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exp.impute.StudentToutl_MCAR.R
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exp.impute.StudentToutl_MCAR.R
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################################################################################
## File: exp.impute.StudentT_MCAR.R ##
## Created by: Pavlo Mozharovskyi ##
## Last revised: 23.07.2018 ##
## ##
## Contains experiments on single depth-based imputation of Student-t family ##
## contaminated with Cauchy distribution under MCAR assumption (Table 2). ##
## ##
################################################################################
source("impute.functions.R")
library(imputeDepth)
library(geometry)
library(norm)
library(missForest)
library(missMDA)
library(rrcov)
library(VIM)
library(mvtnorm)
# Create structures
# ems.depth.TrE <- NULL
ems.depth.Tr2 <- NULL
ems.depth.zm <- NULL
ems.depth.M <- NULL
ems.depth.Mr <- NULL
ems.em <- NULL
ems.forest <- NULL
ems.knn <- NULL
ems.regPCA.1 <- NULL
ems.regPCA.2 <- NULL
ems.mean <- NULL
ems.oracle <- NULL
k <- 1000
# set.seed(1) # t1
# set.seed(2) # t2
# set.seed(3) # t3
# set.seed(5) # t5
# set.seed(10) # t10
set.seed(1000) # t0
cltype <- "SOCK"
nproc <- 32
if (nproc > 1){
# Imputing routine to be calles on a node
imp.worker <- function(i){
# Load packages
source("impute.functions.R")
library(imputeDepth)
library(geometry)
library(norm)
library(missForest)
library(missMDA)
library(rrcov)
library(VIM)
library(mvtnorm)
# Start study
d <- 3
mu <- c(1, 1, 1)
Sigma <- matrix(c(1, 1, 1, 1, 4, 4, 1, 4, 8), nrow = 3, byrow = TRUE)
n <- 100
X.sd <- sqrt(matrix(rep(diag(Sigma), n), nrow = n, byrow = TRUE))
pNA <- 0.25
pOL <- 0.15
# Generate data
Xn <- t(mu + t(rmvt(floor(n * (1 - pOL)), Sigma, 0)))
Xo <- t(mu + t(rmvt(n - floor(n * (1 - pOL)), Sigma, 1)))
X <- rbind(Xn, Xo)
# Add NAs
X.miss <- rbind(prodNA(Xn, pNA / (1 - pOL)), Xo)
cat(sum(is.na(X.miss)), " NAs produced\n")
# Impute
# X.imp.depth.TrE <- impute.depth(X.miss, depth = "halfspace",
# depth.outsiders = "extremeval",
# max.iter = 50, p.extreme = 0.1,
# n.proj = 1000)
X.imp.depth.Tr2 <- impute.depth(X.miss, depth = "halfspace",
parMcd.outsiders = 0.5)
X.imp.depth.zm <- impute.depth(X.miss, depth = "zonoid")
X.imp.depth.M <- impute.depth(X.miss, depth = "Mahalanobis")
X.imp.depth.Mr <- impute.depth(X.miss, depth = "Mahalanobis",
parMcd.impute = 0.75)
X.imp.em <- imputeEm(as.matrix(X.miss))
X.imp.forest <- missForest(X.miss)$ximp
X.imp.knn <- imputeKnn(X.miss)
X.imp.regPCA.1 <- imputePCA(X.miss, ncp = 1)$completeObs
X.imp.regPCA.2 <- imputePCA(X.miss, ncp = 2)$completeObs
X.imp.mean <- imputeMean(X.miss)
X.imp.oracle <- imp.depth.Mahalanobis(X.miss, mu = mu, Sigma = Sigma)
# Calculate raw statistics
# ems.depth.TrE <- sqrt(sum((X.imp.depth.TrE - X)^2) / (n * d * pNA))
ems.depth.Tr2 <- sqrt(sum((X.imp.depth.Tr2 - X)^2) / (n * d * pNA))
ems.depth.zm <- sqrt(sum((X.imp.depth.zm - X)^2) / (n * d * pNA))
ems.depth.M <- sqrt(sum((X.imp.depth.M - X)^2) / (n * d * pNA))
ems.depth.Mr <- sqrt(sum((X.imp.depth.Mr - X)^2) / (n * d * pNA))
ems.em <- sqrt(sum((X.imp.em - X)^2) / (n * d * pNA))
ems.forest <- sqrt(sum((X.imp.forest - X)^2) / (n * d * pNA))
ems.knn <- sqrt(sum((X.imp.knn - X)^2) / (n * d * pNA))
ems.regPCA.1 <- sqrt(sum((X.imp.regPCA.1 - X)^2) / (n * d * pNA))
ems.regPCA.2 <- sqrt(sum((X.imp.regPCA.2 - X)^2) / (n * d * pNA))
ems.mean <- sqrt(sum((X.imp.mean - X)^2) / (n * d * pNA))
ems.oracle <- sqrt(sum((X.imp.oracle - X)^2) / (n * d * pNA))
# Return the errors
return (c(-1, # ems.depth.TrE,
ems.depth.Tr2, ems.depth.zm, ems.depth.M,
ems.depth.Mr, ems.em, ems.forest, ems.knn, ems.regPCA.1,
ems.regPCA.2, ems.mean, ems.oracle))
}
# Printing routine
print.fun <- function(outputs, B, args){
pb <- args$mypb
len.one.run <- args$len.one.run
outputs <- unlist(outputs)
outputs <- outputs[!is.null(outputs)]
setTxtProgressBar(pb, length(outputs)/len.one.run)
}
# The parallel call
library(snowFT)
res <- performParallel(count = nproc, x = 1:k, imp.worker,
printfun = print.fun,
printargs = list(
mypb = txtProgressBar(min = 0,
max = k,
style = 3),
len.one.run = 1), printrepl = 1,
cltype = cltype)
# Assemble results
for (i in 1:k){
# ems.depth.TrE <- c(ems.depth.TrE, res[[i]][1])
ems.depth.Tr2 <- c(ems.depth.Tr2, res[[i]][2])
ems.depth.zm <- c(ems.depth.zm, res[[i]][3])
ems.depth.M <- c(ems.depth.M, res[[i]][4])
ems.depth.Mr <- c(ems.depth.Mr, res[[i]][5])
ems.em <- c(ems.em, res[[i]][6])
ems.forest <- c(ems.forest, res[[i]][7])
ems.knn <- c(ems.knn, res[[i]][8])
ems.regPCA.1 <- c(ems.regPCA.1, res[[i]][9])
ems.regPCA.2 <- c(ems.regPCA.2, res[[i]][10])
ems.mean <- c(ems.mean, res[[i]][11])
ems.oracle <- c(ems.oracle, res[[i]][12])
}
# Save results
save.image(paste("imp_t0_outl-15_MCAR-25_n100-d3-k", i, "_",
gsub(" ", "_", gsub(":", "_", date())), ".RData",
sep = ""))
}else{
# Start study
d <- 3
mu <- c(1, 1, 1)
Sigma <- matrix(c(1, 1, 1, 1, 4, 4, 1, 4, 8), nrow = 3, byrow = TRUE)
n <- 100
pNA <- 0.25
pOL <- 0.15
for (i in 1:k){
cat("Iteration", i, "started.\n")
# Generate data
Xn <- t(mu + t(rmvt(floor(n * (1 - pOL)), Sigma, 0)))
Xo <- t(mu + t(rmvt(n - floor(n * (1 - pOL)), Sigma, 1)))
X <- rbind(Xn, Xo)
# Add NAs
X.miss <- rbind(prodNA(Xn, pNA / (1 - pOL)), Xo)
cat(sum(is.na(X.miss)), " NAs produced\n")
# Impute
# X.imp.depth.TrE <- impute.depth(X.miss, depth = "halfspace",
# depth.outsiders = "extremeval",
# max.iter = 50, p.extreme = 0.1,
# n.proj = 1000)
X.imp.depth.Tr2 <- impute.depth(X.miss, depth = "halfspace",
parMcd.outsiders = 0.5)
X.imp.depth.zm <- impute.depth(X.miss, depth = "zonoid")
X.imp.depth.M <- impute.depth(X.miss, depth = "Mahalanobis")
X.imp.depth.Mr <- impute.depth(X.miss, depth = "Mahalanobis",
parMcd.impute = 0.75)
X.imp.em <- imputeEm(as.matrix(X.miss))
X.imp.forest <- missForest(X.miss)$ximp
X.imp.knn <- imputeKnn(X.miss)
X.imp.regPCA.1 <- imputePCA(X.miss, ncp = 1)$completeObs
X.imp.regPCA.2 <- imputePCA(X.miss, ncp = 2)$completeObs
X.imp.mean <- imputeMean(X.miss)
X.imp.oracle <- imp.depth.Mahalanobis(X.miss, mu = mu, Sigma = Sigma)
# Calculate raw statistics
# ems.depth.TrE <- c(ems.depth.TrE, sqrt(sum((X.imp.depth.TrE - X)^2) /
# (n * d * pNA)))
ems.depth.Tr2 <- c(ems.depth.Tr2, sqrt(sum((X.imp.depth.Tr2 - X)^2) /
(n * d * pNA)))
ems.depth.zm <- c(ems.depth.zm, sqrt(sum((X.imp.depth.zm - X)^2) /
(n * d * pNA)))
ems.depth.M <- c(ems.depth.M, sqrt(sum((X.imp.depth.M - X)^2) /
(n * d * pNA)))
ems.depth.Mr <- c(ems.depth.Mr, sqrt(sum((X.imp.depth.Mr - X)^2) /
(n * d * pNA)))
ems.em <- c(ems.em, sqrt(sum((X.imp.em - X)^2) / (n * d * pNA)))
ems.forest <- c(ems.forest, sqrt(sum((X.imp.forest - X)^2) / (n * d * pNA)))
ems.knn <- c(ems.knn, sqrt(sum((X.imp.knn - X)^2) / (n * d * pNA)))
ems.regPCA.1 <- c(ems.regPCA.1, sqrt(sum((X.imp.regPCA.1 - X)^2) /
(n * d * pNA)))
ems.regPCA.2 <- c(ems.regPCA.2, sqrt(sum((X.imp.regPCA.2 - X)^2) /
(n * d * pNA)))
ems.mean <- c(ems.mean, sqrt(sum((X.imp.mean - X)^2) / (n * d * pNA)))
ems.oracle <- c(ems.oracle, sqrt(sum((X.imp.oracle - X)^2) / (n * d * pNA)))
# Save intermediate results
if (i %% 10 < 1){
save.image(paste("imp_t0_outl-15_MCAR-25_n100-d3-k", i, "_",
gsub(" ", "_", gsub(":", "_", date())), ".RData",
sep = ""))
}
# Calculate statistics
cat("Iteration", i, "finished. Median RMSEs are:\n")
cat(# "d.TukE:", median(ems.depth.TrE),
"d.Tuk:", median(ems.depth.Tr2),
", d.zon:", median(ems.depth.zm), ", d.Mah:", median(ems.depth.M),
", d.MahR:", median(ems.depth.Mr), ", EM:", median(ems.em),
", rPCA1:", median(ems.regPCA.1), ", rPCA2:", median(ems.regPCA.2),
", kNN:", median(ems.knn), ", RF:", median(ems.forest),
", mean:", median(ems.mean), ", orcl:", median(ems.oracle), ".\n")
}
}
errors <- list(# TukeyEE = ems.depth.TrE,
TukeyR2 = ems.depth.Tr2,
zonoidM = ems.depth.zm,
Mahalanobis = ems.depth.M, MahalanobisR = ems.depth.Mr,
em = ems.em,
pca1 = ems.regPCA.1, pca2 = ems.regPCA.2,
knn = ems.knn, forest = ems.forest,
mean = ems.mean, oracle = ems.oracle)
boxplot(errors, main = paste("t0 outl 100-3, MCAR ", pNA, ", k = ", i, sep = ""),
names = c(# "d.TukE",
"d.Tuk", "d.zon",
"d.Mah", "d.MahR",
"EM", "rPCA1", "rPCA2", "kNN", "RF",
"mean", "orcl"),
ylab = "RMSE")
grid()