Select tuning parameters of a model by estimating the respective prediction errors via (repeated) \(K\)-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.
perryTuning(object, ...) # S3 method for function
perryTuning (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, ...)
# S3 method for call
perryTuning (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, ...)
a function or an unevaluated function call
for fitting a model (see call for the
latter).
a formula describing
the model.
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
formula.
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.
a numeric vector or matrix containing the response.
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.
a list of additional arguments to be passed to the model fitting function.
an object of class "cvFolds" (as
returned by cvFolds) or a control object of
class "foldControl" (see
foldControl) defining the folds of the data
for (repeated) \(K\)-fold cross-validation, an object
of class "randomSplits" (as returned by
randomSplits) or a control object of class
"splitControl" (see splitControl)
defining random data splits, or an object of class
"bootSamples" (as returned by
bootSamples) or a control object of class
"bootControl" (see bootControl)
defining bootstrap samples.
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 predict method of the
fitted model.
a list of additional arguments to be
passed to predictFun.
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
cost).
a list of additional arguments to be
passed to the prediction loss function cost.
a character string specifying a
criterion for selecting the best model. Possible values
are "min" (the default) or "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
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.
a numeric value giving a multiplication
factor of the standard error for the selection of the
best model. This is ignored if selectBest is
"min".
a logical indicating whether to fit the final model with the optimal combination of tuning parameters.
an optional character vector giving names for the arguments containing the data to be used in the function call (see “Details”).
the environment in which to
evaluate the function call for fitting the models (see
eval).
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
NA, all available processor cores are used.
a parallel cluster for parallel computing
as generated by makeCluster. If
supplied, this is preferred over ncores.
optional initial seed for the random number
generator (see .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
clusterSetRNGStream for reproducibility in
case the model fitting function involves randomness.
additional arguments to be passed down.
If tuning is an empty list, perryFit
is called to return an object of class "perry".
Otherwise an object of class "perryTuning" (which
inherits from class "perrySelect") with the
following components is returned:
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.
a data frame containing the estimated standard errors of the prediction loss for all combinations of tuning parameter values.
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.
an object giving the data splits used to estimate the prediction error.
the response.
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.
an integer vector giving the indices of the optimal combinations of tuning parameters.
a character string specifying the criterion used for selecting the best model.
a numeric value giving the multiplication factor of the standard error used for the selection of the best model.
a data frame containing the grid of tuning parameter values for which the prediction error was estimated.
the final model fit with the optimal
combination of tuning parameters. This is only returned
if argument final is TRUE.
the matched function call.
(Repeated) \(K\)-fold cross-validation is performed in
the following way. The data are first split into \(K\)
previously obtained blocks of approximately equal size
(given by folds). Each of the \(K\) data blocks
is left out once to fit the model, and predictions are
computed for the observations in the left-out block with
predictFun. Thus a prediction is obtained for
each observation. The response variable and the obtained
predictions for all observations are then passed to the
prediction loss function cost to estimate the
prediction error. For repeated \(K\)-fold
cross-validation (as indicated by 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 is 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 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 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
predictFun returns a matrix, the prediction error
is computed for each column. A typical use case for this
behavior would be if predictFun returns
predictions from an initial model fit and stepwise
improvements thereof.
If formula or 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
formula interface. In this case,
the accepted values for names depend on the
method. For the 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 c("formula", "data")).
Note that names for both arguments should be supplied
even if only one is actually used. For the call
method, which does not have a formula argument, a
character string specifying the argument name for the
data should be supplied (the default is to use
"data").
If 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, 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 c("x",
"y")). It should be noted that the formula or
data arguments take precedence over x.
Hastie, T., Tibshirani, R. and Friedman, J. (2009) The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, 2nd edition.
perryFit, perrySelect,
cvFolds, randomSplits,
bootSamples, cost
# NOT RUN {
data("coleman")
## evaluate MM regression models tuned for 85% and 95% efficiency
tuning <- list(tuning.psi = c(3.443689, 4.685061))
## via model fitting function
# perform cross-validation
# note that the response is extracted from 'data' in
# this example and does not have to be supplied
perryTuning(lmrob, formula = Y ~ ., data = coleman,
tuning = tuning, splits = foldControl(K = 5, R = 10),
cost = rtmspe, costArgs = list(trim = 0.1), seed = 1234)
## via function call
# set up function call
call <- call("lmrob", formula = Y ~ .)
# perform cross-validation
perryTuning(call, data = coleman, y = coleman$Y,
tuning = tuning, splits = foldControl(K = 5, R = 10),
cost = rtmspe, costArgs = list(trim = 0.1), seed = 1234)
# }
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