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

subsample(obj,
  B = 100,
  block.size = 1,
  subratio = NULL,
  stratify = TRUE,
  performance = 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.

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.

performance

Error rate of forest? Used to obtain standard error and confidence region for the ensemble out-of-sample performance.

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. Additionally, performance="TRUE" constructs standard errors and confidence regions for the error rate (OOB performance) of the trained forest.

If the trained forest does not have VIMP values, 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. 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, estimated standard error for VIMP from delete-d estimators are generally larger, which is a form of bias correction, and which occurs primarily for variables with true signal. Confidence interval coverage is generally better under delete-d estimators, but undercoverage for strong variables and overcoverage for noise variables is exhibited by both estimators. This can be considered beneficial if the goal is variable selection (Ishwaran and Lu, 2019).

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. 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. It returns summary information (used for plotting confidence intervals) as well as VIMP from the original forest and VIMP from the subsampled forests. Keep in mind this subsampled VIMP is "raw" in the sense it equals VIMP from a forest constructed with a much smaller sample size. No processing of the subsampled VIMP to the original sample size is done. Also, the returned VIMP is "standardized" (this means for regression families, VIMP is standardized by dividing by the variance of Y and multiplying by 100. For all other families, VIMP is scaled by 100). Use standardize=FALSE if you want unstandardized VIMP.

When printing or plotting results, the default is to standardize VIMP. This can be turned off using the option standardize in those wrappers.

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

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.

Examples

# \donttest{
## ------------------------------------------------------------
## regression
## ------------------------------------------------------------

## traing 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)

## subsample call with joint vimp and confidence region for error rate
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 (slow!!)
reg.dbs.o <- subsample(reg.o, B = 25, bootstrap = TRUE)
print(reg.dbs.o)
plot.subsample(reg.dbs.o)

## ------------------------------------------------------------
## 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
## uses 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]

  ## q-classifier
  oq <- imbalanced(Class ~ ., d, splitrule = "auc",
              importance = TRUE, block.size = 10)

  ## subsample the q-classifier
  smp.oq <- subsample(oq, B = 100)
  plot(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(so)
  plot(so, 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 request forests in 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)
}


# }