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### spls.adapt.aux.R (2014-10)
###
### Adaptive Sparse PLS regression for continuous response
### Short version for multiple call in cross-validation procedure
###
### Copyright 2014-10 Ghislain DURIF
###
### Adapted from R package "spls"
### Reference: Chun H and Keles S (2010)
### "Sparse partial least squares for simultaneous dimension reduction and variable selection",
### Journal of the Royal Statistical Society - Series B, Vol. 72, pp. 3--25.
###
### This file is part of the `plsgenomics' library for R and related languages.
### It is made available under the terms of the GNU General Public
### License, version 2, or at your option, any later version,
### incorporated herein by reference.
###
### This program is distributed in the hope that it will be
### useful, but WITHOUT ANY WARRANTY; without even the implied
### warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
### PURPOSE. See the GNU General Public License for more
### details.
###
### You should have received a copy of the GNU General Public
### License along with this program; if not, write to the Free
### Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
### MA 02111-1307, USA
spls.adapt.aux <- function(Xtrain, sXtrain, Ytrain, sYtrain, lambda.l1, ncomp, weight.mat, Xtest, sXtest, adapt=TRUE, meanXtrain, meanYtrain, sigmaXtrain, sigmaYtrain, center.X, center.Y, scale.X, scale.Y, weighted.center) {
#####################################################################
#### Initialisation
#####################################################################
Xtrain <- as.matrix(Xtrain)
ntrain <- nrow(Xtrain) # nb observations
p <- ncol(Xtrain) # nb covariates
index.p <- c(1:p)
Ytrain <- as.matrix(Ytrain)
q <- ncol(Ytrain)
sXtrain <- as.matrix(sXtrain)
sYtrain <- as.matrix(sYtrain)
Xtest <- as.matrix(Xtest)
ntest <- nrow(Xtest)
if(!is.null(weight.mat)) {
V <- weight.mat
} else {
V <- diag(rep(1,ntrain), ncol=ntrain, nrow=ntrain)
}
#####################################################################
#### Result objects
#####################################################################
betahat <- matrix(0, nrow=p, ncol=1)
betamat <- list()
X1 <- sXtrain
Y1 <- sYtrain
W <- matrix(data=NA, nrow=p, ncol=ncomp) # spls weight over each component
T <- matrix(data=NA, nrow=ntrain, ncol=ncomp) # spls components
P <- matrix(data=NA, nrow=ncomp, ncol=p) # regression of X over T
Q <- matrix(data=NA, nrow=ncomp, ncol=q) # regression of Y over T
#####################################################################
#### Main iteration
#####################################################################
if ( is.null(colnames(sXtrain)) ) {
Xnames <- index.p
} else {
Xnames <- colnames(sXtrain)
}
new2As <- list()
## SPLS
for (k in 1:ncomp) {
## define M
M <- t(X1) %*% (V %*% Y1)
#### soft threshold
Mnorm1 <- median( abs(M) )
M <- M / Mnorm1
## adpative version
if (adapt) {
wi <- 1/abs(M)
what <- ust.adapt(M, lambda.l1, wi)
} else {
## non adaptive version
what <- ust(M, lambda.l1)
}
#### construct active set A
A <- unique( index.p[ what!=0 | betahat[,1]!=0 ] )
new2A <- index.p[ what!=0 & betahat[,1]==0 ]
#### fit pls with selected predictors (meaning in A)
X.A <- sXtrain[ , A, drop=FALSE ]
plsfit <- wpls( Xtrain=X.A, Ytrain=sYtrain, weight.mat=V, ncomp=min(k,length(A)), type="pls1", center.X=FALSE, scale.X=FALSE, center.Y=FALSE, scale.Y=FALSE, weighted.center=FALSE )
#### output storage
# weights
w.k <- matrix(data=what, ncol=1)
w.k <- w.k / sqrt(as.numeric(t(w.k) %*% w.k))
W[,k] <- w.k
# components on total observation space
t.k <- (X1 %*% w.k) / as.numeric(t(w.k) %*% w.k)
T[,k] <- t.k
# regression of X over T
p.k <- (t(X1) %*% (V %*% t.k)) / as.numeric(t(t.k) %*% (V %*% t.k))
P[k,] <- t(p.k)
# regression of Y over T
q.k <- (t(Y1) %*% (V %*% t.k)) / as.numeric(t(t.k) %*% (V %*% t.k))
Q[k,] <- t(q.k)
## update
Y1 <- sYtrain - plsfit$T %*% plsfit$Q
X1 <- sXtrain
X1[,A] <- sXtrain[,A] - plsfit$T %*% plsfit$P
betahat <- matrix( 0, p, q )
betahat[A,] <- matrix( plsfit$coeff, length(A), q )
betamat[[k]] <- betahat # for cv.spls
# variables that join the active set
new2As[[k]] <- new2A
}
##### return objects
hatYtest <- numeric(ntest)
hatYtest.nc <- numeric(ntest)
## predictions
hatYtest <- sXtest %*% betahat
#### betahat for non centered and non scaled data
if((!scale.X) || (weighted.center)) { # if X non scaled, betahat don't have to be corrected regards sd.x
sd.X <- rep(1, p)
} else { # if X is scaled, it has to
sd.X <- sigmaXtrain
}
if((!scale.Y) || (weighted.center)) {
sd.Y <- 1
} else {
sd.Y <- sigmaYtrain
}
betahat.nc <- sd.Y * betahat / sd.X
intercept <- meanYtrain - ( sd.Y * (drop( (meanXtrain / sd.X) %*% betahat)) )
betahat.nc <- as.matrix(c(intercept, betahat.nc))
#### non centered non scaled version of estimation and residuals
hatYtest.nc <- cbind(rep(1,ntest),Xtest) %*% betahat.nc
if ( !is.null(colnames(sXtrain)) ) {
rownames(betahat) <- colnames(sXtrain)
}
#### return object
result <- list( Xtrain=Xtrain, Ytrain=Ytrain, sXtrain=sXtrain, sYtrain=sYtrain, Xtest, sXtest,
betahat=betahat, betahat.nc=betahat.nc,
meanXtrain=meanXtrain, meanYtrain=meanYtrain, sigmaXtrain=sigmaXtrain, sigmaYtrain=sigmaYtrain,
hatYtest=hatYtest, hatYtest.nc=hatYtest.nc
)
class(result) <- "spls.adapt.aux"
return(result)
}
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