(t = -1.5, unit = "cm"), size = rel(1.6)),
axis.title.x=element_text(size=20,face="bold"),
axis.title.y.right=element_text(size=20)
) +
xlab(expression(psi))
pt = p + annotation_custom(grob = textGrob(label = "1 block", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.01,ymax = 0.01, xmin = 0,xmax = 0.5) +
annotation_custom(grob = textGrob(label = "2 blocks", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.2, ymax = 0.2, xmin = 0,xmax = 0.5) +
annotation_custom(grob = textGrob(label = "3 blocks", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.55,ymax = 0.55, xmin = 0,xmax = 0.5) +
annotation_custom(grob = textGrob(label = "4 blocks", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.85,ymax = 0.85, xmin = 0,xmax = 0.5) +
annotation_custom(grob = textGrob(label = "5 blocks", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.99,ymax = 0.99, xmin = 0,xmax = 0.5)
gt <- ggplot_gtable(ggplot_build(pt))
gt$layout$clip[gt$layout$name == "panel"] <- "off"
grid_p = grid.arrange(gt)
ggsave(grid_p, file = paste0("CP_uniform_", i, ".pdf"), device = "pdf", width = 6, height = 5, unit = 'cm', scale = 3, dpi = 300)
}
###########################
## DP process -----
###########################
alpha <- 1
for(i in 1:5){
c0 = c0_list[[i]]
## Compute distances from c0 and generate all possible partitions
dd = CPLogit::dist_from(c0, TRUE)
## Numerator of CP process penalization
CPNum = sapply(psiVal, function(x) CPpenalization(dd$distances, psi = x))
## Numerator of DP process EPP
DPNum = apply(dd$partitions, 1 ,function(x) dpEPPF(partition = x, concentration = alpha))
# p_dir = apply(dd$partitions, 1 ,function(x) dir_eppf(x, 1/2, 5))
### ORDER PARTITIONS
nBlocks = apply(dd$partition, 1, function(x) length(unique(x)))
biggestBlock = apply(dd$partition, 1, function(x) max(table(x)))
indBiggestBlock = order(as.numeric(paste(nBlocks, biggestBlock, sep = "")), decreasing = TRUE)
#
partitionProbs = apply(CPNum, 2, function(x) (DPNum*x)/sum(DPNum*x))
tmp = partitionProbs[indBiggestBlock, ]
df = reshape2::melt(tmp) ## data frame Var1 = partition index Var2 psi index
## Find position of the c0 partition
c0Pos = which(apply(dd$partitions[indBiggestBlock, ], 1, function(x) all(x == c0)))
df$isC0 = as.numeric(df$Var1==c0Pos)
yTicks = c(0, cumsum(tmp[,1])[c(1,16, 41, 51, 52)])
p = ggplot(df, aes(x = Var2, y = value)) +
geom_area(aes(group = Var1, fill = factor(isC0)),col = "grey20" ) +
scale_fill_manual(values = c('grey90',col2))+
theme_minimal(18) +
scale_x_continuous(breaks = 1:7,labels = psiVal, limits = c(1, 7), expand = c(0, 0)) +
theme(legend.position = 'none',plot.margin=grid::unit(c(1,1,1,1), "cm")) +
scale_y_continuous(breaks= yTicks, limits = c(0, 1), expand = c(0, 0),
sec.axis = sec_axis(trans = ~., name = "Cumulative probability", breaks = c(0, 0.2, 0.4, 0.6, 0.8, 1),
labels = c("0.0", "0.2", "0.4", "0.6", "0.8", "1.0"))) +
theme(axis.title.y.left = element_blank(), axis.text.y.left = element_blank(),
axis.ticks.y.left = element_line(size = 0.6, colour = "grey20", linetype = "dotted"),
axis.ticks.length.y.left = unit(2, "cm"),
axis.ticks.length.x.bottom = unit(2, "cm"),
axis.text.y.right = element_text( size = rel(1.6)),
axis.ticks.x = element_blank(),
axis.text.x = element_text(margin = margin(t = -1.5, unit = "cm"), size = rel(1.6)),
axis.title.x=element_text(size=20,face="bold"),
axis.title.y.right=element_text(size=20)
) +
xlab(expression(psi))
pt = p + annotation_custom(grob = textGrob(label = "1 block", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.01,ymax = 0.01, xmin = 0,xmax = 0.5) +
annotation_custom(grob = textGrob(label = "2 blocks", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.2, ymax = 0.2, xmin = 0,xmax = 0.5) +
annotation_custom(grob = textGrob(label = "3 blocks", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.55,ymax = 0.55, xmin = 0,xmax = 0.5) +
annotation_custom(grob = textGrob(label = "4 blocks", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.85,ymax = 0.85, xmin = 0,xmax = 0.5) +
annotation_custom(grob = textGrob(label = "5 blocks", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.99,ymax = 0.99, xmin = 0,xmax = 0.5)
gt <- ggplot_gtable(ggplot_build(pt))
gt$layout$clip[gt$layout$name == "panel"] <- "off"
grid_p = grid.arrange(gt)
ggsave(grid_p, file = paste0("CP_dp_", i, ".pdf"), device = "pdf", height = 15, width = 15, unit = "cm", dpi = 300)
}
###########################
## Pitman Yor -----
###########################
## Fix discount parameter and pick concentration to
## match expected number of clusters under the DP
discount = 0.5
## discount = 0.75
## Check the expected number of clusters matches DP (1.6)
## BNPmix::PYcalibrate(log(5), 5, discount = discount)$strength
for(i in 1:5){
c0 = c0_list[[i]]
## Compute distances from c0 and generate all possible partitions
dd = CPLogit::dist_from(c0, TRUE)
## Numerator of CP process penalization
CPNum = sapply(psiVal, function(x) CPpenalization(dd$distances, psi = x))
alpha = BNPmix::PYcalibrate(log(5), 5, discount = discount)$strength
## Numerator of PY process EPP
PYNum = apply(dd$partitions[-1, ], 1 ,function(x) pyEPPF(partition = x, concentration = alpha, discount = discount))
PYNum = c(1 - sum(PYNum), PYNum)
### ORDER PARTITIONS
nBlocks = apply(dd$partition, 1, function(x) length(unique(x)))
biggestBlock = apply(dd$partition, 1, function(x) max(table(x)))
indBiggestBlock = order(as.numeric(paste(nBlocks, biggestBlock, sep = "")), decreasing = TRUE)
#
partitionProbs = apply(CPNum, 2, function(x) (PYNum*x)/sum(PYNum*x))
tmp = partitionProbs[indBiggestBlock, ]
df = reshape2::melt(tmp) ## data frame Var1 = partition index Var2 psi index
## Find position of the c0 partition
c0Pos = which(apply(dd$partitions[indBiggestBlock, ], 1, function(x) all(x == c0)))
df$isC0 = as.numeric(df$Var1==c0Pos)
yTicks = c(0, cumsum(tmp[,1])[c(1,16, 41, 51, 52)])
p = ggplot(df, aes(x = Var2, y = value)) +
geom_area(aes(group = Var1, fill = factor(isC0)),col = "grey20" ) +
scale_fill_manual(values = c('grey90',col2))+
theme_minimal(18) +
scale_x_continuous(breaks = 1:7,labels = psiVal, limits = c(1, 7), expand = c(0, 0)) +
theme(legend.position = 'none',plot.margin=grid::unit(c(1,1,1,1), "cm")) +
scale_y_continuous(breaks= yTicks, limits = c(0, 1), expand = c(0, 0),
sec.axis = sec_axis(trans = ~., name = "Cumulative probability", breaks = c(0, 0.2, 0.4, 0.6, 0.8, 1),
labels = c("0.0", "0.2", "0.4", "0.6", "0.8", "1.0"))) +
theme(axis.title.y.left = element_blank(), axis.text.y.left = element_blank(),
axis.ticks.y.left = element_line(size = 0.6, colour = "grey20", linetype = "dotted"),
axis.ticks.length.y.left = unit(2, "cm"),
axis.ticks.length.x.bottom = unit(2, "cm"),
axis.text.y.right = element_text( size = rel(1.6)),
axis.ticks.x = element_blank(),
axis.text.x = element_text(margin = margin(t = -1.5, unit = "cm"), size = rel(1.6)),
axis.title.x=element_text(size=20,face="bold"),
axis.title.y.right=element_text(size=20)
) +
xlab(expression(psi))
pt = p + annotation_custom(grob = textGrob(label = "1 block", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.01,ymax = 0.01, xmin = 0,xmax = 0.5) +
annotation_custom(grob = textGrob(label = "2 blocks", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.2, ymax = 0.2, xmin = 0,xmax = 0.5) +
annotation_custom(grob = textGrob(label = "3 blocks", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.55,ymax = 0.55, xmin = 0,xmax = 0.5) +
annotation_custom(grob = textGrob(label = "4 blocks", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.85,ymax = 0.85, xmin = 0,xmax = 0.5) +
annotation_custom(grob = textGrob(label = "5 blocks", hjust = 0, gp = gpar(cex =0.9)), ymin = 0.99,ymax = 0.99, xmin = 0,xmax = 0.5)
gt <- ggplot_gtable(ggplot_build(pt))
gt$layout$clip[gt$layout$name == "panel"] <- "off"
grid_p = grid.arrange(gt)
ggsave(grid_p, file = paste0("CP_py_", i, "_sigma05_ekDP.pdf"), device = "pdf", height = 15, width = 15, unit = "cm", dpi = 300)
}