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# --------------------------------------
# Author: Andreas Alfons
# Erasmus Universiteit Rotterdam
# --------------------------------------
#' Resampling-based prediction error for tuning parameter selection
#'
#' Select tuning parameters of a model by estimating the respective prediction
#' errors via (repeated) \eqn{K}-fold cross-validation, (repeated) random
#' splitting (also known as random subsampling or Monte Carlo
#' cross-validation), or the bootstrap. It is thereby possible to supply a
#' model fitting function or an unevaluated function call to a model fitting
#' function.
#'
#' (Repeated) \eqn{K}-fold cross-validation is performed in the following
#' way. The data are first split into \eqn{K} previously obtained blocks of
#' approximately equal size (given by \code{folds}). Each of the \eqn{K} data
#' blocks is left out once to fit the model, and predictions are computed for
#' the observations in the left-out block with \code{predictFun}. Thus a
#' prediction is obtained for each observation. The response and the obtained
#' predictions for all observations are then passed to the prediction loss
#' function \code{cost} to estimate the prediction error. For repeated
#' \eqn{K}-fold cross-validation (as indicated by \code{splits}), this process
#' is replicated and the estimated prediction errors from all replications are
#' returned.
#'
#' (Repeated) random splitting is performed similarly. In each replication,
#' the data are split into a training set and a test set at random. Then the
#' training data are used to fit the model, and predictions are computed for
#' the test data. Hence only the response values from the test data and the
#' corresponding predictions are passed to the prediction loss function
#' \code{cost}.
#'
#' For the bootstrap estimator, each bootstrap sample is used as training data
#' to fit the model. The out-of-bag estimator uses the observations that do
#' not enter the bootstrap sample as test data and computes the prediction loss
#' function \code{cost} for those out-of-bag observations. The 0.632 estimator
#' is computed as a linear combination of the out-of-bag estimator and the
#' prediction loss of the fitted values of the model computed from the full
#' sample.
#'
#' In any case, if the response is a vector but \code{predictFun} returns a
#' matrix, the prediction error is computed for each column. A typical use
#' case for this behavior would be if \code{predictFun} returns predictions
#' from an initial model fit and stepwise improvements thereof.
#'
#' If \code{formula} or \code{data} are supplied, all variables required for
#' fitting the models are added as one argument to the function call, which is
#' the typical behavior of model fitting functions with a
#' \code{\link[stats]{formula}} interface. In this case, the accepted values
#' for \code{names} depend on the method. For the \code{function} method, a
#' character vector of length two should supplied, with the first element
#' specifying the argument name for the formula and the second element
#' specifying the argument name for the data (the default is to use
#' \code{c("formula", "data")}). Note that names for both arguments should be
#' supplied even if only one is actually used. For the \code{call} method,
#' which does not have a \code{formula} argument, a character string specifying
#' the argument name for the data should be supplied (the default is to use
#' \code{"data"}).
#'
#' If \code{x} is supplied, on the other hand, the predictor matrix and the
#' response are added as separate arguments to the function call. In this
#' case, \code{names} should be a character vector of length two, with the
#' first element specifying the argument name for the predictor matrix and the
#' second element specifying the argument name for the response (the default is
#' to use \code{c("x", "y")}). It should be noted that the \code{formula} or
#' \code{data} arguments take precedence over \code{x}.
#'
#' @aliases coef.perryTuning fitted.perryTuning predict.perryTuning
#' print.perryTuning residuals.perryTuning
#'
#' @param object a function or an unevaluated function call for fitting
#' a model (see \code{\link{call}} for the latter).
#' @param formula a \code{\link[stats]{formula}} describing the model.
#' @param data a data frame containing the variables required for fitting the
#' models. This is typically used if the model in the function call is
#' described by a \code{\link[stats]{formula}}.
#' @param x a numeric matrix containing the predictor variables. This is
#' typically used if the function call for fitting the models requires the
#' predictor matrix and the response to be supplied as separate arguments.
#' @param y a numeric vector or matrix containing the response.
#' @param tuning a list of arguments giving the tuning parameter values to be
#' evaluated. The names of the list components should thereby correspond to
#' the argument names of the tuning parameters. For each tuning parameter, a
#' vector of values can be supplied. The prediction error is then estimated
#' for all possible combinations of tuning parameter values.
#' @param args a list of additional arguments to be passed to the model
#' fitting function.
#' @param splits an object of class \code{"cvFolds"} (as returned by
#' \code{\link{cvFolds}}) or a control object of class \code{"foldControl"}
#' (see \code{\link{foldControl}}) defining the folds of the data for
#' (repeated) \eqn{K}-fold cross-validation, an object of class
#' \code{"randomSplits"} (as returned by \code{\link{randomSplits}}) or a
#' control object of class \code{"splitControl"} (see
#' \code{\link{splitControl}}) defining random data splits, or an object of
#' class \code{"bootSamples"} (as returned by \code{\link{bootSamples}}) or a
#' control object of class \code{"bootControl"} (see \code{\link{bootControl}})
#' defining bootstrap samples.
#' @param predictFun a function to compute predictions for the test data. It
#' should expect the fitted model to be passed as the first argument and the test
#' data as the second argument, and must return either a vector or a matrix
#' containing the predicted values. The default is to use the
#' \code{\link[stats]{predict}} method of the fitted model.
#' @param predictArgs a list of additional arguments to be passed to
#' \code{predictFun}.
#' @param cost a cost function measuring prediction loss. It should expect
#' the observed values of the response to be passed as the first argument and
#' the predicted values as the second argument, and must return either a
#' non-negative scalar value, or a list with the first component containing
#' the prediction error and the second component containing the standard
#' error. The default is to use the root mean squared prediction error
#' (see \code{\link{cost}}).
#' @param costArgs a list of additional arguments to be passed to the
#' prediction loss function \code{cost}.
#' @param selectBest a character string specifying a criterion for selecting
#' the best model. Possible values are \code{"min"} (the default) or
#' \code{"hastie"}. The former selects the model with the smallest prediction
#' error. The latter is useful for models with a tuning parameter controlling
#' the complexity of the model (e.g., penalized regression). It selects the
#' most parsimonious model whose prediction error is no larger than
#' \code{seFactor} standard errors above the prediction error of the best
#' overall model. Note that the models are thereby assumed to be ordered
#' from the most parsimonious one to the most complex one. In particular
#' a one-standard-error rule is frequently applied.
#' @param seFactor a numeric value giving a multiplication factor of the
#' standard error for the selection of the best model. This is ignored if
#' \code{selectBest} is \code{"min"}.
#' @param final a logical indicating whether to fit the final model with the
#' optimal combination of tuning parameters.
#' @param names an optional character vector giving names for the arguments
#' containing the data to be used in the function call (see \dQuote{Details}).
#' @param envir the \code{\link{environment}} in which to evaluate the
#' function call for fitting the models (see \code{\link{eval}}).
#' @param ncores a positive integer giving the number of processor cores to be
#' used for parallel computing (the default is 1 for no parallelization). If
#' this is set to \code{NA}, all available processor cores are used.
#' @param cl a \pkg{parallel} cluster for parallel computing as generated by
#' \code{\link[parallel]{makeCluster}}. If supplied, this is preferred over
#' \code{ncores}.
#' @param seed optional initial seed for the random number generator (see
#' \code{\link{.Random.seed}}). Note that also in case of parallel computing,
#' resampling is performed on the manager process rather than the worker
#' processes. On the parallel worker processes, random number streams are
#' used and the seed is set via \code{\link{clusterSetRNGStream}} for
#' reproducibility in case the model fitting function involves randomness.
#' @param \dots additional arguments to be passed down.
#'
#' @return
#' If \code{tuning} is an empty list, \code{\link{perryFit}} is called to
#' return an object of class \code{"perry"}.
#'
#' Otherwise an object of class \code{"perryTuning"} (which inherits from class
#' \code{"perrySelect"}) with the following components is returned:
#' \describe{
#' \item{\code{pe}}{a data frame containing the estimated prediction errors
#' for all combinations of tuning parameter values. In case of more than one
#' replication, those are average values over all replications.}
#' \item{\code{se}}{a data frame containing the estimated standard errors of
#' the prediction loss for all combinations of tuning parameter values.}
#' \item{\code{reps}}{a data frame containing the estimated prediction
#' errors from all replications for all combinations of tuning parameter
#' values. This is only returned in case of more than one replication.}
#' \item{\code{splits}}{an object giving the data splits used to estimate
#' the prediction error.}
#' \item{\code{y}}{the response.}
#' \item{\code{yHat}}{a list containing the predicted values for all
#' combinations of tuning parameter values. Each list component is again a
#' list containing the corresponding predicted values from all replications.}
#' \item{\code{best}}{an integer vector giving the indices of the optimal
#' combinations of tuning parameters.}
#' \item{\code{selectBest}}{a character string specifying the criterion used
#' for selecting the best model.}
#' \item{\code{seFactor}}{a numeric value giving the multiplication factor of
#' the standard error used for the selection of the best model.}
#' \item{\code{tuning}}{a data frame containing the grid of tuning parameter
#' values for which the prediction error was estimated.}
#' \item{\code{finalModel}}{the final model fit with the optimal combination
#' of tuning parameters. This is only returned if argument \code{final} is
#' \code{TRUE}.}
#' \item{\code{call}}{the matched function call.}
#' }
#'
#' @note
#' The same data splits are used for all combinations of tuning parameter
#' values for maximum comparability.
#'
#' If a final model with the optimal combination of tuning parameters is
#' computed, class \code{"perryTuning"} inherits the \code{coef()},
#' \code{fitted()}, \code{predict()} and \code{residuals()} methods from
#' its component \code{finalModel}.
#'
#' @author Andreas Alfons
#'
#' @references
#' Hastie, T., Tibshirani, R. and Friedman, J. (2009) \emph{The Elements of
#' Statistical Learning: Data Mining, Inference, and Prediction}. Springer,
#' 2nd edition.
#'
#' @seealso \code{\link{perryFit}}, \code{\link{perrySelect}},
#' \code{\link{cvFolds}}, \code{\link{randomSplits}},
#' \code{\link{bootSamples}}, \code{\link{cost}}
#'
#' @example inst/doc/examples/example-perryTuning.R
#'
#' @keywords utilities
#'
#' @export
perryTuning <- function(object, ...) UseMethod("perryTuning")
#' @rdname perryTuning
#' @method perryTuning function
#' @export
perryTuning.function <- function(object, formula, data = NULL, x = NULL, y,
tuning = list(), args = list(),
splits = foldControl(), predictFun = predict,
predictArgs = list(), cost = rmspe,
costArgs = list(),
selectBest = c("min", "hastie"), seFactor = 1,
final = FALSE, names = NULL,
envir = parent.frame(), ncores = 1, cl = NULL,
seed = NULL, ...) {
## initializations
matchedCall <- match.call()
matchedCall[[1]] <- as.name("perryTuning")
# set up unevaluated function call
final <- isTRUE(final)
call <- as.call(c(if(final) substitute(object) else object, args))
# check formula and data
haveFormula <- !missing(formula)
if(haveFormula || !missing(data)) {
if(is.null(names)) names <- c("formula", "data")
if(haveFormula) call[[names[1]]] <- formula
names <- names[-1]
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data"), names(mf), 0)
mf <- mf[c(1, m)]
mf$drop.unused.levels <- TRUE
mf[[1]] <- as.name("model.frame")
data <- eval(mf, envir)
if(is.empty.model(attr(data, "terms"))) stop("empty model")
y <- model.response(data) # extract response from model frame
}
## call method for unevaluated function calls
out <- perryTuning(call, data=data, x=x, y=y, tuning=tuning, splits=splits,
predictFun=predictFun, predictArgs=predictArgs, cost=cost,
costArgs=costArgs, selectBest=selectBest,
seFactor=seFactor, final=final, names=names, envir=envir,
ncores=ncores, cl=cl, seed=seed, ...)
out$call <- matchedCall
out
}
#' @rdname perryTuning
#' @method perryTuning call
#' @export
perryTuning.call <- function(object, data = NULL, x = NULL, y, tuning = list(),
splits = foldControl(), predictFun = predict,
predictArgs = list(), cost = rmspe,
costArgs = list(), selectBest = c("min", "hastie"),
seFactor = 1, final = FALSE, names = NULL,
envir = parent.frame(), ncores = 1, cl = NULL,
seed = NULL, ...) {
## initializations
matchedCall <- match.call()
matchedCall[[1]] <- as.name("perryTuning")
n <- nobs(y)
if(is.null(data)) {
sx <- "x"
nx <- nobs(x)
} else {
sx <- "data"
nx <- nobs(data)
}
if(!isTRUE(n == nx)) stop(sprintf("'%s' must have %d observations", sx, nx))
# create all combinations of tuning parameters
tuning <- do.call(expand.grid, tuning)
nTuning <- nrow(tuning)
pTuning <- ncol(tuning)
if(nTuning == 0 || pTuning == 0) {
# use function perryFit() if no tuning parameters are supplied
out <- perryFit(object, data, x, y, splits=splits, predictFun=predictFun,
predictArgs=predictArgs, cost=cost, costArgs=costArgs,
names=names, envir=envir, ncores=ncores, cl=cl, seed=seed)
return(out)
}
if(!is.null(seed)) set.seed(seed)
## compute data splits
if(hasMethod("perrySplits", class(splits))) splits <- perrySplits(n, splits)
# set up parallel computing if requested
haveCl <- inherits(cl, "cluster")
if(haveCl) haveNcores <- FALSE
else {
if(is.na(ncores)) ncores <- detectCores() # use all available cores
if(!is.numeric(ncores) || is.infinite(ncores) || ncores < 1) {
ncores <- 1 # use default value
warning("invalid value of 'ncores'; using default value")
} else ncores <- as.integer(ncores)
if(nTuning == 1) {
R <- splits$R
if(inherits(splits, "cvFolds") && R == 1) {
ncores <- min(ncores, splits$K)
} else ncores <- min(ncores, R)
} else ncores <- min(ncores, nTuning)
haveNcores <- ncores > 1
}
# check whether parallel computing should be used
useParallel <- haveNcores || haveCl
# set up multicore or snow cluster if not supplied
if(haveNcores) {
if(.Platform$OS.type == "windows") {
cl <- makePSOCKcluster(rep.int("localhost", ncores))
} else cl <- makeForkCluster(ncores)
on.exit(stopCluster(cl))
}
## compute the predictions for each combination of tuning parameters
fits <- seq_len(nTuning)
tn <- names(tuning)
if(useParallel) {
# set seed of the random number stream
if(!is.null(seed)) clusterSetRNGStream(cl, iseed=seed)
else if(haveNcores) clusterSetRNGStream(cl)
if(nTuning == 1) {
yHat <- lapply(fits, function(i) {
# add tuning parameters to function call
for(j in seq_len(pTuning)) object[[tn[j]]] <- tuning[i, j]
# compute the predictions
perryPredictions(object, data, x, y, splits=splits,
predictFun=predictFun, predictArgs=predictArgs,
names=names, envir=envir, cl=cl)
})
} else {
yHat <- parLapply(cl, fits, function(i) {
# add tuning parameters to function call
for(j in seq_len(pTuning)) object[[tn[j]]] <- tuning[i, j]
# compute the predictions
perryPredictions(object, data, x, y, splits=splits,
predictFun=predictFun, predictArgs=predictArgs,
names=names, envir=envir)
})
}
} else {
yHat <- lapply(fits, function(i) {
# add tuning parameters to function call
for(j in seq_len(pTuning)) object[[tn[j]]] <- tuning[i, j]
# compute the predictions
perryPredictions(object, data, x, y, splits=splits,
predictFun=predictFun, predictArgs=predictArgs,
names=names, envir=envir)
})
}
## estimate the prediction loss for each combination of tuning parameters
pe <- lapply(yHat, function(yHat) {
perryCost(splits, y, yHat, cost=cost, costArgs=costArgs)
})
pe <- combineResults(pe, fits=fits)
## select optimal tuning parameters
best <- selectBest(pe$pe, pe$se, method=selectBest, seFactor=seFactor)
## compute final model if requested
final <- isTRUE(final)
if(final) {
# plug data into function call
if(is.null(data)) {
if(is.null(names)) names <- c("x", "y")
object[[names[1]]] <- substitute(x)
object[[names[2]]] <- substitute(y)
} else {
if(is.null(names)) names <- "data"
object[[names]] <- substitute(data)
}
# add optimal combination of tuning parameters to function call
i <- best$best
for(j in seq_len(pTuning)) object[[tn[j]]] <- unique(tuning[i, j])
# evaluate function call to compute final model
# use this environment since data are added with substitute()
finalModel <- try(eval(object))
if(inherits(finalModel, "try-error")) {
final <- FALSE
warn <- gsub("Error in", "In", finalModel)
warning(warn, call.=FALSE)
}
}
## construct return object
names(yHat) <- fits
pe <- c(pe, list(splits=splits, y=y, yHat=yHat), best, list(tuning=tuning))
if(final) pe$finalModel <- finalModel
pe$call <- matchedCall
class(pe) <- c("perryTuning", "perrySelect")
pe
}
## methods
#' @export
coef.perryTuning <- function(object, ...) {
finalModel <- object$finalModel
if(is.null(finalModel)) stop("final model not available")
coef(finalModel, ...)
}
#' @export
fitted.perryTuning <- function(object, ...) {
finalModel <- object$finalModel
if(is.null(finalModel)) stop("final model not available")
fitted(finalModel, ...)
}
#' @export
predict.perryTuning <- function(object, ...) {
finalModel <- object$finalModel
if(is.null(finalModel)) stop("final model not available")
predict(finalModel, ...)
}
#' @export
residuals.perryTuning <- function(object, ...) {
finalModel <- object$finalModel
if(is.null(finalModel)) stop("final model not available")
residuals(finalModel, ...)
}
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