subsample.rfsrc: Subsample Forests for VIMP Confidence Intervals

In randomForestSRC: Fast Unified Random Forests for Survival, Regression, and Classification (RF-SRC)

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 class 'rfsrc'
subsample(obj,
  B = 100,
  block.size = 1,
  importance,
  subratio = NULL,
  stratify = TRUE,
  performance = FALSE,
  performance.only = FALSE,
  joint = FALSE,
  xvar.names = NULL,
  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.
importance	Optional: specifies the type of importance to be used, selected from one of "anti", "permute", "random". If not specified reverts to default importance used by the package. Also, this is over-ridden if the original grow object contains importance, in which case importance used in the original grow call is used.
subratio	Ratio of subsample size to original sample size. The default is approximately equal to the inverse square root of the sample size.
stratify	Use stratified subsampling? See details below.
performance	Generalization error? User can also request standard error and confidence regions for generalization error.
performance.only	Only calculate standard error and confidence region for the generalization error (no VIMP).
joint	Joint VIMP for all variables? Users can also request joint VIMP for specific variables using xvar.names.
xvar.names	Specifies variables for calculating joint VIMP. By default all variables are used.
bootstrap	Use double bootstrap approach in place of subsampling? Much slower, but potentially more accurate.
verbose	Provide verbose output?

Details

Using a previously trained forest, subsamples the data and constructs subsampled forests to estimate standard errors and confidence intervals for VIMP (Ishwaran and Lu, 2019). If bootstrapping is requested, a double bootstrap is applied in place of subsampling. The option performance="TRUE" constructs standard errors and confidence regions for the error rate (OOB performance) of the trained forest. Options joint and xvar.names can be used to obtain joint VIMP for all or some variables.

If the trained forest does not have VIMP values, the algorithm first needs 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. Also, by calling VIMP in the original call, the type of importance used and other related parameters are set by values used in the original call which can eliminate confusion about what parameters are being used in the subsampled forests. For example, the default importance used is not permutation importance. Thus, it is generally advised to call VIMP in the original call.

Subsampled forests are calculated using the same tuning parameters as the original forest. While a sophisticated algorithm is utilized to acquire as many of these parameters as possible, keep in mind 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 of the variance (Shao and Wu, 1989) are returned alongside subsampled variance estimators (Politis and Romano, 1994). While these methods are closely related, the jackknife estimator generally gives *larger* standard errors, which is a form of bias correction, and which occurs primarily for the signal variables.

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. In survival settings, subsampled data may be devoid of deaths and/or have reduced number of competing risks. Note also that stratified sampling is not available for multivariate families–users should especially exercise caution when selecting subsampling rates here.

The function extract.subsample can be used to extract information from the subsampled object. Returned values for VIMP are "standardized" (this means for regression families, VIMP is standardized by dividing by the variance of Y; for all other families, VIMP is unaltered). Use standardize="FALSE" if you want unstandardized VIMP. Setting the option raw="TRUE" returns a more complete set of information that is used by the function plot.subsample.rfsrc for plotting confidence intervals. Keep in mind some of this information will be subsampled VIMP that is "raw" in the sense it equals VIMP from a forest constructed with a much smaller sample size. This option is for experts only.

When printing or plotting results, the default is to standardize VIMP which can be turned off using the option standardize. Also these wrappers preset the "alpha" value used for confidence intervals; users can change this using option alpha.

Value

A list with the following key components:

rf	Original forest grow object.
vmp	Variable importance values for grow forest.
vmpS	Variable importance subsampled values.
subratio	Subratio used.

Author(s)

Hemant Ishwaran and Udaya B. Kogalur

References

Ishwaran H. and Lu M. (2019). Standard errors and confidence intervals for variable importance in random forest regression, classification, and survival. Statistics in Medicine, 38, 558-582.

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

holdout.vimp.rfsrc plot.subsample.rfsrc, rfsrc, vimp.rfsrc

Examples

## ------------------------------------------------------------
## regression
## ------------------------------------------------------------

## training the forest
reg.o <- rfsrc(Ozone ~ ., airquality)

## default subsample call
reg.smp.o <- subsample(reg.o)

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

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

## joint vimp and confidence region for generalization error
reg.smp.o2 <- subsample(reg.o, performance = TRUE,
           joint = TRUE, xvar.names = c("Day", "Month"))
plot.subsample(reg.smp.o2)

## now try the double bootstrap (slower)
reg.dbs.o <- subsample(reg.o, B = 25, bootstrap = TRUE)
print(reg.dbs.o)
plot.subsample(reg.dbs.o)

## standard error and confidence region for generalization error only
gerror <- subsample(reg.o, performance.only = TRUE)
plot.subsample(gerror)

## ------------------------------------------------------------
## classification
## ------------------------------------------------------------

## 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.axis = .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.axis = .7)
}

## ------------------------------------------------------------
## class-imbalanced data using RFQ classifier with G-mean VIMP
## ------------------------------------------------------------

if (library("caret", logical.return = TRUE)) {

  ## experimental settings
  n <- 1000
  q <- 20
  ir <- 6
  f <- as.formula(Class ~ .)
 
  ## simulate the data, create minority class data
  d <- twoClassSim(n, linearVars = 15, noiseVars = q)
  d$Class <- factor(as.numeric(d$Class) - 1)
  idx.0 <- which(d$Class == 0)
  idx.1 <- sample(which(d$Class == 1), sum(d$Class == 1) / ir , replace = FALSE)
  d <- d[c(idx.0,idx.1),, drop = FALSE]

  ## RFQ classifier
  oq <- imbalanced(Class ~ ., d, importance = TRUE, block.size = 10)

  ## subsample the RFQ-classifier
  smp.oq <- subsample(oq, B = 100)
  plot.subsample(smp.oq, cex.axis = .7)

}

## ------------------------------------------------------------
## survival 
## ------------------------------------------------------------

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

## ------------------------------------------------------------
## competing risks
## 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 = "logrankCR", cause = 2)
  cr.smp.o <- subsample(cr.o, B = 100)
  plot.subsample(cr.smp.o, target = 2)
}

## ------------------------------------------------------------
## multivariate 
## ------------------------------------------------------------

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.subsample(so)
  plot.subsample(so, m.target = "rm")
  ##generalization error
  gerror <- subsample(o, performance.only = TRUE)
  plot.subsample(gerror, m.target = "medv")
  plot.subsample(gerror, m.target = "rm")
}

## ------------------------------------------------------------
## largish data example - use rfsrc.fast 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
  ## remember to set forest=TRUE for rfsrc.fast
  o <- rfsrc.fast(Class ~ ., d, ntree = 100,
           forest = TRUE, perf.type = "brier")
  so <- subsample(o, B = 100)
  plot.subsample(so, cex.axis = .7)
}

randomForestSRC documentation built on Sept. 11, 2024, 7:50 p.m.