applyFolds: Cross-Validation and Bootstrapping over Curves

Description Usage Arguments Details Value Note See Also Examples

View source: R/crossvalidation.R

Description

Cross-validation and bootstrapping over curves to compute the empirical risk for hyper-parameter selection.

Usage

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applyFolds(object, folds = cv(rep(1, length(unique(object$id))), type =
  "bootstrap"), grid = 1:mstop(object), fun = NULL, riskFun = NULL,
  numInt = object$numInt, papply = mclapply, mc.preschedule = FALSE,
  showProgress = TRUE, compress = FALSE, ...)

## S3 method for class 'FDboost'
cvrisk(object, folds = cvLong(id = object$id, weights =
  model.weights(object)), grid = 1:mstop(object), papply = mclapply,
  fun = NULL, mc.preschedule = FALSE, ...)

cvLong(id, weights = rep(1, l = length(id)), type = c("bootstrap", "kfold",
  "subsampling", "curves"), B = ifelse(type == "kfold", 10, 25), prob = 0.5,
  strata = NULL)

cvMa(ydim, weights = rep(1, l = ydim[1] * ydim[2]), type = c("bootstrap",
  "kfold", "subsampling", "curves"), B = ifelse(type == "kfold", 10, 25),
  prob = 0.5, strata = NULL, ...)

Arguments

object

fitted FDboost-object

folds

a weight matrix with number of rows equal to the number of observed trajectories.

grid

the grid over which the optimal number of boosting iterations (mstop) is searched.

fun

if fun is NULL, the out-of-bag risk is returned. fun, as a function of object, may extract any other characteristic of the cross-validated models. These are returned as is.

riskFun

only exists in applyFolds; allows to compute other risk functions than the risk of the family that was specified in object. Must be specified as function of arguments (y, f, w = 1), where y is the observed response, f is the prediciton from the model and w is the weight. The risk function must return a scalar numeric value for vector valued imput.

numInt

only exists in applyFolds; the scheme for numerical integration, see numInt in FDboost.

papply

(parallel) apply function, defaults to mclapply, see cvrisk for details.

mc.preschedule

Defaults to FALSE. Preschedule tasks if are parallelized using mclapply? For details see mclapply.

showProgress

logical, defaults to TRUE.

compress

logical, defaults to FALSE. Only used to force a meaningful behaviour of applyFolds with hmatrix objects when using nested resampling.

...

further arguments passed to mclapply

id

the id-vector as integers 1, 2, ... specifying which observations belong to the same curve, deprecated in cvMa().

weights

a numeric vector of (integration) weights, defaults to 1.

type

character argument for specifying the cross-validation method. Currently (stratified) bootstrap, k-fold cross-validation, subsampling and leaving-one-curve-out cross validation (i.e. jack knife on curves) are implemented.

B

number of folds, per default 25 for bootstrap and subsampling and 10 for kfold.

prob

percentage of observations to be included in the learning samples for subsampling.

strata

a factor of the same length as weights for stratification.

ydim

dimensions of response-matrix

Details

The number of boosting iterations is an important hyper-parameter of boosting. It be chosen using the functions applyFolds or cvrisk.FDboost. Those functions they compute honest, i.e., out-of-bag, estimates of the empirical risk for different numbers of boosting iterations. The weights (zero weights correspond to test cases) are defined via the folds matrix, see cvrisk in package mboost.

In case of functional response, we recommend to use applyFolds. It recomputes the model in each fold using FDboost. Thus, all parameters are recomputed, including the smooth offset (if present) and the identifiability constraints (if present, only relevant for bolsc, brandomc and bbsc). Note, that the function applyFolds expects folds that give weights per curve without considering integration weights.

The function cvrisk.FDboost is a wrapper for cvrisk in package mboost. It overrides the default for the folds, so that the folds are sampled on the level of curves (not on the level of single observations, which does not make sense for functional response). Note that the smooth offset and the computation of the identifiability constraints are not part of the refitting if cvrisk is used. Per default the integration weights of the model fit are used to compute the prediction errors (as the integration weights are part of the default folds). Note that in cvrisk the weights are rescaled to sum up to one.

The functions cvMa and cvLong can be used to build an appropriate weight matrix for functional response to be used with cvrisk as sampling is done on the level of curves. The probability for each curve to enter a fold is equal over all curves. The function cvMa takes the dimensions of the response matrix as input argument and thus can only be used for regularly observed response. The function cvLong takes the id variable and the weights as arguments and thus can be used for responses in long format that are potentially observed irregularly.

If strata is defined sampling is performed in each stratum separately thus preserving the distribution of the strata variable in each fold.

Value

cvMa and cvLong return a matrix of sampling weights to be used in cvrisk.

The functions applyFolds and cvrisk.FDboost return a cvrisk-object, which is a matrix of the computed out-of-bag risk. The matrix has the folds in rows and the number of boosting iteratins in columns. Furhtermore, the matrix has attributes including:

risk

name of the applied risk function

call

model call of the model object

mstop

gird of stopping iterations that is used

type

name for the type of folds

Note

Use argument mc.cores = 1L to set the numbers of cores that is used in parallel computation. On Windows only 1 core is possible, mc.cores = 1, which is the default.

See Also

cvrisk to perform cross-validation with scalar response.

Examples

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Ytest <- matrix(rnorm(15), ncol = 3) # 5 trajectories, each with 3 observations 
Ylong <- as.vector(Ytest)
## 4-folds for bootstrap for the response in long format without integration weights
cvMa(ydim = c(5,3), type = "bootstrap", B = 4)  
cvLong(id = rep(1:5, times = 3), type = "bootstrap", B = 4)

if(require(fda)){
 ## load the data
 data("CanadianWeather", package = "fda")
 
 ## use data on a daily basis 
 canada <- with(CanadianWeather, 
                list(temp = t(dailyAv[ , , "Temperature.C"]),
                     l10precip = t(dailyAv[ , , "log10precip"]),
                     l10precip_mean = log(colMeans(dailyAv[ , , "Precipitation.mm"]), base = 10),
                     lat = coordinates[ , "N.latitude"],
                     lon = coordinates[ , "W.longitude"],
                     region = factor(region),
                     place = factor(place),
                     day = 1:365,  ## corresponds to t: evaluation points of the fun. response 
                     day_s = 1:365))  ## corresponds to s: evaluation points of the fun. covariate
 
## center temperature curves per day 
canada$tempRaw <- canada$temp
canada$temp <- scale(canada$temp, scale = FALSE) 
rownames(canada$temp) <- NULL ## delete row-names 
  
## fit the model  
mod <- FDboost(l10precip ~ 1 + bolsc(region, df = 4) + 
                 bsignal(temp, s = day_s, cyclic = TRUE, boundary.knots = c(0.5, 365.5)), 
               timeformula = ~ bbs(day, cyclic = TRUE, boundary.knots = c(0.5, 365.5)), 
               data = canada)
mod <- mod[75]

## Not run: 
  #### create folds for 3-fold bootstrap: one weight for each curve
  set.seed(123)
  folds_bs <- cv(weights = rep(1, mod$ydim[1]), type = "bootstrap", B = 3)

  ## compute out-of-bag risk on the 3 folds for 1 to 75 boosting iterations  
  cvr <- applyFolds(mod, folds = folds_bs, grid = 1:75)

  ## weights per observation point  
  folds_bs_long <- folds_bs[rep(1:nrow(folds_bs), times = mod$ydim[2]), ]
  attr(folds_bs_long, "type") <- "3-fold bootstrap"
  ## compute out-of-bag risk on the 3 folds for 1 to 75 boosting iterations  
  cvr3 <- cvrisk(mod, folds = folds_bs_long, grid = 1:75)

## End(Not run)

## Not run: 
  ## plot the out-of-bag risk
  par(mfrow = c(1,3))
  plot(cvr); legend("topright", lty=2, paste(mstop(cvr)))
  plot(cvr3); legend("topright", lty=2, paste(mstop(cvr3)))

## End(Not run)

}

FDboost documentation built on Aug. 6, 2018, 9:04 a.m.