replicate.R
In jstriaukas/LassoNet: 3CoSE Algorithm
#'
#' run_simulations.single function runs a single scenario simulation
#'
run_simulations.single <- function(p,beta.x, beta.0, M, lambda.1, lambda.2, t, n, nfolds = 10, tol = 1e-6, n.iter = 1e10, m.iter, mc = FALSE){
if(!mc)OUTPUT <-lapply(1:t, main.loop.single,
p,beta.x,
beta.0, M, lambda.1, lambda.2,
n, nfolds, tol, n.iter, m.iter)
if(mc)OUTPUT <- sfLapply(1:t, main.loop.single,
p,beta.x,
beta.0, M, lambda.1, lambda.2,
n, nfolds, tol, n.iter, m.iter)
return(OUTPUT)
}
simul.data.single <- function(p, n, beta.x, q = 10) {
X1 <- array(0,c(n,p))
Y1 <- array(0,c(n,1))
prop <- p/(q+1)
# storage
b1mat <- matrix(t(beta.x),q+1,prop)
sig <- 0.51
for (jj in 1:n) {
X1.temp <- matrix(0,prop,q+1)
TF <- rnorm(prop,mean = 0, sd = 1)
for (ii in 1:prop) {
x.temp <- rnorm(q,mean=rep(sign(b1mat[1,ii])*sign(b1mat[2:11,ii])*0.7*TF[ii],q), sd = sqrt(sig))
X1.temp[ii,] <- c(TF[ii], x.temp)
}
X1[jj,] <- as.vector(t(X1.temp))
}
# computing variance of each scenario:
epsilon <- rnorm(n, mean = 0, sd = 1)
sig.1 <- sqrt(sum((beta.x)^2)/4)
Y1 <- X1%*%beta.x + sig.1*epsilon
return(list(Y1 = Y1, X1 = X1))
}
main.loop.single <- function(dt,p,beta.x, beta.0, M, lambda.1, lambda.2, n, nfolds = 10, tol = 1e-6, n.iter = 1e10, m.iter = 2e1){
#---params---#
n1 <- length(lambda.1)
n2 <- length(lambda.2)
# storage
msfeCV.norm <- array(0,c(n2,n1,nfolds))
msfeCV.comb <- array(0,c(n2,n1,nfolds))
msfeCV.fix <- array(0,c(n2,n1,nfolds))
msfeCV.lasso <- array(0,c(n2,n1,nfolds))
OUTPUT <- NULL
MSFE.norm <- NULL
MSFE.comb <- NULL
MSFE.fix <- NULL
MSFE.lasso <- NULL
lam.comb.norm <- NULL
lam.comb.comb <- NULL
lam.comb.fix <- NULL
lam.comb.lasso <- NULL
std.cv.norm <- NULL
std.cv.comb <- NULL
std.cv.fix <- NULL
std.cv.lasso <- NULL
PRED.ERROR.NORM <- NULL
PRED.ERROR.COMB <- NULL
PRED.ERROR.FIX <- NULL
PRED.ERROR.LASSO <- NULL
PRED.ERROR.null <- NULL
PRED.ERROR.true <- NULL
#--data train (cross validate) [i] and test [i+1]---#
# i-th data set: training and validating:
data.sim <- simul.data.single(p, n, beta.x)
X1 <- scale(data.sim$X1 , center = TRUE, scale = TRUE)
Y1 <- scale(data.sim$Y1, center = TRUE, scale = FALSE)
# i-th data set: testing and computing statistics:
data.sim.test <- simul.data.single(p, n, beta.x)
X1.test <- scale(data.sim.test$X1 , center = TRUE, scale = TRUE)
Y1.test <- scale(data.sim.test$Y1 , center = TRUE, scale = FALSE)
if (nfolds < 2)
stop("nfolds must be bigger than 2; at least 3 would be good; nfolds=10 recommended")
crossval.ind <- CVfold(n,K = nfolds, is.random = FALSE)
CVOUTPUT <- cv.par(nfolds, dt, crossval.ind, X1, Y1, M, beta.0, lambda.1, lambda.2, m.iter, n.iter, tol)
for(d in 1:nfolds){
# store estimates of connections, convergence and info if signs alternate
beta.norm <- CVOUTPUT[[d]]$beta.norm
beta.comb <- CVOUTPUT[[d]]$beta.comb
beta.fix <- CVOUTPUT[[d]]$beta.fix
beta.lasso <- CVOUTPUT[[d]]$beta.lasso
X1.val <- CVOUTPUT[[d]]$X1.val
Y1.val <- CVOUTPUT[[d]]$Y1.val
for (jj in 1:n2) { # ii - lasso, jj - network
for (ii in 1:n1){
msfeCV.norm[jj,ii,d] <- mean((Y1.val - X1.val%*%as.numeric(beta.norm[,jj,ii]))^2)
msfeCV.comb[jj,ii,d] <- mean((Y1.val - X1.val%*%as.numeric(beta.comb[,jj,ii]))^2)
msfeCV.fix[jj,ii,d] <- mean((Y1.val - X1.val%*%as.numeric(beta.fix[,jj,ii]))^2)
msfeCV.lasso[1,ii,d] <- mean((Y1.val - X1.val%*%as.numeric(beta.lasso[,1,ii]))^2)
}
}
}
# average of CV error curves:
OUTPUT$MSFE.norm <- apply(msfeCV.norm, c(1,2), "mean")
OUTPUT$MSFE.comb <- apply(msfeCV.comb, c(1,2), "mean")
OUTPUT$MSFE.fix <- apply(msfeCV.fix, c(1,2), "mean")
OUTPUT$MSFE.lasso <- apply(msfeCV.lasso, c(1,2), "mean")
OUTPUT$std.cv.norm <- apply(msfeCV.norm, c(1,2), "sd")/sqrt(nfolds)
OUTPUT$std.cv.comb <- apply(msfeCV.comb, c(1,2), "sd")/sqrt(nfolds)
OUTPUT$std.cv.fix <- apply(msfeCV.fix, c(1,2), "sd")/sqrt(nfolds)
OUTPUT$std.cv.lasso <- apply(msfeCV.lasso, c(1,2), "sd")/sqrt(nfolds)
lam.comb.norm <- which(OUTPUT$MSFE.norm == min(OUTPUT$MSFE.norm), arr.ind = T)
lam.comb.comb <- which(OUTPUT$MSFE.comb == min(OUTPUT$MSFE.comb), arr.ind = T)
lam.comb.fix <- which(OUTPUT$MSFE.fix == min(OUTPUT$MSFE.fix), arr.ind = T)
lam.comb.lasso <- which(OUTPUT$MSFE.lasso == min(OUTPUT$MSFE.lasso), arr.ind = T)
OUTPUT$optim.lam.norm <- c(lambda.1[lam.comb.norm[2]], lambda.2[lam.comb.norm[1]])
OUTPUT$optim.lam.comb <- c(lambda.1[lam.comb.comb[2]], lambda.2[lam.comb.comb[1]])
OUTPUT$optim.lam.fix <- c(lambda.1[lam.comb.fix[2]], lambda.2[lam.comb.fix[1]])
OUTPUT$optim.lam.lasso <- c(lambda.1[lam.comb.lasso[2]])
cat('*** Norm Lap ***')
M.int <- mat.to.laplacian(M, type = "normalized")
OUT.NORM <- lasso.net.grid(X1,Y1,beta.0,OUTPUT$optim.lam.norm[1],OUTPUT$optim.lam.norm[2], M.int, m.iter = m.iter, n.iter = n.iter, iscpp = T, tol = tol, alt.num = 4 )
OUTPUT$OUT.NORM <- OUT.NORM
cat('*** Fixed Norm ***')
M.int <- mat.to.laplacian(M, type = "normalized")
OUT.FIX <- lasso.net.fixed(X1,Y1,beta.0,OUTPUT$optim.lam.fix[1],OUTPUT$optim.lam.fix[2], M.int, n.iter = n.iter, iscpp = T, tol = tol )
OUTPUT$OUT.FIX <- OUT.FIX
cat('*** Comb Lap ***')
M.int <- mat.to.laplacian(M, type = "combinatorial")
OUT.COMB <- lasso.net.grid(X1,Y1,beta.0,OUTPUT$optim.lam.comb[1],OUTPUT$optim.lam.comb[2], M.int, m.iter = m.iter, n.iter = n.iter, iscpp = T, tol = tol, alt.num = 4 )
OUTPUT$OUT.COMB <- OUT.COMB
cat('*** Lasso ***')
OUT.LASSO <- lasso.net.grid(X1,Y1,beta.0,OUTPUT$optim.lam.lasso[1],0, M, m.iter = m.iter, n.iter = n.iter, iscpp = T, tol = tol, alt.num = 4 )
OUTPUT$OUT.LASSO <- OUT.LASSO
PRED.ERROR.NORM <- mean((Y1.test - X1.test%*%OUT.NORM$beta)^2)
PRED.ERROR.COMB <- mean((Y1.test - X1.test%*%OUT.COMB$beta)^2)
PRED.ERROR.FIX <- mean((Y1.test - X1.test%*%OUT.FIX$beta)^2)
PRED.ERROR.LASSO <- mean((Y1.test - X1.test%*%OUT.LASSO$beta)^2)
OUTPUT$PRED.ERROR.true <- mean((Y1.test - X1.test%*%beta.x)^2)
OUTPUT$PRED.ERROR.null <- mean((Y1.test)^2)
return(OUTPUT = OUTPUT)
}
cv.par <- function(d, dt, crossval.ind, X1, Y1, M, beta.0, lambda.1, lambda.2, m.iter, n.iter, tol) {
CVOUTPUT <-lapply(1:d, cv.loop,
dt, crossval.ind, X1, Y1,
M, beta.0,
lambda.1, lambda.2, m.iter,
n.iter, tol)
return(CVOUTPUT)
}
cv.loop <- function(ds, dt, crossval.ind, X1, Y1, M, beta.0, lambda.1, lambda.2, m.iter, n.iter, tol){
CVOUTPUT <- NULL
cat("Cross validation data set - ", ds, "\n")
cat("Data set - ", dt, "\n")
train.ind <- crossval.ind[[ds]]$train
val.ind <- crossval.ind[[ds]]$validate
X1.train <- X1[train.ind,]
Y1.train <- Y1[train.ind]
X1.val <- X1[val.ind,]
Y1.val <- Y1[val.ind]
cat('*** Norm Lap ***')
M.int <- mat.to.laplacian(M, type = "normalized")
output.train <- lasso.net.grid(X1.train,Y1.train,beta.0,lambda.1,lambda.2, M.int, m.iter = m.iter, n.iter = n.iter, iscpp = T, tol = tol, alt.num = 4 )
CVOUTPUT$beta.norm <- output.train$beta
cat('*** Fixed Norm ***')
M.int <- mat.to.laplacian(M, type = "normalized")
output.train <- lasso.net.fixed(X1.train,Y1.train,beta.0,lambda.1,lambda.2, M.int, n.iter = n.iter, iscpp = T, tol = tol )
CVOUTPUT$beta.fix <- output.train$beta
cat('*** Comb Lap ***')
M.int <- mat.to.laplacian(M, type = "combinatorial")
output.train <- lasso.net.grid(X1.train,Y1.train,beta.0,lambda.1,lambda.2, M.int, m.iter = m.iter, n.iter = n.iter, iscpp = T, tol = tol, alt.num = 4 )
CVOUTPUT$beta.comb <- output.train$beta
cat('*** Lasso ***')
output.train <- lasso.net.grid(X1.train,Y1.train,beta.0,lambda.1,0, M, m.iter = m.iter, n.iter = n.iter, iscpp = T, tol = tol, alt.num = 4 )
CVOUTPUT$beta.lasso <- output.train$beta
CVOUTPUT$X1.val <- X1.val
CVOUTPUT$Y1.val <- Y1.val
return(CVOUTPUT = CVOUTPUT)
}
CVfold <- function(n,K=10, is.random = FALSE){
# determine if draw random indices or sequential
if(is.random){
id <- sample(n,replace = FALSE)
} else {
id <- seq(n)
}
# get indices:
k <- as.integer(n*seq(1,K-1)/K)
k <- matrix(c(0,rep(k,each=2),n),ncol=2,byrow=TRUE)
k[,1] <- k[,1]+1
ind <- lapply(seq.int(K),function(x,k,d) list(train=d[!(seq(d) %in% seq(k[x,1],k[x,2]))],validate=d[seq(k[x,1],k[x,2])]),k=k,d=id)
return(ind)
}
jstriaukas/LassoNet documentation built on Jan. 21, 2020, 1:45 p.m.
R Package Documentation
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#'
#' run_simulations.single function runs a single scenario simulation
#'
run_simulations.single <- function(p,beta.x, beta.0, M, lambda.1, lambda.2, t, n, nfolds = 10, tol = 1e-6, n.iter = 1e10, m.iter, mc = FALSE){
if(!mc)OUTPUT <-lapply(1:t, main.loop.single,
p,beta.x,
beta.0, M, lambda.1, lambda.2,
n, nfolds, tol, n.iter, m.iter)
if(mc)OUTPUT <- sfLapply(1:t, main.loop.single,
p,beta.x,
beta.0, M, lambda.1, lambda.2,
n, nfolds, tol, n.iter, m.iter)
return(OUTPUT)
}
simul.data.single <- function(p, n, beta.x, q = 10) {
X1 <- array(0,c(n,p))
Y1 <- array(0,c(n,1))
prop <- p/(q+1)
# storage
b1mat <- matrix(t(beta.x),q+1,prop)
sig <- 0.51
for (jj in 1:n) {
X1.temp <- matrix(0,prop,q+1)
TF <- rnorm(prop,mean = 0, sd = 1)
for (ii in 1:prop) {
x.temp <- rnorm(q,mean=rep(sign(b1mat[1,ii])*sign(b1mat[2:11,ii])*0.7*TF[ii],q), sd = sqrt(sig))
X1.temp[ii,] <- c(TF[ii], x.temp)
}
X1[jj,] <- as.vector(t(X1.temp))
}
# computing variance of each scenario:
epsilon <- rnorm(n, mean = 0, sd = 1)
sig.1 <- sqrt(sum((beta.x)^2)/4)
Y1 <- X1%*%beta.x + sig.1*epsilon
return(list(Y1 = Y1, X1 = X1))
}
main.loop.single <- function(dt,p,beta.x, beta.0, M, lambda.1, lambda.2, n, nfolds = 10, tol = 1e-6, n.iter = 1e10, m.iter = 2e1){
#---params---#
n1 <- length(lambda.1)
n2 <- length(lambda.2)
# storage
msfeCV.norm <- array(0,c(n2,n1,nfolds))
msfeCV.comb <- array(0,c(n2,n1,nfolds))
msfeCV.fix <- array(0,c(n2,n1,nfolds))
msfeCV.lasso <- array(0,c(n2,n1,nfolds))
OUTPUT <- NULL
MSFE.norm <- NULL
MSFE.comb <- NULL
MSFE.fix <- NULL
MSFE.lasso <- NULL
lam.comb.norm <- NULL
lam.comb.comb <- NULL
lam.comb.fix <- NULL
lam.comb.lasso <- NULL
std.cv.norm <- NULL
std.cv.comb <- NULL
std.cv.fix <- NULL
std.cv.lasso <- NULL
PRED.ERROR.NORM <- NULL
PRED.ERROR.COMB <- NULL
PRED.ERROR.FIX <- NULL
PRED.ERROR.LASSO <- NULL
PRED.ERROR.null <- NULL
PRED.ERROR.true <- NULL
#--data train (cross validate) [i] and test [i+1]---#
# i-th data set: training and validating:
data.sim <- simul.data.single(p, n, beta.x)
X1 <- scale(data.sim$X1 , center = TRUE, scale = TRUE)
Y1 <- scale(data.sim$Y1, center = TRUE, scale = FALSE)
# i-th data set: testing and computing statistics:
data.sim.test <- simul.data.single(p, n, beta.x)
X1.test <- scale(data.sim.test$X1 , center = TRUE, scale = TRUE)
Y1.test <- scale(data.sim.test$Y1 , center = TRUE, scale = FALSE)
if (nfolds < 2)
stop("nfolds must be bigger than 2; at least 3 would be good; nfolds=10 recommended")
crossval.ind <- CVfold(n,K = nfolds, is.random = FALSE)
CVOUTPUT <- cv.par(nfolds, dt, crossval.ind, X1, Y1, M, beta.0, lambda.1, lambda.2, m.iter, n.iter, tol)
for(d in 1:nfolds){
# store estimates of connections, convergence and info if signs alternate
beta.norm <- CVOUTPUT[[d]]$beta.norm
beta.comb <- CVOUTPUT[[d]]$beta.comb
beta.fix <- CVOUTPUT[[d]]$beta.fix
beta.lasso <- CVOUTPUT[[d]]$beta.lasso
X1.val <- CVOUTPUT[[d]]$X1.val
Y1.val <- CVOUTPUT[[d]]$Y1.val
for (jj in 1:n2) { # ii - lasso, jj - network
for (ii in 1:n1){
msfeCV.norm[jj,ii,d] <- mean((Y1.val - X1.val%*%as.numeric(beta.norm[,jj,ii]))^2)
msfeCV.comb[jj,ii,d] <- mean((Y1.val - X1.val%*%as.numeric(beta.comb[,jj,ii]))^2)
msfeCV.fix[jj,ii,d] <- mean((Y1.val - X1.val%*%as.numeric(beta.fix[,jj,ii]))^2)
msfeCV.lasso[1,ii,d] <- mean((Y1.val - X1.val%*%as.numeric(beta.lasso[,1,ii]))^2)
}
}
}
# average of CV error curves:
OUTPUT$MSFE.norm <- apply(msfeCV.norm, c(1,2), "mean")
OUTPUT$MSFE.comb <- apply(msfeCV.comb, c(1,2), "mean")
OUTPUT$MSFE.fix <- apply(msfeCV.fix, c(1,2), "mean")
OUTPUT$MSFE.lasso <- apply(msfeCV.lasso, c(1,2), "mean")
OUTPUT$std.cv.norm <- apply(msfeCV.norm, c(1,2), "sd")/sqrt(nfolds)
OUTPUT$std.cv.comb <- apply(msfeCV.comb, c(1,2), "sd")/sqrt(nfolds)
OUTPUT$std.cv.fix <- apply(msfeCV.fix, c(1,2), "sd")/sqrt(nfolds)
OUTPUT$std.cv.lasso <- apply(msfeCV.lasso, c(1,2), "sd")/sqrt(nfolds)
lam.comb.norm <- which(OUTPUT$MSFE.norm == min(OUTPUT$MSFE.norm), arr.ind = T)
lam.comb.comb <- which(OUTPUT$MSFE.comb == min(OUTPUT$MSFE.comb), arr.ind = T)
lam.comb.fix <- which(OUTPUT$MSFE.fix == min(OUTPUT$MSFE.fix), arr.ind = T)
lam.comb.lasso <- which(OUTPUT$MSFE.lasso == min(OUTPUT$MSFE.lasso), arr.ind = T)
OUTPUT$optim.lam.norm <- c(lambda.1[lam.comb.norm[2]], lambda.2[lam.comb.norm[1]])
OUTPUT$optim.lam.comb <- c(lambda.1[lam.comb.comb[2]], lambda.2[lam.comb.comb[1]])
OUTPUT$optim.lam.fix <- c(lambda.1[lam.comb.fix[2]], lambda.2[lam.comb.fix[1]])
OUTPUT$optim.lam.lasso <- c(lambda.1[lam.comb.lasso[2]])
cat('*** Norm Lap ***')
M.int <- mat.to.laplacian(M, type = "normalized")
OUT.NORM <- lasso.net.grid(X1,Y1,beta.0,OUTPUT$optim.lam.norm[1],OUTPUT$optim.lam.norm[2], M.int, m.iter = m.iter, n.iter = n.iter, iscpp = T, tol = tol, alt.num = 4 )
OUTPUT$OUT.NORM <- OUT.NORM
cat('*** Fixed Norm ***')
M.int <- mat.to.laplacian(M, type = "normalized")
OUT.FIX <- lasso.net.fixed(X1,Y1,beta.0,OUTPUT$optim.lam.fix[1],OUTPUT$optim.lam.fix[2], M.int, n.iter = n.iter, iscpp = T, tol = tol )
OUTPUT$OUT.FIX <- OUT.FIX
cat('*** Comb Lap ***')
M.int <- mat.to.laplacian(M, type = "combinatorial")
OUT.COMB <- lasso.net.grid(X1,Y1,beta.0,OUTPUT$optim.lam.comb[1],OUTPUT$optim.lam.comb[2], M.int, m.iter = m.iter, n.iter = n.iter, iscpp = T, tol = tol, alt.num = 4 )
OUTPUT$OUT.COMB <- OUT.COMB
cat('*** Lasso ***')
OUT.LASSO <- lasso.net.grid(X1,Y1,beta.0,OUTPUT$optim.lam.lasso[1],0, M, m.iter = m.iter, n.iter = n.iter, iscpp = T, tol = tol, alt.num = 4 )
OUTPUT$OUT.LASSO <- OUT.LASSO
PRED.ERROR.NORM <- mean((Y1.test - X1.test%*%OUT.NORM$beta)^2)
PRED.ERROR.COMB <- mean((Y1.test - X1.test%*%OUT.COMB$beta)^2)
PRED.ERROR.FIX <- mean((Y1.test - X1.test%*%OUT.FIX$beta)^2)
PRED.ERROR.LASSO <- mean((Y1.test - X1.test%*%OUT.LASSO$beta)^2)
OUTPUT$PRED.ERROR.true <- mean((Y1.test - X1.test%*%beta.x)^2)
OUTPUT$PRED.ERROR.null <- mean((Y1.test)^2)
return(OUTPUT = OUTPUT)
}
cv.par <- function(d, dt, crossval.ind, X1, Y1, M, beta.0, lambda.1, lambda.2, m.iter, n.iter, tol) {
CVOUTPUT <-lapply(1:d, cv.loop,
dt, crossval.ind, X1, Y1,
M, beta.0,
lambda.1, lambda.2, m.iter,
n.iter, tol)
return(CVOUTPUT)
}
cv.loop <- function(ds, dt, crossval.ind, X1, Y1, M, beta.0, lambda.1, lambda.2, m.iter, n.iter, tol){
CVOUTPUT <- NULL
cat("Cross validation data set - ", ds, "\n")
cat("Data set - ", dt, "\n")
train.ind <- crossval.ind[[ds]]$train
val.ind <- crossval.ind[[ds]]$validate
X1.train <- X1[train.ind,]
Y1.train <- Y1[train.ind]
X1.val <- X1[val.ind,]
Y1.val <- Y1[val.ind]
cat('*** Norm Lap ***')
M.int <- mat.to.laplacian(M, type = "normalized")
output.train <- lasso.net.grid(X1.train,Y1.train,beta.0,lambda.1,lambda.2, M.int, m.iter = m.iter, n.iter = n.iter, iscpp = T, tol = tol, alt.num = 4 )
CVOUTPUT$beta.norm <- output.train$beta
cat('*** Fixed Norm ***')
M.int <- mat.to.laplacian(M, type = "normalized")
output.train <- lasso.net.fixed(X1.train,Y1.train,beta.0,lambda.1,lambda.2, M.int, n.iter = n.iter, iscpp = T, tol = tol )
CVOUTPUT$beta.fix <- output.train$beta
cat('*** Comb Lap ***')
M.int <- mat.to.laplacian(M, type = "combinatorial")
output.train <- lasso.net.grid(X1.train,Y1.train,beta.0,lambda.1,lambda.2, M.int, m.iter = m.iter, n.iter = n.iter, iscpp = T, tol = tol, alt.num = 4 )
CVOUTPUT$beta.comb <- output.train$beta
cat('*** Lasso ***')
output.train <- lasso.net.grid(X1.train,Y1.train,beta.0,lambda.1,0, M, m.iter = m.iter, n.iter = n.iter, iscpp = T, tol = tol, alt.num = 4 )
CVOUTPUT$beta.lasso <- output.train$beta
CVOUTPUT$X1.val <- X1.val
CVOUTPUT$Y1.val <- Y1.val
return(CVOUTPUT = CVOUTPUT)
}
CVfold <- function(n,K=10, is.random = FALSE){
# determine if draw random indices or sequential
if(is.random){
id <- sample(n,replace = FALSE)
} else {
id <- seq(n)
}
# get indices:
k <- as.integer(n*seq(1,K-1)/K)
k <- matrix(c(0,rep(k,each=2),n),ncol=2,byrow=TRUE)
k[,1] <- k[,1]+1
ind <- lapply(seq.int(K),function(x,k,d) list(train=d[!(seq(d) %in% seq(k[x,1],k[x,2]))],validate=d[seq(k[x,1],k[x,2])]),k=k,d=id)
return(ind)
}
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