/
exp.impute.large.R
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exp.impute.large.R
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################################################################################
## File: exp.impute.large.R ##
## Created by: Pavlo Mozharovskyi ##
## Last revised: 22.07.2018 ##
## ##
## Contains experiments on single depth-based imputation for the large data ##
## set (Figure 3). ##
## ##
################################################################################
source("impute.functions.R")
library(imputeDepth)
library(geometry)
library(norm)
library(missForest)
library(missMDA)
library(rrcov)
library(VIM)
library(mvtnorm)
# Create structures
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
# Start study
n <- 1000
d <- 6
pNA <- 0.15
k <- 500
# Create structure for times
times.depths <- matrix(NA, nrow = k, ncol = 4)
cltype <- "SOCK"
nproc <- 32
set.seed(1)
if (nproc > 1){
# Imputing routine to be called on a tread
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 <- 6
n <- 1000
mu <- rep(0, d)
Sigma <- diag(d)
for (i in 1:d){
for (j in 1:d){
Sigma[i,j] <- 2^(-abs(i - j))
}
}
X.sd <- sqrt(matrix(rep(diag(Sigma), n), nrow = n, byrow = TRUE))
pNA <- 0.15
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")
# Saving structure for times
t.depths <- rep(-1, 4)
# Impute
a <- system.time(
X.imp.depth.Tr2 <- impute.depth(X.miss, depth = "randomTukey",
parMcd.outsiders = 0.85,
n.proj = 1000)
)
t.depths[1] <- a[3]
a <- system.time(
X.imp.depth.zm <- impute.depth(X.miss, depth = "zonoid",
parMcd.outsiders = 0.85)
)
t.depths[2] <- a[3]
a <- system.time(
X.imp.depth.M <- impute.depth(X.miss, depth = "Mahalanobis",
parMcd.impute = 1)
)
t.depths[3] <- a[3]
a <- system.time(
X.imp.depth.Mr <- impute.depth(X.miss, depth = "Mahalanobis",
parMcd.impute = 0.85)
)
t.depths[4] <- a[3]
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)$completeObs
X.imp.mean <- imputeMean(X.miss)
X.imp.oracle <- imp.depth.Mahalanobis(X.miss, mu = mu, Sigma = Sigma)
# Calculate raw statistics
ems.depth.Tr2 <- sqrt(sum((X.imp.depth.Tr2 - X)^2) / (n * d * pNA))
ems.depth.zm <- sqrt(sum((X.imp.depth.zm - X)^2) / (n * d * pNA))
ems.depth.M <- sqrt(sum((X.imp.depth.M - X)^2) / (n * d * pNA))
ems.depth.Mr <- sqrt(sum((X.imp.depth.Mr - X)^2) / (n * d * pNA))
ems.em <- sqrt(sum((X.imp.em - X)^2) / (n * d * pNA))
ems.forest <- sqrt(sum((X.imp.forest - X)^2) / (n * d * pNA))
ems.knn <- sqrt(sum((X.imp.knn - X)^2) / (n * d * pNA))
ems.regPCA.1 <- sqrt(sum((X.imp.regPCA.1 - X)^2) / (n * d * pNA))
ems.regPCA.2 <- sqrt(sum((X.imp.regPCA.2 - X)^2) / (n * d * pNA))
ems.mean <- sqrt(sum((X.imp.mean - X)^2) / (n * d * pNA))
ems.oracle <- sqrt(sum((X.imp.oracle - X)^2) / (n * d * pNA))
# Return the errors and the times
assembled <- list(errors = c(ems.depth.Tr2, ems.depth.zm,
ems.depth.M, ems.depth.Mr, ems.em, ems.forest,
ems.knn, ems.regPCA.1, ems.regPCA.2, ems.mean,
ems.oracle),
times = t.depths)
return (assembled)
}
# Printing routine
print.fun <- function(outputs, B, args){
pb <- args$mypb
len.one.run <- args$len.one.run
outputs <- unlist(outputs)
outputs <- outputs[!is.null(outputs)]
setTxtProgressBar(pb, length(outputs)/len.one.run)
}
# The parallel call
library(snowFT)
res <- performParallel(count = nproc, x = 1:k, imp.worker,
printfun = print.fun,
printargs = list(
mypb = txtProgressBar(min = 0,
max = k,
style = 3),
len.one.run = 1), printrepl = 1,
cltype = cltype)
# Assemble results
for (i in 1:k){
ems.depth.Tr2 <- c(ems.depth.Tr2, res[[i]]$errors[1])
ems.depth.zm <- c(ems.depth.zm, res[[i]]$errors[2])
ems.depth.M <- c(ems.depth.M, res[[i]]$errors[3])
ems.depth.Mr <- c(ems.depth.Mr, res[[i]]$errors[4])
ems.em <- c(ems.em, res[[i]]$errors[5])
ems.forest <- c(ems.forest, res[[i]]$errors[6])
ems.knn <- c(ems.knn, res[[i]]$errors[7])
ems.regPCA.1 <- c(ems.regPCA.1, res[[i]]$errors[8])
ems.regPCA.2 <- c(ems.regPCA.2, res[[i]]$errors[9])
ems.mean <- c(ems.mean, res[[i]]$errors[10])
ems.oracle <- c(ems.oracle, res[[i]]$errors[11])
times.depths[i,] <- res[[i]]$times
}
# Save results
save.image(paste("large_k", i, "_",
gsub(" ", "_", gsub(":", "_", date())), ".RData",
sep = ""))
}else{
for (i in 1:k){
cat("Iteration", i, "started.\n")
# Add NAs
X.miss <- prodNA(X, pNA, entire.rows = FALSE)
numNA <- sum(is.na(X.miss))
cat((numNA), " NAs produced\n")
# Impute
a <- system.time(
X.imp.depth.Tr2 <- impute.depth(X.miss, depth = "randomTukey",
parMcd.outsiders = 0.85,
n.proj = 1000)
)
times.depths[i,1] <- a[3]
a <- system.time(
X.imp.depth.zm <- impute.depth(X.miss, depth = "zonoid",
parMcd.outsiders = 0.85)
)
times.depths[i,2] <- a[3]
a <- system.time(
X.imp.depth.M <- impute.depth(X.miss, depth = "Mahalanobis",
parMcd.impute = 1)
)
times.depths[i,3] <- a[3]
a <- system.time(
X.imp.depth.Mr <- impute.depth(X.miss, depth = "Mahalanobis",
parMcd.impute = 0.85)
)
times.depths[i,4] <- a[3]
X.imp.em <- imputeEm(as.matrix(X.miss))
X.imp.forest <- missForest(X.miss)$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.Tr2 <- c(ems.depth.Tr2, sqrt(sum((X.imp.depth.Tr2 - X)^2,
na.rm = TRUE) / numNA))
ems.depth.zm <- c(ems.depth.zm, sqrt(sum((X.imp.depth.zm - X)^2,
na.rm = TRUE) / numNA))
ems.depth.M <- c(ems.depth.M, sqrt(sum((X.imp.depth.M - X)^2,
na.rm = TRUE) / numNA))
ems.depth.Mr <- c(ems.depth.Mr, sqrt(sum((X.imp.depth.Mr - X)^2,
na.rm = TRUE) / numNA))
ems.em <- c(ems.em, sqrt(sum((X.imp.em - X)^2, na.rm = TRUE) / numNA))
ems.forest <- c(ems.forest, sqrt(sum((X.imp.forest - X)^2,
na.rm = TRUE) / numNA))
ems.knn <- c(ems.knn, sqrt(sum((X.imp.knn - X)^2, na.rm = TRUE) / numNA))
ems.regPCA.1 <- c(ems.regPCA.1, sqrt(sum((X.imp.regPCA.1 - X)^2,
na.rm = TRUE) / numNA))
ems.regPCA.2 <- c(ems.regPCA.2, sqrt(sum((X.imp.regPCA.2 - X)^2,
na.rm = TRUE) / numNA))
ems.mean <- c(ems.mean, sqrt(sum((X.imp.mean - X)^2,
na.rm = TRUE) / numNA))
ems.oracle <- c(ems.oracle, sqrt(sum((X.imp.oracle - X)^2,
na.rm = TRUE) / numNA))
# Save intermediate results
if (i %% 10 < 1){
save.image(paste("large_k", i, "_",
gsub(" ", "_", gsub(":", "_", date())), ".RData",
sep = ""))
}
# Calculate statistics
cat("Iteration", i, "finished. Median RMSEs are:\n")
cat("d.Tuk:", median(ems.depth.Tr2), ", c.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")
}
}
ems.depth.Tr2 <- ems.depth.Tr2[ems.depth.Tr2 <= 2]
ems.depth.zm <- ems.depth.zm[ems.depth.zm <= 2]
ems.depth.M <- ems.depth.M[ems.depth.M <= 2]
ems.depth.Mr <- ems.depth.Mr[ems.depth.Mr <= 2]
ems.em <- ems.em[ems.em <= 2]
ems.forest <- ems.forest[ems.forest <= 2]
ems.knn <- ems.knn[ems.knn <= 2]
ems.regPCA.1 <- ems.regPCA.1[ems.regPCA.1 <= 2]
ems.regPCA.2 <- ems.regPCA.2[ems.regPCA.2 <= 2]
ems.mean <- ems.mean[ems.mean <= 2]
ems.oracle <- ems.oracle[ems.oracle <= 2]
errors <- list(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("Large data, n = ", n, ", d = ", d, ", MCAR ",
pNA, ", k = ", i, sep = ""),
names = c("d.Tuk", "d.zon",
"d.Mah", "d.MahR",
"EM", "rPCA1", "rPCA2", "kNN", "RF",
"mean", "orcl"),
ylab = "RMSE")
grid()