R/spls.adapt.R

In plsgenomics: PLS Analyses for Genomics

### spls.adapt.R  (2014-10)
###
###    Adaptive Sparse PLS regression for continuous response
###
### 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 <- function(Xtrain, Ytrain, lambda.l1, ncomp, weight.mat=NULL, Xtest=NULL, adapt=TRUE, center.X=TRUE, center.Y=TRUE, scale.X=TRUE, scale.Y=TRUE, weighted.center=FALSE) {
	
	#####################################################################
	#### 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)
	
	if(!is.null(Xtest)) {
		ntest <- nrow(Xtest)
	}
	
	
	#####################################################################
	#### Tests on type input
	#####################################################################
	# On Xtrain
	if ((!is.matrix(Xtrain)) || (!is.numeric(Xtrain))) {
		stop("Message from spls.adapt: Xtrain is not of valid type")
	}
	
	if (p==1) {
		stop("Message from spls.adapt: p=1 is not valid")}
	
	# On Xtest if necessary
	if (!is.null(Xtest)) {
		
		if (is.vector(Xtest)==TRUE) {
			Xtest <- matrix(Xtest,nrow=1)
		}
		
		Xtest <- as.matrix(Xtest)
		ntest <- nrow(Xtest) 
		
		if ((!is.matrix(Xtest)) || (!is.numeric(Xtest))) {
			stop("Message from spls.adapt: Xtest is not of valid type")}
		
		if (p != ncol(Xtest)) {
			stop("Message from spls.adapt: columns of Xtest and columns of Xtrain must be equal")
		}	
	}
	
	# On Ytrain
	if ((!is.matrix(Ytrain)) || (!is.numeric(Ytrain))) {
		stop("Message from spls.adapt: Ytrain is not of valid type")
	}
	
	if (q != 1) {
		stop("Message from spls.adapt: Ytrain must be univariate")
	}
	
	if (nrow(Ytrain)!=ntrain) {
		stop("Message from spls.adapt: the number of observations in Ytrain is not equal to the Xtrain row number")
	}
	
	# On weighting matrix V
	if(!is.null(weight.mat)) { # weighting in scalar product (in observation space of dimension n)
		V <- as.matrix(weight.mat) 
		
		if ((!is.matrix(V)) || (!is.numeric(V))) {
			stop("Message from spls.adapt: V is not of valid type")}
		
		if ((ntrain != ncol(V)) || (ntrain != nrow(V))) {
			stop("Message from spls.adapt: wrong dimension for V, must be a square matrix of size the number of observations in Xtrain")
		}
	} else { # no weighting in scalar product
		V <- diag(rep(1, ntrain), nrow=ntrain, ncol=ntrain)
	}
	
	# On hyper parameter: lambda.ridge, lambda.l1
	if ((!is.numeric(lambda.l1)) || (lambda.l1<0) || (lambda.l1>1)) {
		stop("Message from spls.adapt: lambda is not of valid type")
	}
	
	# ncomp type
	if ((!is.numeric(ncomp)) || (round(ncomp)-ncomp!=0) || (ncomp<1) || (ncomp>p)) {
		stop("Message from spls.adapt: ncomp is not of valid type")
	}
	
	# On weighted.center
	if ( (weighted.center) && (is.null(weight.mat))) {
		stop("Message from spls.adapt: if the centering is weighted, the weighting matrix V should be provided")
	}
	
	
	#####################################################################
	#### centering and scaling
	#####################################################################
	if (!weighted.center) {
		
		# Xtrain mean
		meanXtrain <- apply(Xtrain, 2, mean)
		
		# Xtrain sd
		sigmaXtrain <- apply(Xtrain, 2, sd)
		# test if predictors with null variance
		if ( any( sigmaXtrain < .Machine$double.eps )) {
			stop("Some of the columns of the predictor matrix have zero variance.")
		}
		
		# centering & eventually scaling X
		if(center.X && scale.X) {
			sXtrain <- scale( Xtrain, center=meanXtrain, scale=sigmaXtrain)
		} else if(center.X && !scale.X) {
			sXtrain <- scale( Xtrain, center=meanXtrain, scale=FALSE)
		} else {
			sXtrain <- Xtrain
		}
		
		# Y mean
		meanYtrain <- apply(Ytrain, 2, mean)
		
		# Y sd
		sigmaYtrain <- apply(Ytrain, 2, sd)
		# test if predictors with null variance
		if ( any( sigmaYtrain < .Machine$double.eps )) {
			stop("The response matrix has zero variance.")
		}
		# centering & eventually scaling Y
		if(center.Y && scale.Y) {
			sYtrain <- scale( Ytrain, center=meanYtrain, scale=sigmaYtrain )
		} else if(center.Y && !scale.Y) {
			sYtrain <- scale( Ytrain, center=meanYtrain, scale=FALSE )
		} else {
			sYtrain <- Ytrain
		}
		
		# Xtest
		if (!is.null(Xtest)) {
			
			## centering and scaling depend on Xtest
			if(center.X && scale.X) {
				sXtest <- scale( Xtest, center=meanXtrain, scale=sigmaXtrain)
			} else if(center.X && !scale.X) {
				sXtest <- scale( Xtest, center=meanXtrain, scale=FALSE)
			} else {
				sXtest <- Xtest
			}
			
		}
		
	} else { # weighted scaling
		
		sumV <- sum(diag(V))
		
		# X mean
		meanXtrain <- matrix(diag(V), nrow=1) %*% Xtrain / sumV
		
		# X sd
		sigmaXtrain <- apply(Xtrain, 2, sd)
		# test if predictors with null variance
		if ( any( sigmaXtrain < .Machine$double.eps ) ) {
			stop("Some of the columns of the predictor matrix have zero variance.")
		}
		# centering & eventually scaling X
		sXtrain <- scale( Xtrain, center=meanXtrain, scale=FALSE )
		
		# Y mean
		meanYtrain <- matrix(diag(V), nrow=1) %*% Ytrain / sumV
		
		# Y sd
		sigmaYtrain <- apply(Ytrain, 2, sd)
		# test if predictors with null variance
		if ( any( sigmaYtrain < .Machine$double.eps ) ) {
			stop("The response matrix have zero variance.")
		}
		# centering & eventually scaling Y
		sYtrain <- scale( Ytrain, center=meanYtrain, scale=FALSE )
		
		# Xtest
		if (!is.null(Xtest)) {
			sXtest <- scale( Xtest, center=meanXtrain, scale=FALSE )
		}
		
	}
	
	
	#####################################################################
	#### 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(Xtrain)) ) {
		Xnames <- index.p
	} else { 
		Xnames <- colnames(Xtrain)
	}
	
	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
	
	hatY <- numeric(ntrain)
	hatY.nc <- numeric(ntrain)
	
	## components in lower subspace of selected variables
	T.low <- plsfit$T
	
	## estimations
	hatY <- sXtrain %*% betahat
	
	## residuals
	residuals <- sYtrain - hatY
	
	#### 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
	hatY.nc <- cbind(rep(1,ntrain),Xtrain) %*% betahat.nc
	residuals.nc <- Ytrain - hatY.nc
	
	
	## predictions
	if(!is.null(Xtest)) {
		hatYtest <- sXtest %*% betahat
		hatYtest.nc <- cbind(rep(1,ntest),Xtest) %*% betahat.nc
	} else {
		hatYtest <- NULL
		hatYtest.nc <- NULL
	}
	
	
	if ( !is.null(colnames(Xtrain)) ) {
		rownames(betahat) <- colnames(Xtrain)
	}
	
	
	#### return object
	result <- list( Xtrain=Xtrain, Ytrain=Ytrain, sXtrain=sXtrain, sYtrain=sYtrain,
				 betahat=betahat, betahat.nc=betahat.nc,
				 meanXtrain=meanXtrain, meanYtrain=meanYtrain, sigmaXtrain=sigmaXtrain, sigmaYtrain=sigmaYtrain,
				 X.score=T, X.score.low=T.low, X.loading=P, Y.loading=Q, X.weight=W, 
				 residuals=residuals, residuals.nc=residuals.nc,
				 hatY=hatY, hatY.nc=hatY.nc,
				 hatYtest=hatYtest, hatYtest.nc=hatYtest.nc,
				 A=A, betamat=betamat, new2As=new2As,
				 lambda.l1=lambda.l1, ncomp=ncomp,
				 V=V, adapt=adapt)
	
	class(result) <- "spls.adapt"
	return(result)
	
	
}