Hold out VIMP is calculated from the error rate of mini ensembles of trees (blocks of trees) grown with and without a variable. Applies to all families.

holdout.vimp(formula, data,
ntree = function(p, vtry){1000 * p / vtry},
nsplit = 10,
ntime = 50,
sampsize = function(x){x * .632},
samptype = "swor",
block.size = 10,
vtry = 1,
...)

## Arguments

formula

A symbolic description of the model to be fit.

data

Data frame containing the y-outcome and x-variables.

ntree

Function specifying requested number of trees used for growing the forest. Inputs are dimension and number of holdout variables. The requested number of trees can also be a number.

nsplit

Non-negative integer value specifying number of random split points used to split a node (deterministic splitting corresponds to the value zero and is much slower).

ntime

Integer value used for survival to constrain ensemble calculations to a grid of ntime time points.

sampsize

Function specifying size of subsampled data. Can also be a number.

samptype

Type of bootstrap used.

vtry

Number of variables randomly selected to be held out when growing a tree. This can also be set to a list for a targeted hold out VIMP analysis. See details below for more information.

block.size

Specifies number of trees in a block when calculating holdout variable importance.

...

Further arguments to be passed to rfsrc.

## Details

Holdout variable importance (holdout VIMP) is based on comparing error performance of two mini forests of trees (blocks of trees): the first in which a random set of vtry features are held out (the holdout forest), and the second in which no features are held out (the baseline forest).

To summarize, holdout VIMP measures the importance of a variable when that variable is truly removed from the tree growing process.

Specifically, if a feature is held out in a block of trees, we refer to this as the (feature, block) pair. The bootstrap for the trees in a (feature, block) pair are identical in both forests. That is, the holdout block is grown by holding out the feature, and the baseline block is grown over the same trees, with the same bootstrap, but without holding out any features. vtry controls how many features are held out in every tree. If set to one (default), only one variable is held out in every tree. Once a (feature, block) of trees has been grown, holdout VIMP for a given variable v is calculated as follows. Gather the block of trees where the feature was held out (from the holdout forest) and calculate OOB prediction error. Next gather the corresponding block of trees where v was not held out (from the baseline forest) and calculate OOB prediction error. Holdout VIMP for the (feature, block) pair is the difference between these two values. The final holdout VIMP estimate for a feature v is obtained by averaging holdout VIMP for (feature=v, block) over all blocks.

Accuracy of hold out VIMP depends critically on total number of trees. If total number of trees is too small, then number of times a variable is held out will be small and OOB error can suffer from high variance. Therefore, ntree should be set fairly high---we recommend using 1000 times the number of features. Increasing vtry is another way to increase number of times a variable is held out and therefore reduces the burden of growing a large number of trees. In particular, total number of trees needed decreases linearly with vtry. The default ntree equals 1000 trees for each feature divided by vtry. Keep in mind intrepretation of holdout VIMP is altered when vtry is different than one. Thus this option should be used with caution.

Accuracy also depends on the value of block.size. Smaller values generally produce better results but are more computationally demanding. The most computationally demanding, but most accurate, is block.size=1. This is similar to how block.size is used for usual variable importance: see the help file for rfsrc for details. Note the value of block.size should not exceed ntree divided by number of features, otherwise there may not be enough trees to satisify the target block size for a feature and missing values will result.

A targeted hold out VIMP analysis can be requested by setting vtry to a list with two entries. The first entry is a vector of integer values specifying the variables of interest. The second entry is a boolean logical flag indicating whether individual or joint VIMP should be calculated. For example, suppose variables 1, 4 and 5 are our variables of interest. To calculate holdout VIMP for these variables, and these variables only, vtry would be specified by

vtry = list(xvar = c(1, 4, 5), joint = FALSE)

On the other hand, if we are interested in the joint effect when we remove the three variables simultaneously, then

vtry = list(xvar = c(1, 4, 5), joint = TRUE)

The benefits of a targeted analysis is that the user may have a pre-conceived idea of which variables are interesting. Only VIMP for these variables will be calculated which greatly reduces computational time. Another benefit is that when joint VIMP is requested, this provides the user with a way to assess importance of specific groups of variables. See the iris example below for illustration.

## Value

Invisibly a list with the following components (which themselves can be lists):

importance

Holdout VIMP.

baseline

Prediction error for the baseline forest.

holdout

Prediction error for the holdout forest.

## Author

Hemant Ishwaran and Udaya B. Kogalur

## References

Lu M. and Ishwaran H. (2018). Expert Opinion: A prediction-based alternative to p-values in regression models. J. Thoracic and Cardiovascular Surgery, 155(3), 1130--1136.

vimp.rfsrc

## Examples

# \donttest{

## ------------------------------------------------------------
## regression analysis
## ------------------------------------------------------------

## new York air quality measurements
airq.obj <- holdout.vimp(Ozone ~ ., data = airquality, na.action = "na.impute")
print(airq.obj$importance) ## ------------------------------------------------------------ ## classification analysis ## ------------------------------------------------------------ ## iris data iris.obj <- holdout.vimp(Species ~., data = iris) print(iris.obj$importance)

## iris data using brier prediction error
iris.obj <- holdout.vimp(Species ~., data = iris, perf.type = "brier")
print(iris.obj$importance) ## ------------------------------------------------------------ ## illustration of targeted holdout vimp analysis ## ------------------------------------------------------------ ## iris data - only interested in variables 3 and 4 vtry <- list(xvar = c(3, 4), joint = FALSE) print(holdout.vimp(Species ~., data = iris, vtry = vtry)$impor)

## iris data - joint importance of variables 3 and 4
vtry <- list(xvar = c(3, 4), joint = TRUE)
print(holdout.vimp(Species ~., data = iris, vtry = vtry)$impor) ## iris data - joint importance of variables 1 and 2 vtry <- list(xvar = c(1, 2), joint = TRUE) print(holdout.vimp(Species ~., data = iris, vtry = vtry)$impor)

## ------------------------------------------------------------
## imbalanced classification (using RFQ)
## ------------------------------------------------------------

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

## experimental settings
n <- 400
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$Class == 1) / ir , replace = FALSE) d <- d[c(idx.0,idx.1),, drop = FALSE] ## VIMP for RFQ with and without blocking vmp1 <- imbalanced(f, d, importance = TRUE, block.size = 1)$importance[, 1]
vmp10 <- imbalanced(f, d, importance = TRUE, block.size = 10)$importance[, 1] ## holdout VIMP for RFQ with and without blocking hvmp1 <- holdout.vimp(f, d, rfq = TRUE, perf.type = "g.mean", block.size = 1)$importance[, 1]
hvmp10 <- holdout.vimp(f, d, rfq =  TRUE,
perf.type = "g.mean", block.size = 10)$importance[, 1] ## compare VIMP values imp <- 100 * cbind(vmp1, vmp10, hvmp1, hvmp10) legn <- c("vimp-1", "vimp-10","hvimp-1", "hvimp-10") colr <- rep(4,20+q) colr[1:20] <- 2 ylim <- range(c(imp)) nms <- 1:(20+q) par(mfrow=c(2,2)) barplot(imp[,1],col=colr,las=2,main=legn[1],ylim=ylim,names.arg=nms) barplot(imp[,2],col=colr,las=2,main=legn[2],ylim=ylim,names.arg=nms) barplot(imp[,3],col=colr,las=2,main=legn[3],ylim=ylim,names.arg=nms) barplot(imp[,4],col=colr,las=2,main=legn[4],ylim=ylim,names.arg=nms) } ## ------------------------------------------------------------ ## multivariate regression analysis ## ------------------------------------------------------------ mtcars.mreg <- holdout.vimp(Multivar(mpg, cyl) ~., data = mtcars, vtry = 3, block.size = 1, samptype = "swr", sampsize = dim(mtcars)[1]) print(mtcars.mreg$importance)

## ------------------------------------------------------------
## mixed outcomes analysis
## ------------------------------------------------------------

mtcars.new <- mtcars
mtcars.new$cyl <- factor(mtcars.new$cyl)
mtcars.new$carb <- factor(mtcars.new$carb, ordered = TRUE)
mtcars.mix <- holdout.vimp(cbind(carb, mpg, cyl) ~., data = mtcars.new,
ntree = 100,
block.size = 2,
vtry = 1)
print(mtcars.mix$importance) ##------------------------------------------------------------ ## survival analysis ##------------------------------------------------------------ ## Primary biliary cirrhosis (PBC) of the liver data(pbc, package = "randomForestSRC") pbc.obj <- holdout.vimp(Surv(days, status) ~ ., pbc, nsplit = 10, ntree = 1000, na.action = "na.impute") print(pbc.obj$importance)

##------------------------------------------------------------
## competing risks
##------------------------------------------------------------

## WIHS analysis
## cumulative incidence function (CIF) for HAART and AIDS stratified by IDU

data(wihs, package = "randomForestSRC")
wihs.obj <- holdout.vimp(Surv(time, status) ~ ., wihs,
nsplit = 3,
ntree = 100)
print(wihs.obj\$importance)

# }