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figure2.R
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figure2.R
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#'
#' Piotr.Sobczyk (at) pwr.edu.pl
#'
#'
path_to_matlab=NULL
if(is.null(path_to_matlab)) stop("Please specify variable path_to_matlab in file 'figure2.R'")
source("data_generation_robustness_fixed_effects.R")
library(pesel)
library(FactoMineR)
library(pryr)
library(softImpute)
args <- commandArgs(trailingOnly = TRUE)
print(args)
if(identical(args, character(0))) args <- c("")
id=args[[1]]
#set seed based on ID
set.seed(strtoi(charToRaw(id)))
SNRs <- c(0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1)
vars <- c(50, 2000)
ns <- c(2000, 50)
numb.repetitions <- 100
k <- 5
scale <- TRUE
maxPC <- 2*k
methods.names <- c("PESEL n hetero", "Laplace evidence", "PESEL p hetero",
"GCV", "PESEL p homo", "Passemier", "CSV")
results <- NULL
tabela <- matrix(0, nrow=length(methods.names), ncol=numb.repetitions)
for(i in 1:length(SNRs)){
for(j in 1:length(vars)){
SNR <- SNRs[i]
var <- vars[j]
n <- ns[j]
sim.data_old <- data.simulation.model(n, SNR, var, k)
for(rep in 1:numb.repetitions) {
sim.data <- data.fixed.model(object=sim.data_old, n = n, SNR = SNR,
numb.vars = var, k = k, scale = scale)
BICs <- pesel(sim.data$X, 1, maxPC, method = "heterogenous", asymptotics = "n")$vals
tabela[1,rep] <- which.max(BICs)
BICs <- sapply(1:maxPC, function(j) pca.Laplace(sim.data$X, j))
tabela[2,rep] <- which.max(BICs)
BICs <- pesel(sim.data$X, 1, maxPC, method = "heterogenous", asymptotics = "p")$vals
tabela[3,rep] <- which.max(BICs)
estimatedNpc <- estim_ncp(sim.data$X, ncp.min = 1, ncp.max = maxPC, method = "GCV")$ncp
tabela[4,rep] <- estimatedNpc
BICs <- pesel(sim.data$X, 1, maxPC, method = "homogenous", asymptotics = "p")$vals
tabela[5,rep] <- which.max(BICs)
xFileName = paste0("x_", id, ".csv")
write.table(sim.data$X, sep=",", dec=".", file = xFileName, col.names=FALSE, row.names = FALSE)
command = paste0(path_to_matlab, " -nodisplay -r \"id='", id,
"'; kmax=", maxPC, "; run('estimating_pcs_passemier2.m'); exit\"")
system(command, ignore.stdout = TRUE, ignore.stderr = TRUE)
resFileName = paste0("res_", id, ".csv")
result = read.csv(resFileName)
if(is.na(result$sigma)){
tabela[6,rep] <- 1
} else{
tabela[6,rep] <- min(result$k,maxPC)
}
n.folds <- 10
folds <- NULL
p <- var
fold.size <- n*p/n.folds
free.indices <- 1:(n*p)
selected <- NULL
temp <- sample(free.indices, size = fold.size, replace = FALSE)
folds[temp] <- 1
selected <- c(selected, temp)
for(fold.i in 2:n.folds){
temp <- sample(free.indices[-selected], size = fold.size, replace = FALSE)
folds[temp] <- fold.i
selected <- c(selected, temp)
}
### creating lambda grid
lam0 <- lambda0(sim.data$X)
lamseq=exp(seq(from=log(lam0),to=log(1),length=20))
### cross-validation
error <- matrix(0, nrow=n.folds, ncol=20)
for(fold.i in 1:n.folds){
xs <- sim.data$X
xs[which(folds==fold.i)] <- NA
for(lambda.j in seq_along(lamseq)){
lambda=lamseq[lambda.j]
fits=softImpute(xs, rank.max=5, type="svd", lambda = lambda)
if(fits$d[1]!=0){
error[fold.i,lambda.j] <- sum((sim.data$X-fits$u%*%diag(fits$d)%*%t(fits$v))[which(folds==fold.i)]^2)
} else {
error[fold.i,lambda.j] <- sum((sim.data$X[which(folds==fold.i)])^2)
}
}
}
#estimating sigma
fits=softImpute(sim.data$X, rank.max = 5, lambda = lamseq[which.min(colMeans(error))],type="svd")
deg.free <- sum(fits$d>0)
if(deg.free!=0){
sigma.hat <- sum((sim.data$X-fits$u%*%diag(fits$d)%*%t(fits$v))^2)/(n*(p-deg.free))
} else{
sigma.hat <- sum((sim.data$X)^2)/(n*(p-deg.free))
}
command = paste0(path_to_matlab, " -nodisplay -r \"id='", id,
"'; maxPC=", maxPC, "; sigma=", sigma.hat, "; run('csv_function'); exit\"")
system(command, ignore.stdout = TRUE, ignore.stderr = TRUE)
result = read.csv(resFileName)
if(is.na(result$sigma)){
tabela[7,rep] <- 1
} else{
tabela[7,rep] <- min(result$k,maxPC)
}
results[[paste0(SNR, "_", var)]] <- tabela
}
}
}
# filename <- paste0("fixed_effects_simulations_big_n_", args[[1]], "_", gsub("-", "_", Sys.Date()), ".Rdata")
# save.image(filename)
####################
####### Plot #######
####################
library(dplyr)
library(ggplot2)
background="white"
main_color="darkred"
PeselPlotTheme <- theme(
legend.position = "bottom",
legend.direction = "horizontal",
legend.box = "horizontal",
legend.title = element_text(face = "italic", size = 17),
legend.background = element_rect(fill = background),
legend.key = element_rect(fill = background, colour = background),
legend.text = element_text(size = 16),
plot.background = element_rect(fill = background, colour = background),
panel.background = element_rect(fill = background),
panel.background = element_rect(fill = "white"),
plot.title = element_text(face = "italic", size = 24, vjust = 1),
panel.grid.major.x = element_blank(),
panel.grid.major.y = element_line(),
panel.grid.minor.y = element_line(),
panel.grid.minor.x = element_line(colour = "gray95", size=1.5),
axis.title = element_text(size = 17),
axis.text = element_text(size = 15),
strip.text.x = element_text(size = 17, colour = "white"),
strip.background = element_rect(fill = main_color),
axis.ticks.x = element_blank()
)
scheme.names <- c("Big n", "Big p")
y <- NULL
result <- results
characteristics <- lapply(strsplit(names(result), "_"), as.numeric)
for(i in 1:length(result)){
y <- rbind(y, data.frame(pc=as.vector(result[[i]]), method=rep(method.names, numb.repetitions),
snr=characteristics[[i]][1], variables=characteristics[[i]][2]))
}
y$pc <- pmax(1,floor(y$pc))
selected.snrs <- c(0.250, 0.375, 0.500, 0.625, 0.750, 0.875, 1)
selected.variables.number <- c(50, 2000)
selected.method2 <- method.names[c(1,2,3,4,6,7)]
y %>% filter(method %in% selected.method2,
snr %in% selected.snrs,
variables %in% selected.variables.number) %>%
mutate(snr=factor(snr), scenario=ifelse(variables==50, "n=2000, p=50", "n=50, p=2000")) %>%
group_by(snr, scenario, method) %>%
summarise(MeanPCs=mean(pc), SdPCs=sd(pc)/sqrt(n())) -> data5
new.lables=expression(paste("PESEL", phantom()["n"]^{"hetero"}), "CSV", "GCV",
paste("PESEL", phantom()["p"]^{"hetero"}), "Laplace Evidence",
"Passemier")
ggplot(data5, aes(x=snr, y=MeanPCs)) +
geom_line(aes(group=method, color=method, linetype=method), size=1.2) +
geom_linerange(aes(ymin=MeanPCs-SdPCs, ymax=MeanPCs+SdPCs, color=method, alpha=1)) +
facet_grid(.~scenario) +
ggtitle(paste0("Estimated number of PCs as a function of SNR")) +
xlab("Signal to noise ratio (SNR)") +
ylab("Mean estimated number of principal components") +
scale_linetype_manual(values=c("solid", "dashed", "dotdash", "dotted", "longdash", "twodash")[seq_along(method.names)],
labels = new.lables) +
scale_color_discrete("Method", labels = new.lables) +
scale_x_discrete(breaks=selected.snrs[-c(2,4)]) +
sobczykPlotTheme +
guides(colour=guide_legend(nrow=2,byrow=TRUE), alpha=FALSE,
linetype=guide_legend("Method",nrow=2,byrow=TRUE, override.aes = c(size=1.7),
label.position = "bottom", label.hjust = 0.5,
title.position = "left", keyheight=3, keywidth=14))
ggsave(filename = "figure2.png", height = 8, width = 14)