perryTuning: Resampling-based prediction error for tuning parameter...

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

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.

Usage

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  perryTuning(object, ...)

  ## S3 method for class '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 class '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, ...)

Arguments

object

a function or an unevaluated function call for fitting a model (see call for the latter).

formula

a formula describing the model.

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 formula.

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.

y

a numeric vector or matrix containing the response.

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.

args

a list of additional arguments to be passed to the model fitting function.

splits

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.

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 predict method of the fitted model.

predictArgs

a list of additional arguments to be passed to predictFun.

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 cost).

costArgs

a list of additional arguments to be passed to the prediction loss function cost.

selectBest

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.

seFactor

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".

final

a logical indicating whether to fit the final model with the optimal combination of tuning parameters.

names

an optional character vector giving names for the arguments containing the data to be used in the function call (see “Details”).

envir

the environment in which to evaluate the function call for fitting the models (see eval).

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 NA, all available processor cores are used.

cl

a parallel cluster for parallel computing as generated by makeCluster. If supplied, this is preferred over ncores.

seed

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.

Details

(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 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 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 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.

Value

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:

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.

se

a data frame containing the estimated standard errors of the prediction loss for all combinations of tuning parameter values.

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.

splits

an object giving the data splits used to estimate the prediction error.

y

the response.

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.

best

an integer vector giving the indices of the optimal combinations of tuning parameters.

selectBest

a character string specifying the criterion used for selecting the best model.

seFactor

a numeric value giving the multiplication factor of the standard error used for the selection of the best model.

tuning

a data frame containing the grid of tuning parameter values for which the prediction error was estimated.

finalModel

the final model fit with the optimal combination of tuning parameters. This is only returned if argument final is TRUE.

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 "perryTuning" inherits the coef(), fitted(), predict() and residuals() methods from its component finalModel.

Author(s)

Andreas Alfons

References

Hastie, T., Tibshirani, R. and Friedman, J. (2009) The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, 2nd edition.

See Also

perryFit, perrySelect, cvFolds, randomSplits, bootSamples, cost

Examples

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library("perryExamples")
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)

aalfons/perry documentation built on May 10, 2019, 2:06 a.m.