R: Subsample Forests for VIMP Confidence Intervals

subsample.rfsrc {randomForestSRC} | R Documentation

## 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,
      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?

### Details

Given a forest object, 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.

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. 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 two methods are closely related, estimated standard error for VIMP from delete-d estimators are generally larger than from subsampled estimators, 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, but undercoverage for strong variables and overcoverage for noise variables is exhibited by both estimators. This however may be 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` conveniently extracts 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, all 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(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 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 = 25, subratio = .5)

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

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

    ## extract subsampled VIMP
    print(extract.subsample(reg.smp.o)$vmpS)

    ## extract unstandardized subsampled VIMP
    print(extract.subsample(reg.smp.o, standardize=FALSE)$vmpS)

    ## 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 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.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 example
    ## uses q-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 example
    ## ------------------------------------------------------------

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

[Package randomForestSRC version 2.11.0 Index]