randomForestSRC (version 2.8.0)

subsample: Subsample Forests for VIMP Confidence Intervals

Description

Use subsampling to calculate confidence intervals and standard errors for VIMP (variable importance). Applies to all families.

Usage

# S3 method for rfsrc
subsample(obj,
  B = 100,
  block.size = 1,
  subratio = NULL,
  stratify = TRUE,
  joint = FALSE,
  bootstrap = FALSE,
  verbose = TRUE)

Arguments

obj

A forest grow object.

B

Number of subsamples (or number of bootstraps).

block.size

Specifies number of trees in a block when calculating VIMP. This is over-ridden if VIMP is present in the original grow call in which case the grow value is used.

subratio

Ratio of subsample size to original sample size. The default is the inverse square root of the sample size.

stratify

Use stratified subsampling? See details below.

joint

Include the VIMP for all variables jointly perturbed? This is useful reference problems where one might be suspicious that many (or all) variables are noise.

bootstrap

Use double bootstrap approach in place of subsampling? Much slower, but potentially more accurate.

verbose

Provide verbose output?

Value

A list with the following key components:

rf

Original forest grow object.

vmp

Variable importance subsampled values.

Details

Given a forest object, subsamples the forest to obtain standard errors and confidence intervals for VIMP (Ishwaran and Lu, 2018). If bootstrapping is requested, then the double bootstrap is applied in place of subsampling.

If VIMP is not present in the original forest object, the algorithm will first need to calculate VIMP. Therefore, if the user plans to make repeated calls to subsample, it is advisable to include VIMP in the original grow call. Note that the subsampled forest inherits the same tuning parameters as the original forests. While a sophisticated algorithm is utilized to acquire as many of the original forest parameters as possible to be applied to the subsampled forest, there are some conditions where this will fail: for example there are certain settings where the user has specified non-standard sampling in the grow forest.

Delete-d jackknife estimators (Shao and Wu, 1989) are returned along with subsampling estimators (Politis and Romano, 1994). While these two methods are closely related, standard errors for delete-d estimators are generally larger than the subsampled estimates, which is a form of bias correction, which occurs primarily for variables with true signal. Confidence interval coverage is generally better under delete-d estimators. Note that undercoverage for strong variables and overcoverage for noise variables exhibited by both estimators may be beneficial if the goal is variable selection (Ishwaran and Lu, 2018).

By default, stratified subsampling is used for classification, survival, and competing risk families. For classification, stratification is on the class label, while for survival and competing risk, stratification is on the event type and censoring. Users are discouraged from over-riding this option, especially in small sample settings, as this could lead to error due to subsampled data not having full representation of class labels in classification settings, and in survival settings, subsampled data may be devoid of deaths and/or have reduced number of competing risks. Finally, note that stratified sampling is not available for multivariate families in which case users should especially exercise caution when selecting subsampling rates.

Note that subsampling and bootstrapping do not take into account missing data imputation that may have been performed on the forest grow object. In such cases there is no guarantee that standard errors and confidence intervals will be accurate.

The function extract.subsample is useful for studying the subsampled object. This function has been exported for the convenience of users to experiment with.

When printing and or plotting results, the default setting is to standardize VIMP, where for regression families, VIMP is standardized by dividing by the variance and multiplying by 100. For all other families, VIMP is scaled by 100. This can be turned off using the option standardize in those wrappers.

References

Ishwaran H. and Lu M. (2018). Standard errors and confidence intervals for variable importance in random forest regression, classification, and survival. Statistics in Medicine (in press).

Politis, D.N. and Romano, J.P. (1994). Large sample confidence regions based on subsamples under minimal assumptions. The Annals of Statistics, 22(4):2031-2050.

Shao, J. and Wu, C.J. (1989). A general theory for jackknife variance estimation. The Annals of Statistics, 17(3):1176-1197.

See Also

plot.subsample, rfsrc, vimp

Examples

# NOT RUN {
## ------------------------------------------------------------
## regression example
## ------------------------------------------------------------

## grow the forest - request VIMP
reg.o <- rfsrc(mpg ~ ., mtcars)

## very small sample size so need largish subratio
reg.smp.o <- subsample(reg.o, B = 100, subratio = .5)

## plot confidence regions
plot.subsample(reg.smp.o)

## summary of results
print(reg.smp.o)

## now try the double bootstrap (slow!!)
reg.dbs.o <- subsample(reg.o, B = 100, bootstrap = TRUE)
print(reg.dbs.o)
plot.subsample(reg.dbs.o)

## ------------------------------------------------------------
## classification example
## ------------------------------------------------------------

## 3 non-linear, 15 linear, and 5 noise variables 
if (library("caret", logical.return = TRUE)) {
  d <- twoClassSim(1000, linearVars = 15, noiseVars = 5)

  ## VIMP based on (default) misclassification error
  cls.o <- rfsrc(Class ~ ., d)
  cls.smp.o <- subsample(cls.o, B = 100)
  plot.subsample(cls.smp.o, cex = .7)

  ## same as above, but with VIMP defined using normalized Brier score
  cls.o2 <- rfsrc(Class ~ ., d, perf.type = "brier")
  cls.smp.o2 <- subsample(cls.o2, B = 100)
  plot.subsample(cls.smp.o2, cex = .7)
}

## ------------------------------------------------------------
## survival example
## ------------------------------------------------------------

data(pbc, package = "randomForestSRC")
srv.o <- rfsrc(Surv(days, status) ~ ., pbc)
srv.smp.o <- subsample(srv.o, B = 100)
plot.subsample(srv.smp.o)

## ------------------------------------------------------------
## competing risk example
## target event is death (event = 2)
## ------------------------------------------------------------

if (library("survival", logical.return = TRUE)) {
  data(pbc, package = "survival")
  pbc$id <- NULL
  cr.o <- rfsrc(Surv(time, status) ~ ., pbc, splitrule = "logrank", cause = 2)
  cr.smp.o <- subsample(cr.o, B = 100)
  plot.subsample(cr.smp.o, target = 2)
}

## ------------------------------------------------------------
## multivariate family
## ------------------------------------------------------------

if (library("mlbench", logical.return = TRUE)) {
  ## simulate the data 
  data(BostonHousing)
  bh <- BostonHousing
  bh$rm <- factor(round(bh$rm))
  o <- rfsrc(cbind(medv, rm) ~ ., bh)
  so <- subsample(o)
  plot(so)
  plot(so, m.target = "rm")
}

## ------------------------------------------------------------
## largish data example - use rfsrcFast for fast forests
## ------------------------------------------------------------

if (library("caret", logical.return = TRUE)) {
  ## largish data set
  d <- twoClassSim(1000, linearVars = 15, noiseVars = 5)

  ## use a subsampled forest with Brier score performance
  o <- rfsrcFast(Class ~ ., d, ntree = 100, perf.type = "brier")
  so <- subsample(o, B = 100)
  plot.subsample(so, cex = .7)
}


# }