holdout.vimp.rfsrc.RdHold 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,
...)A symbolic description of the model to be fit.
Data frame containing the y-outcome and x-variables.
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.
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).
Integer value used for survival to
constrain ensemble calculations to a grid of ntime time points.
Function specifying size of subsampled data. Can also be a number.
Type of bootstrap used.
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.
Specifies number of trees in a block when calculating holdout variable importance.
Further arguments to be passed to rfsrc.
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.
Invisibly a list with the following components (which themselves can be lists):
Holdout VIMP.
Prediction error for the baseline forest.
Prediction error for the holdout forest.
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.
# \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)
# }