Results/Numerical_results_simulation_study.R
In chstaerk/SubBoost: Subspace Boosting With Multivariable Base-learners
library("xtable")
# Detailed numeric results
take_element <- function(list,element1,element2,nSim){
#l = length(list)
l = nSim
vec = numeric(l)
for (i in 1:l) vec[i] = list[[i]][[element1]][[element2]]
return(vec)
}
take_element3 <- function(list,element1,element2,element3,nSim){
l = nSim
vec = numeric(l)
for (i in 1:l) vec[i] = list[[i]][[element1]][[element2]][[element3]]
return(vec)
}
test_comp <- function(results, names_adjusted, metric, digi, nSim, results_criterion=NULL, names_adjusted_criterion=NULL) {
names_results <- rep("",length(results[[1]]))
for (i in 1:length(results[[1]])) names_results[i] <- gsub("_results","",names(results[[1]][i]))
mat <- matrix(NA, length(names_adjusted), nSim)
rownames(mat) <- names_adjusted
for (name in names_adjusted){
i <- which(name == names_results)
mat[name,] <- take_element(results,i,metric,nSim)
}
#rownames(mat) <- names_adjusted
if (!is.null(results_criterion)) {
mat[1,] <- take_element3(results_criterion,1,3,metric,nSim)
mat[2,] <- take_element3(results_criterion,2,3,metric,nSim)
mat <- rbind(take_element3(results_criterion,1,1,metric,nSim),
take_element3(results_criterion,2,1,metric,nSim), mat)
rownames(mat) <- names_adjusted_criterion
names_adjusted <- names_adjusted_criterion
}
#if (metric==4) mat <- sqrt(mat)
means <- format(round(rowMeans(mat), digi), nsmall=digi)
medians <- format(round(apply(mat ,1, median), digi), nsmall=digi)
sd <- format(round(apply(mat ,1, sd), digi), nsmall=digi)
IQR <- format(round(apply(mat ,1, IQR), digi), nsmall=digi)
minimizer <- names(which.min(rowMeans(mat)))
#minimizer <- names(which.min(medians))
pvalues <- rep(NA, length(names_adjusted))
names(pvalues) <- names_adjusted
for (method in names_adjusted){
if (method!=minimizer){
wtest <- wilcox.test(mat[method,], mat[minimizer,], paired = TRUE, alternative = "two.sided")
pvalues[method] <- format(round(wtest$p.value, 3), nsmall=digi)
if (pvalues[method]<0.001) pvalues[method] = "<0.001"
}
}
return(list(means=means, sd=sd, medians=medians, IQR=IQR, pvalues=pvalues))
}
method_names <- c("SubBoost","RSubBoost","AdaSubBoost",
"L2Boost", "XGBoost", "TwinBoost","StabSel", "Lasso", "ENet", "ReLasso")
names_adjusted <- method_names
names_adjusted[names_adjusted=="L2Boost"] <- "Boost"
names_adjusted[names_adjusted=="StabSel"] <- "Stability"
names_adjusted[names_adjusted=="XGBoost"] <- "XGBoostCD"
digi <- 3
digi_Time <- 3
load("Sim_Toeplitz08_p20_n100_nSim500_Iter1000_fixedS0_4_autostop_25_07.RData")
nSim = results$nSim
lowdim_FP <- test_comp(results, names_adjusted, 1, digi, nSim)
lowdim_FN <- test_comp(results, names_adjusted, 2, digi, nSim)
lowdim_Est <- test_comp(results, names_adjusted, 3, digi, nSim)
lowdim_Pred <- test_comp(results, names_adjusted, 4, digi, nSim)
lowdim_Time <- test_comp(results, names_adjusted, 5, digi_Time, nSim)
results_tab <- rbind(
paste(lowdim_FP$medians, " (", lowdim_FP$IQR,")", sep=""),
paste(lowdim_FP$means, " (", lowdim_FP$sd,")", sep=""),
lowdim_FP$pvalues,
paste(lowdim_FN$medians, " (", lowdim_FN$IQR,")", sep=""),
paste(lowdim_FN$means, " (", lowdim_FN$sd,")", sep=""),
lowdim_FN$pvalues,
paste(lowdim_Est$medians, " (", lowdim_Est$IQR,")", sep=""),
paste(lowdim_Est$means, " (", lowdim_Est$sd,")", sep=""),
lowdim_Est$pvalues,
paste(lowdim_Pred$medians, " (", lowdim_Pred$IQR,")", sep=""),
paste(lowdim_Pred$means, " (", lowdim_Pred$sd,")", sep=""),
lowdim_Pred$pvalues,
paste(lowdim_Time$means, " (", lowdim_Time$sd,")", sep=""))
results_tab <- cbind(rep(c("Median FP (IQR)", "Mean FP (SD)", "P-value",
"Median FN (IQR)", "Mean FN (SD)", "P-value",
"Median MSE (IQR)", "Mean MSE (SD)", "P-value",
"Median RMSE (IQR)", "Mean RMSE (SD)", "P-value",
"Mean Time in s (SD)"), 1),
results_tab)
colnames(results_tab)[1] <- ""
#rownames(results_tab) <- rep(c("Mean model size", "p-value", "Mean absolute error", "p-value"), 4)
print(xtable(results_tab), include.rownames=FALSE)
###################################################################
method_names <- c("RSubBoost", "AdaSubBoost",
"L2Boost", "XGBoost", "TwinBoost", "StabSel", "Lasso", "ENet", "ReLasso")
names_adjusted <- method_names
names_adjusted[names_adjusted=="L2Boost"] <- "Boost"
names_adjusted[names_adjusted=="StabSel"] <- "Stability"
names_adjusted[names_adjusted=="XGBoost"] <- "XGBoostCD"
load("Sim_Toeplitz08_p1000_n100_nSim500_Iter5000_fixedS0_10_autostop_25_07.RData")
setting_FP <- test_comp(results, names_adjusted, 1, digi, nSim)
setting_FN <- test_comp(results, names_adjusted, 2, digi, nSim)
setting_Est <- test_comp(results, names_adjusted, 3, digi, nSim)
setting_Pred <- test_comp(results, names_adjusted, 4, digi, nSim)
setting_Time <- test_comp(results, names_adjusted, 5, digi_Time, nSim)
results_tab <- rbind(
paste(setting_FP$medians, " (", setting_FP$IQR,")", sep=""),
paste(setting_FP$means, " (", setting_FP$sd,")", sep=""),
setting_FP$pvalues,
paste(setting_FN$medians, " (", setting_FN$IQR,")", sep=""),
paste(setting_FN$means, " (", setting_FN$sd,")", sep=""),
setting_FN$pvalues,
paste(setting_Est$medians, " (", setting_Est$IQR,")", sep=""),
paste(setting_Est$means, " (", setting_Est$sd,")", sep=""),
setting_Est$pvalues,
paste(setting_Pred$medians, " (", setting_Pred$IQR,")", sep=""),
paste(setting_Pred$means, " (", setting_Pred$sd,")", sep=""),
setting_Pred$pvalues,
paste(setting_Time$means, " (", setting_Time$sd,")", sep=""))
results_tab <- cbind(rep(c("Median FP (IQR)", "Mean FP (SD)", "P-value",
"Median FN (IQR)", "Mean FN (SD)", "P-value",
"Median MSE (IQR)", "Mean MSE (SD)", "P-value",
"Median RMSE (IQR)", "Mean RMSE (SD)", "P-value",
"Mean Time in s (SD)"), 1),
results_tab)
colnames(results_tab)[1] <- ""
#rownames(results_tab) <- rep(c("Mean model size", "p-value", "Mean absolute error", "p-value"), 4)
print(xtable(results_tab), include.rownames=FALSE)
###########################################################################
load("Sim_Toeplitz08_p1000_n100_nSim500_Iter5000_randomS0_10_autostop_25_07.RData")
setting_FP <- test_comp(results, names_adjusted, 1, digi, nSim)
setting_FN <- test_comp(results, names_adjusted, 2, digi, nSim)
setting_Est <- test_comp(results, names_adjusted, 3, digi, nSim)
setting_Pred <- test_comp(results, names_adjusted, 4, digi, nSim)
setting_Time <- test_comp(results, names_adjusted, 5, digi_Time, nSim)
results_tab <- rbind(
paste(setting_FP$medians, " (", setting_FP$IQR,")", sep=""),
paste(setting_FP$means, " (", setting_FP$sd,")", sep=""),
setting_FP$pvalues,
paste(setting_FN$medians, " (", setting_FN$IQR,")", sep=""),
paste(setting_FN$means, " (", setting_FN$sd,")", sep=""),
setting_FN$pvalues,
paste(setting_Est$medians, " (", setting_Est$IQR,")", sep=""),
paste(setting_Est$means, " (", setting_Est$sd,")", sep=""),
setting_Est$pvalues,
paste(setting_Pred$medians, " (", setting_Pred$IQR,")", sep=""),
paste(setting_Pred$means, " (", setting_Pred$sd,")", sep=""),
setting_Pred$pvalues,
paste(setting_Time$means, " (", setting_Time$sd,")", sep=""))
results_tab <- cbind(rep(c("Median FP (IQR)", "Mean FP (SD)", "P-value",
"Median FN (IQR)", "Mean FN (SD)", "P-value",
"Median MSE (IQR)", "Mean MSE (SD)", "P-value",
"Median RMSE (IQR)", "Mean RMSE (SD)", "P-value",
"Mean Time in s (SD)"), 1),
results_tab)
colnames(results_tab)[1] <- ""
#rownames(results_tab) <- rep(c("Mean model size", "p-value", "Mean absolute error", "p-value"), 4)
print(xtable(results_tab), include.rownames=FALSE)
#################################################################
method_names <- c("RSubBoost", "AdaSubBoost",
"L2Boost", "XGBoost", "TwinBoost", "StabSel", "Lasso", "ENet", "ReLasso")
names_adjusted <- method_names
names_adjusted[names_adjusted=="L2Boost"] <- "Boost"
names_adjusted[names_adjusted=="StabSel"] <- "Stability"
names_adjusted[names_adjusted=="XGBoost"] <- "XGBoostCD"
names_adjusted_criterion <- c("RSubBoost AIC", "AdaSubBoost AIC", "RSubBoost EBIC1", "AdaSubBoost EBIC1",
"L2Boost", "XGBoost","TwinBoost","StabSel", "Lasso", "ENet", "ReLasso")
load("Sim_Toeplitz08_p1000_n1000_nSim500_Iter10000_fixedS0_100_autostop_choice_of_criterion_19_07.RData")
results_criterion <- results
load("Sim_Toeplitz08_p1000_n1000_nSim500_Iter10000_fixedS0_100_autostop_25_07.RData")
setting_FP <- test_comp(results, names_adjusted, 1, digi, nSim, results_criterion, names_adjusted_criterion)
setting_FN <- test_comp(results, names_adjusted, 2, digi, nSim, results_criterion, names_adjusted_criterion)
setting_Est <- test_comp(results, names_adjusted, 3, digi, nSim, results_criterion, names_adjusted_criterion)
setting_Pred <- test_comp(results, names_adjusted, 4, digi, nSim, results_criterion, names_adjusted_criterion)
setting_Time <- test_comp(results, names_adjusted, 5, digi, nSim, results_criterion, names_adjusted_criterion)
results_tab <- rbind(
paste(setting_FP$medians, " (", setting_FP$IQR,")", sep=""),
paste(setting_FP$means, " (", setting_FP$sd,")", sep=""),
setting_FP$pvalues,
paste(setting_FN$medians, " (", setting_FN$IQR,")", sep=""),
paste(setting_FN$means, " (", setting_FN$sd,")", sep=""),
setting_FN$pvalues,
paste(setting_Est$medians, " (", setting_Est$IQR,")", sep=""),
paste(setting_Est$means, " (", setting_Est$sd,")", sep=""),
setting_Est$pvalues,
paste(setting_Pred$medians, " (", setting_Pred$IQR,")", sep=""),
paste(setting_Pred$means, " (", setting_Pred$sd,")", sep=""),
setting_Pred$pvalues,
paste(setting_Time$means, " (", setting_Time$sd,")", sep=""))
results_tab <- cbind(rep(c("Median FP (IQR)", "Mean FP (SD)", "P-value",
"Median FN (IQR)", "Mean FN (SD)", "P-value",
"Median MSE (IQR)", "Mean MSE (SD)", "P-value",
"Median RMSE (IQR)", "Mean RMSE (SD)", "P-value",
"Mean Time in s (SD)"), 1),
results_tab)
colnames(results_tab)[1] <- ""
#rownames(results_tab) <- rep(c("Mean model size", "p-value", "Mean absolute error", "p-value"), 4)
print(xtable(results_tab), include.rownames=FALSE)
chstaerk/SubBoost documentation built on Dec. 19, 2021, 4:06 p.m.
R Package Documentation
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library("xtable")
# Detailed numeric results
take_element <- function(list,element1,element2,nSim){
#l = length(list)
l = nSim
vec = numeric(l)
for (i in 1:l) vec[i] = list[[i]][[element1]][[element2]]
return(vec)
}
take_element3 <- function(list,element1,element2,element3,nSim){
l = nSim
vec = numeric(l)
for (i in 1:l) vec[i] = list[[i]][[element1]][[element2]][[element3]]
return(vec)
}
test_comp <- function(results, names_adjusted, metric, digi, nSim, results_criterion=NULL, names_adjusted_criterion=NULL) {
names_results <- rep("",length(results[[1]]))
for (i in 1:length(results[[1]])) names_results[i] <- gsub("_results","",names(results[[1]][i]))
mat <- matrix(NA, length(names_adjusted), nSim)
rownames(mat) <- names_adjusted
for (name in names_adjusted){
i <- which(name == names_results)
mat[name,] <- take_element(results,i,metric,nSim)
}
#rownames(mat) <- names_adjusted
if (!is.null(results_criterion)) {
mat[1,] <- take_element3(results_criterion,1,3,metric,nSim)
mat[2,] <- take_element3(results_criterion,2,3,metric,nSim)
mat <- rbind(take_element3(results_criterion,1,1,metric,nSim),
take_element3(results_criterion,2,1,metric,nSim), mat)
rownames(mat) <- names_adjusted_criterion
names_adjusted <- names_adjusted_criterion
}
#if (metric==4) mat <- sqrt(mat)
means <- format(round(rowMeans(mat), digi), nsmall=digi)
medians <- format(round(apply(mat ,1, median), digi), nsmall=digi)
sd <- format(round(apply(mat ,1, sd), digi), nsmall=digi)
IQR <- format(round(apply(mat ,1, IQR), digi), nsmall=digi)
minimizer <- names(which.min(rowMeans(mat)))
#minimizer <- names(which.min(medians))
pvalues <- rep(NA, length(names_adjusted))
names(pvalues) <- names_adjusted
for (method in names_adjusted){
if (method!=minimizer){
wtest <- wilcox.test(mat[method,], mat[minimizer,], paired = TRUE, alternative = "two.sided")
pvalues[method] <- format(round(wtest$p.value, 3), nsmall=digi)
if (pvalues[method]<0.001) pvalues[method] = "<0.001"
}
}
return(list(means=means, sd=sd, medians=medians, IQR=IQR, pvalues=pvalues))
}
method_names <- c("SubBoost","RSubBoost","AdaSubBoost",
"L2Boost", "XGBoost", "TwinBoost","StabSel", "Lasso", "ENet", "ReLasso")
names_adjusted <- method_names
names_adjusted[names_adjusted=="L2Boost"] <- "Boost"
names_adjusted[names_adjusted=="StabSel"] <- "Stability"
names_adjusted[names_adjusted=="XGBoost"] <- "XGBoostCD"
digi <- 3
digi_Time <- 3
load("Sim_Toeplitz08_p20_n100_nSim500_Iter1000_fixedS0_4_autostop_25_07.RData")
nSim = results$nSim
lowdim_FP <- test_comp(results, names_adjusted, 1, digi, nSim)
lowdim_FN <- test_comp(results, names_adjusted, 2, digi, nSim)
lowdim_Est <- test_comp(results, names_adjusted, 3, digi, nSim)
lowdim_Pred <- test_comp(results, names_adjusted, 4, digi, nSim)
lowdim_Time <- test_comp(results, names_adjusted, 5, digi_Time, nSim)
results_tab <- rbind(
paste(lowdim_FP$medians, " (", lowdim_FP$IQR,")", sep=""),
paste(lowdim_FP$means, " (", lowdim_FP$sd,")", sep=""),
lowdim_FP$pvalues,
paste(lowdim_FN$medians, " (", lowdim_FN$IQR,")", sep=""),
paste(lowdim_FN$means, " (", lowdim_FN$sd,")", sep=""),
lowdim_FN$pvalues,
paste(lowdim_Est$medians, " (", lowdim_Est$IQR,")", sep=""),
paste(lowdim_Est$means, " (", lowdim_Est$sd,")", sep=""),
lowdim_Est$pvalues,
paste(lowdim_Pred$medians, " (", lowdim_Pred$IQR,")", sep=""),
paste(lowdim_Pred$means, " (", lowdim_Pred$sd,")", sep=""),
lowdim_Pred$pvalues,
paste(lowdim_Time$means, " (", lowdim_Time$sd,")", sep=""))
results_tab <- cbind(rep(c("Median FP (IQR)", "Mean FP (SD)", "P-value",
"Median FN (IQR)", "Mean FN (SD)", "P-value",
"Median MSE (IQR)", "Mean MSE (SD)", "P-value",
"Median RMSE (IQR)", "Mean RMSE (SD)", "P-value",
"Mean Time in s (SD)"), 1),
results_tab)
colnames(results_tab)[1] <- ""
#rownames(results_tab) <- rep(c("Mean model size", "p-value", "Mean absolute error", "p-value"), 4)
print(xtable(results_tab), include.rownames=FALSE)
###################################################################
method_names <- c("RSubBoost", "AdaSubBoost",
"L2Boost", "XGBoost", "TwinBoost", "StabSel", "Lasso", "ENet", "ReLasso")
names_adjusted <- method_names
names_adjusted[names_adjusted=="L2Boost"] <- "Boost"
names_adjusted[names_adjusted=="StabSel"] <- "Stability"
names_adjusted[names_adjusted=="XGBoost"] <- "XGBoostCD"
load("Sim_Toeplitz08_p1000_n100_nSim500_Iter5000_fixedS0_10_autostop_25_07.RData")
setting_FP <- test_comp(results, names_adjusted, 1, digi, nSim)
setting_FN <- test_comp(results, names_adjusted, 2, digi, nSim)
setting_Est <- test_comp(results, names_adjusted, 3, digi, nSim)
setting_Pred <- test_comp(results, names_adjusted, 4, digi, nSim)
setting_Time <- test_comp(results, names_adjusted, 5, digi_Time, nSim)
results_tab <- rbind(
paste(setting_FP$medians, " (", setting_FP$IQR,")", sep=""),
paste(setting_FP$means, " (", setting_FP$sd,")", sep=""),
setting_FP$pvalues,
paste(setting_FN$medians, " (", setting_FN$IQR,")", sep=""),
paste(setting_FN$means, " (", setting_FN$sd,")", sep=""),
setting_FN$pvalues,
paste(setting_Est$medians, " (", setting_Est$IQR,")", sep=""),
paste(setting_Est$means, " (", setting_Est$sd,")", sep=""),
setting_Est$pvalues,
paste(setting_Pred$medians, " (", setting_Pred$IQR,")", sep=""),
paste(setting_Pred$means, " (", setting_Pred$sd,")", sep=""),
setting_Pred$pvalues,
paste(setting_Time$means, " (", setting_Time$sd,")", sep=""))
results_tab <- cbind(rep(c("Median FP (IQR)", "Mean FP (SD)", "P-value",
"Median FN (IQR)", "Mean FN (SD)", "P-value",
"Median MSE (IQR)", "Mean MSE (SD)", "P-value",
"Median RMSE (IQR)", "Mean RMSE (SD)", "P-value",
"Mean Time in s (SD)"), 1),
results_tab)
colnames(results_tab)[1] <- ""
#rownames(results_tab) <- rep(c("Mean model size", "p-value", "Mean absolute error", "p-value"), 4)
print(xtable(results_tab), include.rownames=FALSE)
###########################################################################
load("Sim_Toeplitz08_p1000_n100_nSim500_Iter5000_randomS0_10_autostop_25_07.RData")
setting_FP <- test_comp(results, names_adjusted, 1, digi, nSim)
setting_FN <- test_comp(results, names_adjusted, 2, digi, nSim)
setting_Est <- test_comp(results, names_adjusted, 3, digi, nSim)
setting_Pred <- test_comp(results, names_adjusted, 4, digi, nSim)
setting_Time <- test_comp(results, names_adjusted, 5, digi_Time, nSim)
results_tab <- rbind(
paste(setting_FP$medians, " (", setting_FP$IQR,")", sep=""),
paste(setting_FP$means, " (", setting_FP$sd,")", sep=""),
setting_FP$pvalues,
paste(setting_FN$medians, " (", setting_FN$IQR,")", sep=""),
paste(setting_FN$means, " (", setting_FN$sd,")", sep=""),
setting_FN$pvalues,
paste(setting_Est$medians, " (", setting_Est$IQR,")", sep=""),
paste(setting_Est$means, " (", setting_Est$sd,")", sep=""),
setting_Est$pvalues,
paste(setting_Pred$medians, " (", setting_Pred$IQR,")", sep=""),
paste(setting_Pred$means, " (", setting_Pred$sd,")", sep=""),
setting_Pred$pvalues,
paste(setting_Time$means, " (", setting_Time$sd,")", sep=""))
results_tab <- cbind(rep(c("Median FP (IQR)", "Mean FP (SD)", "P-value",
"Median FN (IQR)", "Mean FN (SD)", "P-value",
"Median MSE (IQR)", "Mean MSE (SD)", "P-value",
"Median RMSE (IQR)", "Mean RMSE (SD)", "P-value",
"Mean Time in s (SD)"), 1),
results_tab)
colnames(results_tab)[1] <- ""
#rownames(results_tab) <- rep(c("Mean model size", "p-value", "Mean absolute error", "p-value"), 4)
print(xtable(results_tab), include.rownames=FALSE)
#################################################################
method_names <- c("RSubBoost", "AdaSubBoost",
"L2Boost", "XGBoost", "TwinBoost", "StabSel", "Lasso", "ENet", "ReLasso")
names_adjusted <- method_names
names_adjusted[names_adjusted=="L2Boost"] <- "Boost"
names_adjusted[names_adjusted=="StabSel"] <- "Stability"
names_adjusted[names_adjusted=="XGBoost"] <- "XGBoostCD"
names_adjusted_criterion <- c("RSubBoost AIC", "AdaSubBoost AIC", "RSubBoost EBIC1", "AdaSubBoost EBIC1",
"L2Boost", "XGBoost","TwinBoost","StabSel", "Lasso", "ENet", "ReLasso")
load("Sim_Toeplitz08_p1000_n1000_nSim500_Iter10000_fixedS0_100_autostop_choice_of_criterion_19_07.RData")
results_criterion <- results
load("Sim_Toeplitz08_p1000_n1000_nSim500_Iter10000_fixedS0_100_autostop_25_07.RData")
setting_FP <- test_comp(results, names_adjusted, 1, digi, nSim, results_criterion, names_adjusted_criterion)
setting_FN <- test_comp(results, names_adjusted, 2, digi, nSim, results_criterion, names_adjusted_criterion)
setting_Est <- test_comp(results, names_adjusted, 3, digi, nSim, results_criterion, names_adjusted_criterion)
setting_Pred <- test_comp(results, names_adjusted, 4, digi, nSim, results_criterion, names_adjusted_criterion)
setting_Time <- test_comp(results, names_adjusted, 5, digi, nSim, results_criterion, names_adjusted_criterion)
results_tab <- rbind(
paste(setting_FP$medians, " (", setting_FP$IQR,")", sep=""),
paste(setting_FP$means, " (", setting_FP$sd,")", sep=""),
setting_FP$pvalues,
paste(setting_FN$medians, " (", setting_FN$IQR,")", sep=""),
paste(setting_FN$means, " (", setting_FN$sd,")", sep=""),
setting_FN$pvalues,
paste(setting_Est$medians, " (", setting_Est$IQR,")", sep=""),
paste(setting_Est$means, " (", setting_Est$sd,")", sep=""),
setting_Est$pvalues,
paste(setting_Pred$medians, " (", setting_Pred$IQR,")", sep=""),
paste(setting_Pred$means, " (", setting_Pred$sd,")", sep=""),
setting_Pred$pvalues,
paste(setting_Time$means, " (", setting_Time$sd,")", sep=""))
results_tab <- cbind(rep(c("Median FP (IQR)", "Mean FP (SD)", "P-value",
"Median FN (IQR)", "Mean FN (SD)", "P-value",
"Median MSE (IQR)", "Mean MSE (SD)", "P-value",
"Median RMSE (IQR)", "Mean RMSE (SD)", "P-value",
"Mean Time in s (SD)"), 1),
results_tab)
colnames(results_tab)[1] <- ""
#rownames(results_tab) <- rep(c("Mean model size", "p-value", "Mean absolute error", "p-value"), 4)
print(xtable(results_tab), include.rownames=FALSE)
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