validateFDboost: Cross-Validation and Bootstrapping over Curves

In FDboost: Boosting Functional Regression Models

Cross-Validation and Bootstrapping over Curves

Description

DEPRECATED! The function validateFDboost() is deprecated, use applyFolds and bootstrapCI instead.

Usage

validateFDboost(
  object,
  response = NULL,
  folds = cv(rep(1, length(unique(object$id))), type = "bootstrap"),
  grid = 1:mstop(object),
  fun = NULL,
  getCoefCV = TRUE,
  riskopt = c("mean", "median"),
  mrdDelete = 0,
  refitSmoothOffset = TRUE,
  showProgress = TRUE,
  ...
)

Arguments

object	fitted FDboost-object
response	optional, specify a response vector for the computation of the prediction errors. Defaults to NULL which means that the response of the fitted model is used.
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.
getCoefCV	logical, defaults to TRUE. Should the coefficients and predictions be computed for all the models on the sampled data?
riskopt	how is the optimal stopping iteration determined. Defaults to the mean, but median is possible as well.
mrdDelete	Delete values that are mrdDelete percent smaller than the mean of the response. Defaults to 0 which means that only response values being 0 are not used in the calculation of the MRD (= mean relative deviation).
refitSmoothOffset	logical, should the offset be refitted in each learning sample? Defaults to TRUE. In cvrisk the offset of the original model fit in object is used in all folds.
showProgress	logical, defaults to TRUE.
...	further arguments passed to mclapply

Details

The number of boosting iterations is an important hyper-parameter of boosting and can be chosen using the function validateFDboost as they compute honest, i.e., out-of-bag, estimates of the empirical risk for different numbers of boosting iterations.

The function validateFDboost is especially suited to models with functional response. Using the option refitSmoothOffset the offset is refitted on each fold. Note, that the function validateFDboost expects folds that give weights per curve without considering integration weights. The integration weights of object are used to compute the empirical risk as integral. The argument response can be useful in simulation studies where the true value of the response is known but for the model fit the response is used with noise.

Value

The function validateFDboost returns a validateFDboost-object, which is a named list containing:

response	the response
yind	the observation points of the response
id	the id variable of the response
folds	folds that were used
grid	grid of possible numbers of boosting iterations
coefCV	if getCoefCV is TRUE the estimated coefficient functions in the folds
predCV	if getCoefCV is TRUE the out-of-bag predicted values of the response
oobpreds	if the type of folds is curves the out-of-bag predictions for each trajectory
oobrisk	the out-of-bag risk
oobriskMean	the out-of-bag risk at the minimal mean risk
oobmse	the out-of-bag mean squared error (MSE)
oobrelMSE	the out-of-bag relative mean squared error (relMSE)
oobmrd	the out-of-bag mean relative deviation (MRD)
oobrisk0	the out-of-bag risk without consideration of integration weights
oobmse0	the out-of-bag mean squared error (MSE) without consideration of integration weights
oobmrd0	the out-of-bag mean relative deviation (MRD) without consideration of integration weights
format	one of "FDboostLong" or "FDboost" depending on the class of the object
fun_ret	list of what fun returns if fun was specified

Examples

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]

  #### create folds for 3-fold bootstrap: one weight for each curve
  set.seed(124)
  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)

  ## compute out-of-bag risk and coefficient estimates on folds  
  cvr2 <- validateFDboost(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)

  ## plot the out-of-bag risk
  oldpar <- par(mfrow = c(1,3))
  plot(cvr); legend("topright", lty=2, paste(mstop(cvr)))
  plot(cvr2)
  plot(cvr3); legend("topright", lty=2, paste(mstop(cvr3)))

  ## plot the estimated coefficients per fold
  ## more meaningful for higher number of folds, e.g., B = 100 
  par(mfrow = c(2,2))
  plotPredCoef(cvr2, terms = FALSE, which = 1)
  plotPredCoef(cvr2, terms = FALSE, which = 3)
  
  ## compute out-of-bag risk and predictions for leaving-one-curve-out cross-validation
  cvr_jackknife <- validateFDboost(mod, folds = cvLong(unique(mod$id), 
                                   type = "curves"), grid = 1:75)
  plot(cvr_jackknife)
  ## plot oob predictions per fold for 3rd effect 
  plotPredCoef(cvr_jackknife, which = 3) 
  ## plot coefficients per fold for 2nd effect
  plotPredCoef(cvr_jackknife, which = 2, terms = FALSE)
  
  par(oldpar)

}

FDboost documentation built on Aug. 12, 2023, 5:13 p.m.