README.md
In Elsa-Yang98/ConformalSmallest: Efficient Tuning-Free Conformal Prediction
ConformalSmallest
This package implements two selection algorithms for conformal prediction regions to obtain the smallest prediction set in practice; these are called “efficiency first” and “validity first” conformal prediction algorithms, EFCP and VFCP for short. For details please refer to our paper.
Installation
You can install the released version of ConformalSmallest from CRAN with:
install.packages("ConformalSmallest")
Or directly from github
devtools::install_github("Elsa-Yang98/ConformalSmallest")
Vignettes
Please refer to the vignettes for two examples on how to apply EFCP and VFCP to tuning-free ridge regression and conformal quantile regression using the package and on how to interpret the results.
Example
This is a basic example which shows you how to solve a common problem:
library(ConformalSmallest)
## basic example code
Example 1: Tuning free ridge regression with conformal prediction
library(glmnet)
library(MASS)
library(mvtnorm)
source("ginverse.fun.R")
source("functions.R")
name=paste("linear_fm_t3",sep="")
df <- 3 #degrees of freedom
l <- 60 #number of dimensions
l.lambda <- 100
lambda_seq <- seq(0,200,l=l.lambda)
dim <- round(seq(5,300,l=l))
alpha <- 0.1
n <- 200 #number of training samples
n0 <- 100 #number of prediction points
nrep <- 100 #number of independent trials
rho <- 0.5
cov.efcp <- len.efcp <- matrix(0,nrep,l)
cov.vfcp <- len.vfcp <- matrix(0,nrep,l)
cov.naive <- len.naive <- matrix(0,nrep,l)
cov.param <- len.param <- matrix(0,nrep,l)
cov.star <- len.star <- matrix(0,nrep,l)
cov.cv10 <- len.cv10 <- matrix(0,nrep,l)
cov.cv5 <- len.cv5 <- matrix(0,nrep,l)
cov.cvloo <- len.cvloo <- matrix(0,nrep,l)
out.efcp.up <- out.efcp.lo <- matrix(0,n0,l)
out.vfcp.up <- out.vfcp.lo <- matrix(0,n0,l)
out.naive.up <- out.naive.lo <- matrix(0,n0,l)
out.param.up <- out.param.lo <- matrix(0,n0,l)
out.star.up <- out.star.lo <- matrix(0,n0,l)
out.cv10.up <- out.cv10.lo <- matrix(0,n0,l)
out.cv5.up <- out.cv5.lo <- matrix(0,n0,l)
out.cvloo.up <- out.cvloo.lo <- matrix(0,n0,l)
for(i in 1:nrep){
cat(i,"\n")
for (r in 1:l){
d <- dim[r]
set.seed(i)
Sigma <- matrix(rho,d,d)
diag(Sigma) <- rep(1,d)
X <- rmvt(n,Sigma,df) #multivariate t distribution
beta <- rep(1:5,d/5)
eps <- rt(n,df)*(1+sqrt(X[,1]^2+X[,2]^2))
Y <- X%*%beta+eps
X0 <- rmvt(n0,Sigma,df)
eps0 <- rt(n0,df)*(1+sqrt(X0[,1]^2+X0[,2]^2))
Y0 <- X0%*%beta+eps0
out.param <- ginverse.fun(X,Y,X0,alpha=alpha)
out.param.lo[,r] <- out.param$lo
out.param.up[,r] <- out.param$up
cov.param[i,r] <- mean(out.param.lo[,r] <= Y0 & Y0 <= out.param.up[,r])
len.param[i,r] <- mean(out.param.up[,r]-out.param.lo[,r])
out.efcp <- efcp_ridge(X,Y,X0,lambda=lambda_seq,alpha=alpha)
out.efcp.up[,r] <- out.efcp$up
out.efcp.lo[,r] <- out.efcp$lo
cov.efcp[i,r] <- mean(out.efcp.lo[,r] <= Y0 & Y0 <= out.efcp.up[,r])
len.efcp[i,r] <- mean(out.efcp.up[,r]-out.efcp.lo[,r])
out.vfcp <- vfcp_ridge(X,Y,X0,lambda=lambda_seq,alpha=alpha)
out.vfcp.up[,r] <- out.vfcp$up
out.vfcp.lo[,r] <- out.vfcp$lo
cov.vfcp[i,r] <- mean(out.vfcp.lo[,r] <= Y0 & Y0 <= out.vfcp.up[,r])
len.vfcp[i,r] <- mean(out.vfcp.up[,r]-out.vfcp.lo[,r])
out.naive <- naive.fun(X,Y,X0,alpha=alpha)
out.naive.up[,r] <- out.naive$up
out.naive.lo[,r] <- out.naive$lo
cov.naive[i,r] <- mean(out.naive.lo[,r] <= Y0 & Y0 <= out.naive.up[,r])
len.naive[i,r] <- mean(out.naive.up[,r]-out.naive.lo[,r])
out.star <- star.fun(X,Y,X0,lambda=lambda_seq,alpha=alpha)
out.star.up[,r] <- out.star$up
out.star.lo[,r] <- out.star$lo
cov.star[i,r] <- mean(out.star.lo[,r] <= Y0 & Y0 <= out.star.up[,r])
len.star[i,r] <- mean(out.star.up[,r] - out.star.lo[,r])
out.cv5 <- cv.fun(X,Y,X0,lambda=lambda_seq,alpha=alpha,nfolds=5)
out.cv5.up[,r] <- out.cv5$up
out.cv5.lo[,r] <- out.cv5$lo
cov.cv5[i,r] <- mean(out.cv5.lo[,r] <= Y0 & Y0 <= out.cv5.up[,r])
len.cv5[i,r] <- mean(out.cv5.up[,r] - out.cv5.lo[,r])
}
}
df.cov <- data.frame(dim,apply(cov.param,2,mean),apply(cov.naive,2,mean),apply(cov.vfcp,2,mean),apply(cov.star,2,mean),apply(cov.cv5,2,mean), apply(cov.efcp,2,mean))
df.len <- data.frame(dim,apply(len.param,2,mean),apply(len.naive,2,mean),apply(len.vfcp,2,mean),apply(len.star,2,mean),apply(len.cv5,2,mean), apply(len.efcp,2,mean))
save(dim,cov.param, cov.naive, cov.vfcp, cov.star, cov.cv5, cov.efcp, file = "cov100_t3.RData" )
save(dim,len.param, len.naive, len.vfcp, len.star, len.cv5, len.efcp, file = "len100_t3.RData" )
Example 2: Tuning free conformal quantile regression with random forest
This output the right panal of Figure 1 in our paper.
df <- 3
d <- 3
l.lambda <- 100
lambda_seq <- seq(0,200,l=l.lambda)
nset <- c(50,100,500,1000,5000)
alpha <- 0.1 #miscoverage level
n0 <- 100 #number of prediction points
nrep <- 100 #number of independent trials
rho <- 0.5
evaluations <- expand.grid(1:nrep, nset, c("efficient", "valid"))
no_eval <- nrow(evaluations)
width_mat <- cov_mat <- data.frame(number = rep(0, no_eval),
rep = evaluations[,1],
nset = evaluations[,2],
method = evaluations[,3])
colnames(width_mat) <- colnames(cov_mat) <- c("number", "rep", "sample size", "method")
Sigma <- matrix(rho,d,d)
diag(Sigma) <- rep(1,d) #covariance matrix for X
for(idx in 1:nrow(evaluations)){
set.seed(evaluations[idx, 1])
if(idx%%1 == 0){
print(idx)
}
n <- evaluations[idx, 2]
X <- rmvt(n,Sigma,df) #multivariate t distribution
eps1 <- rt(n,df)*(1+sqrt(X[,1]^2+X[,2]^2))
eps2 <- rt(n,df)*(1+sqrt(X[,1]^4+X[,2]^4))
Y <- rpois(n,sin(X[,1])^2 + cos(X[,2])^4+0.01 )+0.03*X[,1]*eps1+25*(runif(n,0,1)<0.01)*eps2
X0 <- rmvt(n0,Sigma,df)
eps01 <- rt(n0,df)*(1+sqrt(X0[,1]^2+X0[,2]^2))
eps02 <- rt(n0,df)*(1+sqrt(X0[,1]^4+X0[,2]^4))
Y0 <- rpois(n0,sin(X0[,1])^2 + cos(X0[,2])^4+0.01 )+0.03*X0[,1]*eps01+25*(runif(n0,0,1)<0.01)*eps02
width_mat[idx,3] <- cov_mat[idx, 3] <- n
method <- evaluations[idx, 3]
width_mat[idx,4] <- cov_mat[idx, 4] <- method
width_mat[idx, 2] <- cov_mat[idx, 2] <- evaluations[idx, 1]
if(method == "valid"){
split <- c(1/2, 1/2)
} else {
split <- 1/2
}
beta_grid <- seq(1e-03, 4, length = 20)*alpha
mtry_grid <- unique(ceiling(seq(1/10, 1, length = 20)*d))
ntree_grid <- seq(50, 400, by = 50)
tmp <- try(conf_CQR_reg(X, Y, split = split, beta_grid, mtry_grid, ntree_grid, method = method, alpha = alpha))
while (class(tmp)=="try-error"){
tmp <- try(conf_CQR_reg(X, Y, split = split, beta_grid, mtry_grid, ntree_grid, method = method, alpha = alpha),silent=TRUE)
}
width_mat[idx, 1] <- tmp$width
cov_mat[idx, 1] <- mean(tmp$pred_set(X0, Y0))
}
par(mfrow <- c(1,2))
width_efcp <- width_vfcp <- sd_width_efcp <- sd_width_vfcp <- NULL
#sd_efcp <- sd_vfcp <- NULL
for(n in nset){
TMP <- width_mat[evaluations[,3] == "efficient", ]
TMP_prime <- TMP[TMP[,3] == n,]
TMP <- width_mat[evaluations[,3] == "valid", ]
TMP_prime_vfcp <- TMP[TMP[,3] == n,]
TMP_prime_vfcp_clean =TMP_prime_vfcp[ TMP_prime_vfcp[,1]<=10^5,1]
width_efcp <- c(width_efcp, mean(TMP_prime[,1] / TMP_prime_vfcp[,1]))
sd_width_efcp <- c(sd_width_efcp, sd(TMP_prime[,1]/ TMP_prime_vfcp[,1])/sqrt(nrep))
#sd_efcp = c(sd_efcp , sd(TMP_prime[,1])/sqrt(nrep) )
width_vfcp <- c(width_vfcp, mean(TMP_prime_vfcp[,1] / TMP_prime_vfcp[,1]))
sd_width_vfcp <- c(sd_width_vfcp, sd(TMP_prime_vfcp[,1]/ TMP_prime_vfcp[,1])/sqrt(nrep))
#sd_vfcp = c(sd_vfcp , sd(TMP_prime_vfcp[,1])/sqrt(nrep) )
}
#plot(dim, width_efcp, type = 'l', ylim = range(c(width_efcp+sd_efcp)), lwd = 2)
plot(nset, width_efcp, type = 'l', ylim =c(-10,25), lwd = 2)
lines(nset, width_efcp - sd_width_efcp, type = 'l', lty = 2, lwd = 2)
lines(nset, width_efcp + sd_width_efcp, type = 'l', lty = 2, lwd = 2)
lines(nset, width_vfcp, type = 'l', ylim = range(c(width_efcp, width_vfcp)), lwd = 2, col = "red")
lines(nset, width_vfcp - sd_width_vfcp, type = 'l', lty = 2, lwd = 2, col = "red")
lines(nset, width_vfcp + sd_width_vfcp, type = 'l', lty = 2, lwd = 2, col = "red")
abline(h = 1)
cov_efcp <- cov_vfcp <-sd_cov_efcp <- sd_cov_vfcp <- NULL
for(n in nset){
TMP <- cov_mat[evaluations[,3] == "efficient", ]
TMP_prime <- TMP[TMP[,3] == n,]
cov_efcp <- c( cov_efcp, mean(TMP_prime[,1] ) )
sd_cov_efcp <- c(sd_cov_efcp, sd(TMP_prime[,1])/sqrt(nrep))
TMP <- cov_mat[evaluations[,3] == "valid", ]
TMP_prime <- TMP[TMP[,3] == n,]
cov_vfcp <- c(cov_vfcp, mean(TMP_prime[,1]))
sd_cov_vfcp <- c(sd_cov_vfcp, sd(TMP_prime[,1])/sqrt(nrep))
}
plot(nset, cov_efcp, type = 'l', ylim = c(0, 1), lwd = 2)
lines(nset, cov_vfcp, type = 'l', col = "red", lwd = 2)
abline(h = 1-alpha)
save(nset,nrep,width_mat, cov_mat, evaluations, width_efcp, sd_cov_efcp, sd_width_efcp,width_vfcp, sd_cov_vfcp,sd_width_vfcp, cov_efcp, cov_vfcp, alpha, file = "pois-100-repetitions.RData" )
Elsa-Yang98/ConformalSmallest documentation built on Dec. 17, 2021, 6:28 p.m.
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
ConformalSmallest
This package implements two selection algorithms for conformal prediction regions to obtain the smallest prediction set in practice; these are called “efficiency first” and “validity first” conformal prediction algorithms, EFCP and VFCP for short. For details please refer to our paper.
Installation
You can install the released version of ConformalSmallest from CRAN with:
install.packages("ConformalSmallest")
Or directly from github
devtools::install_github("Elsa-Yang98/ConformalSmallest")
Vignettes
Please refer to the vignettes for two examples on how to apply EFCP and VFCP to tuning-free ridge regression and conformal quantile regression using the package and on how to interpret the results.
Example
This is a basic example which shows you how to solve a common problem:
library(ConformalSmallest)
## basic example code
Example 1: Tuning free ridge regression with conformal prediction
library(glmnet)
library(MASS)
library(mvtnorm)
source("ginverse.fun.R")
source("functions.R")
name=paste("linear_fm_t3",sep="")
df <- 3 #degrees of freedom
l <- 60 #number of dimensions
l.lambda <- 100
lambda_seq <- seq(0,200,l=l.lambda)
dim <- round(seq(5,300,l=l))
alpha <- 0.1
n <- 200 #number of training samples
n0 <- 100 #number of prediction points
nrep <- 100 #number of independent trials
rho <- 0.5
cov.efcp <- len.efcp <- matrix(0,nrep,l)
cov.vfcp <- len.vfcp <- matrix(0,nrep,l)
cov.naive <- len.naive <- matrix(0,nrep,l)
cov.param <- len.param <- matrix(0,nrep,l)
cov.star <- len.star <- matrix(0,nrep,l)
cov.cv10 <- len.cv10 <- matrix(0,nrep,l)
cov.cv5 <- len.cv5 <- matrix(0,nrep,l)
cov.cvloo <- len.cvloo <- matrix(0,nrep,l)
out.efcp.up <- out.efcp.lo <- matrix(0,n0,l)
out.vfcp.up <- out.vfcp.lo <- matrix(0,n0,l)
out.naive.up <- out.naive.lo <- matrix(0,n0,l)
out.param.up <- out.param.lo <- matrix(0,n0,l)
out.star.up <- out.star.lo <- matrix(0,n0,l)
out.cv10.up <- out.cv10.lo <- matrix(0,n0,l)
out.cv5.up <- out.cv5.lo <- matrix(0,n0,l)
out.cvloo.up <- out.cvloo.lo <- matrix(0,n0,l)
for(i in 1:nrep){
cat(i,"\n")
for (r in 1:l){
d <- dim[r]
set.seed(i)
Sigma <- matrix(rho,d,d)
diag(Sigma) <- rep(1,d)
X <- rmvt(n,Sigma,df) #multivariate t distribution
beta <- rep(1:5,d/5)
eps <- rt(n,df)*(1+sqrt(X[,1]^2+X[,2]^2))
Y <- X%*%beta+eps
X0 <- rmvt(n0,Sigma,df)
eps0 <- rt(n0,df)*(1+sqrt(X0[,1]^2+X0[,2]^2))
Y0 <- X0%*%beta+eps0
out.param <- ginverse.fun(X,Y,X0,alpha=alpha)
out.param.lo[,r] <- out.param$lo
out.param.up[,r] <- out.param$up
cov.param[i,r] <- mean(out.param.lo[,r] <= Y0 & Y0 <= out.param.up[,r])
len.param[i,r] <- mean(out.param.up[,r]-out.param.lo[,r])
out.efcp <- efcp_ridge(X,Y,X0,lambda=lambda_seq,alpha=alpha)
out.efcp.up[,r] <- out.efcp$up
out.efcp.lo[,r] <- out.efcp$lo
cov.efcp[i,r] <- mean(out.efcp.lo[,r] <= Y0 & Y0 <= out.efcp.up[,r])
len.efcp[i,r] <- mean(out.efcp.up[,r]-out.efcp.lo[,r])
out.vfcp <- vfcp_ridge(X,Y,X0,lambda=lambda_seq,alpha=alpha)
out.vfcp.up[,r] <- out.vfcp$up
out.vfcp.lo[,r] <- out.vfcp$lo
cov.vfcp[i,r] <- mean(out.vfcp.lo[,r] <= Y0 & Y0 <= out.vfcp.up[,r])
len.vfcp[i,r] <- mean(out.vfcp.up[,r]-out.vfcp.lo[,r])
out.naive <- naive.fun(X,Y,X0,alpha=alpha)
out.naive.up[,r] <- out.naive$up
out.naive.lo[,r] <- out.naive$lo
cov.naive[i,r] <- mean(out.naive.lo[,r] <= Y0 & Y0 <= out.naive.up[,r])
len.naive[i,r] <- mean(out.naive.up[,r]-out.naive.lo[,r])
out.star <- star.fun(X,Y,X0,lambda=lambda_seq,alpha=alpha)
out.star.up[,r] <- out.star$up
out.star.lo[,r] <- out.star$lo
cov.star[i,r] <- mean(out.star.lo[,r] <= Y0 & Y0 <= out.star.up[,r])
len.star[i,r] <- mean(out.star.up[,r] - out.star.lo[,r])
out.cv5 <- cv.fun(X,Y,X0,lambda=lambda_seq,alpha=alpha,nfolds=5)
out.cv5.up[,r] <- out.cv5$up
out.cv5.lo[,r] <- out.cv5$lo
cov.cv5[i,r] <- mean(out.cv5.lo[,r] <= Y0 & Y0 <= out.cv5.up[,r])
len.cv5[i,r] <- mean(out.cv5.up[,r] - out.cv5.lo[,r])
}
}
df.cov <- data.frame(dim,apply(cov.param,2,mean),apply(cov.naive,2,mean),apply(cov.vfcp,2,mean),apply(cov.star,2,mean),apply(cov.cv5,2,mean), apply(cov.efcp,2,mean))
df.len <- data.frame(dim,apply(len.param,2,mean),apply(len.naive,2,mean),apply(len.vfcp,2,mean),apply(len.star,2,mean),apply(len.cv5,2,mean), apply(len.efcp,2,mean))
save(dim,cov.param, cov.naive, cov.vfcp, cov.star, cov.cv5, cov.efcp, file = "cov100_t3.RData" )
save(dim,len.param, len.naive, len.vfcp, len.star, len.cv5, len.efcp, file = "len100_t3.RData" )
Example 2: Tuning free conformal quantile regression with random forest
This output the right panal of Figure 1 in our paper.
df <- 3
d <- 3
l.lambda <- 100
lambda_seq <- seq(0,200,l=l.lambda)
nset <- c(50,100,500,1000,5000)
alpha <- 0.1 #miscoverage level
n0 <- 100 #number of prediction points
nrep <- 100 #number of independent trials
rho <- 0.5
evaluations <- expand.grid(1:nrep, nset, c("efficient", "valid"))
no_eval <- nrow(evaluations)
width_mat <- cov_mat <- data.frame(number = rep(0, no_eval),
rep = evaluations[,1],
nset = evaluations[,2],
method = evaluations[,3])
colnames(width_mat) <- colnames(cov_mat) <- c("number", "rep", "sample size", "method")
Sigma <- matrix(rho,d,d)
diag(Sigma) <- rep(1,d) #covariance matrix for X
for(idx in 1:nrow(evaluations)){
set.seed(evaluations[idx, 1])
if(idx%%1 == 0){
print(idx)
}
n <- evaluations[idx, 2]
X <- rmvt(n,Sigma,df) #multivariate t distribution
eps1 <- rt(n,df)*(1+sqrt(X[,1]^2+X[,2]^2))
eps2 <- rt(n,df)*(1+sqrt(X[,1]^4+X[,2]^4))
Y <- rpois(n,sin(X[,1])^2 + cos(X[,2])^4+0.01 )+0.03*X[,1]*eps1+25*(runif(n,0,1)<0.01)*eps2
X0 <- rmvt(n0,Sigma,df)
eps01 <- rt(n0,df)*(1+sqrt(X0[,1]^2+X0[,2]^2))
eps02 <- rt(n0,df)*(1+sqrt(X0[,1]^4+X0[,2]^4))
Y0 <- rpois(n0,sin(X0[,1])^2 + cos(X0[,2])^4+0.01 )+0.03*X0[,1]*eps01+25*(runif(n0,0,1)<0.01)*eps02
width_mat[idx,3] <- cov_mat[idx, 3] <- n
method <- evaluations[idx, 3]
width_mat[idx,4] <- cov_mat[idx, 4] <- method
width_mat[idx, 2] <- cov_mat[idx, 2] <- evaluations[idx, 1]
if(method == "valid"){
split <- c(1/2, 1/2)
} else {
split <- 1/2
}
beta_grid <- seq(1e-03, 4, length = 20)*alpha
mtry_grid <- unique(ceiling(seq(1/10, 1, length = 20)*d))
ntree_grid <- seq(50, 400, by = 50)
tmp <- try(conf_CQR_reg(X, Y, split = split, beta_grid, mtry_grid, ntree_grid, method = method, alpha = alpha))
while (class(tmp)=="try-error"){
tmp <- try(conf_CQR_reg(X, Y, split = split, beta_grid, mtry_grid, ntree_grid, method = method, alpha = alpha),silent=TRUE)
}
width_mat[idx, 1] <- tmp$width
cov_mat[idx, 1] <- mean(tmp$pred_set(X0, Y0))
}
par(mfrow <- c(1,2))
width_efcp <- width_vfcp <- sd_width_efcp <- sd_width_vfcp <- NULL
#sd_efcp <- sd_vfcp <- NULL
for(n in nset){
TMP <- width_mat[evaluations[,3] == "efficient", ]
TMP_prime <- TMP[TMP[,3] == n,]
TMP <- width_mat[evaluations[,3] == "valid", ]
TMP_prime_vfcp <- TMP[TMP[,3] == n,]
TMP_prime_vfcp_clean =TMP_prime_vfcp[ TMP_prime_vfcp[,1]<=10^5,1]
width_efcp <- c(width_efcp, mean(TMP_prime[,1] / TMP_prime_vfcp[,1]))
sd_width_efcp <- c(sd_width_efcp, sd(TMP_prime[,1]/ TMP_prime_vfcp[,1])/sqrt(nrep))
#sd_efcp = c(sd_efcp , sd(TMP_prime[,1])/sqrt(nrep) )
width_vfcp <- c(width_vfcp, mean(TMP_prime_vfcp[,1] / TMP_prime_vfcp[,1]))
sd_width_vfcp <- c(sd_width_vfcp, sd(TMP_prime_vfcp[,1]/ TMP_prime_vfcp[,1])/sqrt(nrep))
#sd_vfcp = c(sd_vfcp , sd(TMP_prime_vfcp[,1])/sqrt(nrep) )
}
#plot(dim, width_efcp, type = 'l', ylim = range(c(width_efcp+sd_efcp)), lwd = 2)
plot(nset, width_efcp, type = 'l', ylim =c(-10,25), lwd = 2)
lines(nset, width_efcp - sd_width_efcp, type = 'l', lty = 2, lwd = 2)
lines(nset, width_efcp + sd_width_efcp, type = 'l', lty = 2, lwd = 2)
lines(nset, width_vfcp, type = 'l', ylim = range(c(width_efcp, width_vfcp)), lwd = 2, col = "red")
lines(nset, width_vfcp - sd_width_vfcp, type = 'l', lty = 2, lwd = 2, col = "red")
lines(nset, width_vfcp + sd_width_vfcp, type = 'l', lty = 2, lwd = 2, col = "red")
abline(h = 1)
cov_efcp <- cov_vfcp <-sd_cov_efcp <- sd_cov_vfcp <- NULL
for(n in nset){
TMP <- cov_mat[evaluations[,3] == "efficient", ]
TMP_prime <- TMP[TMP[,3] == n,]
cov_efcp <- c( cov_efcp, mean(TMP_prime[,1] ) )
sd_cov_efcp <- c(sd_cov_efcp, sd(TMP_prime[,1])/sqrt(nrep))
TMP <- cov_mat[evaluations[,3] == "valid", ]
TMP_prime <- TMP[TMP[,3] == n,]
cov_vfcp <- c(cov_vfcp, mean(TMP_prime[,1]))
sd_cov_vfcp <- c(sd_cov_vfcp, sd(TMP_prime[,1])/sqrt(nrep))
}
plot(nset, cov_efcp, type = 'l', ylim = c(0, 1), lwd = 2)
lines(nset, cov_vfcp, type = 'l', col = "red", lwd = 2)
abline(h = 1-alpha)
save(nset,nrep,width_mat, cov_mat, evaluations, width_efcp, sd_cov_efcp, sd_width_efcp,width_vfcp, sd_cov_vfcp,sd_width_vfcp, cov_efcp, cov_vfcp, alpha, file = "pois-100-repetitions.RData" )
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