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#' cross validation function for lars algorithm
#'
#' @title cross validation
#' @author Quentin Grimonprez
#' @param X the matrix (of size n*p) of the covariates.
#' @param y a vector of length n with the response.
#' @param nbFolds the number of folds for the cross-validation.
#' @param index Values at which prediction error should be computed. When mode = "fraction", this is the fraction of the saturated |beta|.
#' The default value is seq(0,1,by=0.01). When mode="lambda", this is values of lambda.
#' @param mode Either "fraction" or "lambda". Type of values containing in partition.
#' @param maxSteps Maximal number of steps for lars algorithm.
#' @param partition partition in nbFolds folds of y. Must be a vector of same size than y containing the index of folds.
#' @param intercept If TRUE, there is an intercept in the model.
#' @param eps Tolerance of the algorithm.
#' @return A list containing
#' \describe{
#' \item{cv}{Mean prediction error for each value of index.}
#' \item{cvError}{Standard error of cv.}
#' \item{minCv}{Minimal cv criterion.}
#' \item{minIndex}{Value of index for which the cv criterion is minimal.}
#' \item{index}{Values at which prediction error should be computed. This is the fraction of the saturated |beta|. The default value is seq(0,1,by=0.01).}
#' \item{maxSteps}{Maximum number of steps of the lars algorithm.}
#' }
#' @examples
#' dataset=simul(50,10000,0.4,10,50,matrix(c(0.1,0.8,0.02,0.02),nrow=2))
#' result=HDcvlars(dataset$data,dataset$response,5)
#' @export
#'
HDcvlars <- function(X,y,nbFolds=10,index=seq(0,1,by=0.01),mode=c("fraction","lambda"),maxSteps=3*min(dim(X)),partition=NULL,intercept=TRUE,eps=.Machine$double.eps^0.5)
{
#check arguments
mode <- match.arg(mode)
if(missing(X))
stop("X is missing.")
if(missing(y))
stop("y is missing.")
index=unique(index)
.checkcvlars(X,y,maxSteps,eps,nbFolds,index,intercept,mode)
if(!is.null(partition))
{
if(!is.numeric(partition) || !is.vector(partition))
stop("partition must be a vector of integer.")
if(length(partition)!=length(y))
stop("partition and y must have the same size.")
part=table(partition)
nbFolds=length(part)
if(max(part)-min(part)>1)
stop("Size of different folds are not good.")
nam=as.numeric(names(part))
for(i in 1:length(nam))
{
if(!(nam[i]==i))
stop("check the number in the partition vector.")
}
#reorder the partition in decreasing order of size
ord=order(part,decreasing=TRUE)
partb=partition
for(i in 1:nbFolds)
partition[partb==ord[i]]=i
partition=partition-1
}
else
partition=-1
lambdaMode=FALSE
if(mode=="lambda")
lambdaMode=TRUE
# call lars algorithm
val=.Call( "cvlars",X,y,nrow(X),ncol(X),maxSteps,intercept,eps,nbFolds,partition,index,lambdaMode,PACKAGE = "HDPenReg" )
#create the output object
cv=list(cv=val$cv,cvError=val$cvError,minCv=min(val$cv),minIndex=index[which.min(val$cv)],index=index,maxSteps=maxSteps,mode=mode)
class(cv)="HDcvlars"
return(cv)
}
# check arguments from cvlars
.checkcvlars=function(X,y,maxSteps,eps,nbFolds,index,intercept,mode)
{
## X: matrix of real
if(!is.numeric(X) || !is.matrix(X))
stop("X must be a matrix of real")
## y: vector of real
if(!is.numeric(y) || !is.vector(y))
stop("y must be a vector of real")
if(length(y)!=nrow(X))
stop("The number of rows of X doesn't match with the length of y")
## maxSteps
if(!.is.wholenumber(maxSteps))
stop("maxSteps must be a positive integer")
if(maxSteps<=0)
stop("maxSteps must be a positive integer")
## nbFolds
if(!.is.wholenumber(nbFolds))
stop("nbFolds must be a positive integer")
if(nbFolds<=0)
stop("nbFolds must be a positive integer")
if(nbFolds>length(y))
stop("nbFolds must be lower than the number of samples")
## eps
if(!is.double(eps))
stop("eps must be a positive real")
if(eps<=0)
stop("eps must be a positive real")
## index
if(!is.numeric(index) || !is.vector(index))
stop("index must be a vector")
if( (mode=="fraction") && (max(index)>1 || min(index)<0))
stop("index must be a vector of real between 0 and 1")
if( (mode=="lambda") && (min(index)<0))
stop("index must be a vector of positive real")
##intercept
if(!is.logical(intercept))
stop("intercept must be a boolean")
}
#' plot cross validation mean square error
#'
#' @title plot cross validation mean square error
#' @author Quentin Grimonprez
#' @param x Output from HDcvlars function.
#' @param ... graphical parameters
#' @aliases plot.HDcvlars
#' @method plot HDcvlars
#' @examples
#' dataset=simul(50,10000,0.4,10,50,matrix(c(0.1,0.8,0.02,0.02),nrow=2))
#' result=HDcvlars(dataset$data,dataset$response,5)
#' plot(result)
#' @export
#'
plot.HDcvlars=function(x,...)
{
if(missing(x))
stop("x is missing.")
if(class(x)!="HDcvlars")
stop("x must be an output of the HDcvlars function.")
index=x$index
minIndex=x$minIndex
lab="Fraction L1 Norm"
if(x$mode=="lambda")
{
lab="log(lambda)"
index=log(index)
minIndex=log(minIndex)
}
plot(index, x$cv, type = "b", ylim = range(x$cv, x$cv + x$cvError, x$cv - x$cvError),xlab=lab,ylab="Cross-Validated MSE",...)
lines(index, x$cv+x$cvError,lty=2)
lines(index, x$cv-x$cvError,lty=2)
abline(v=minIndex,lty="dotted",col="blue")
invisible()
}
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