Bagging Classification, Regression and Survival Trees
Bagging for classification, regression and survival trees.
## S3 method for class 'factor'
ipredbagg(y, X=NULL, nbagg=25, control=
rpart.control(minsplit=2, cp=0, xval=0),
comb=NULL, coob=FALSE, ns=length(y), keepX = TRUE, ...)
## S3 method for class 'numeric'
ipredbagg(y, X=NULL, nbagg=25, control=rpart.control(xval=0),
comb=NULL, coob=FALSE, ns=length(y), keepX = TRUE, ...)
## S3 method for class 'Surv'
ipredbagg(y, X=NULL, nbagg=25, control=rpart.control(xval=0),
comb=NULL, coob=FALSE, ns=dim(y)[1], keepX = TRUE, ...)
## S3 method for class 'data.frame'
bagging(formula, data, subset, na.action=na.rpart, ...)y |
the response variable: either a factor vector of class labels
(bagging classification trees), a vector of numerical values
(bagging regression trees) or an object of class
|
X |
a data frame of predictor variables. |
nbagg |
an integer giving the number of bootstrap replications. |
coob |
a logical indicating whether an out-of-bag estimate of the
error rate (misclassification error, root mean squared error
or Brier score) should be computed.
See |
control |
options that control details of the |
comb |
a list of additional models for model combination, see below
for some examples. Note that argument |
ns |
number of sample to draw from the learning sample. By default,
the usual bootstrap n out of n with replacement is performed.
If |
keepX |
a logical indicating whether the data frame of predictors
should be returned. Note that the computation of the
out-of-bag estimator requires |
formula |
a formula of the form |
data |
optional data frame containing the variables in the model formula. |
subset |
optional vector specifying a subset of observations to be used. |
na.action |
function which indicates what should happen when
the data contain |
... |
additional parameters passed to |
The random forest implementations randomForest
and cforest are more flexible and reliable for computing
bootstrap-aggregated trees than this function and should be used instead.
Bagging for classification and regression trees were suggested by Breiman (1996a, 1998) in order to stabilise trees.
The trees in this function are computed using the implementation in the
rpart package. The generic function ipredbagg
implements methods for different responses. If y is a factor,
classification trees are constructed. For numerical vectors
y, regression trees are aggregated and if y is a survival
object, bagging survival trees (Hothorn et al, 2003) is performed.
The function bagging offers a formula based interface to
ipredbagg.
nbagg bootstrap samples are drawn and a tree is constructed
for each of them. There is no general rule when to stop the tree
growing. The size of the
trees can be controlled by control argument
or prune.classbagg. By
default, classification trees are as large as possible whereas regression
trees and survival trees are build with the standard options of
rpart.control. If nbagg=1, one single tree is
computed for the whole learning sample without bootstrapping.
If coob is TRUE, the out-of-bag sample (Breiman,
1996b) is used to estimate the prediction error
corresponding to class(y). Alternatively, the out-of-bag sample can
be used for model combination, an out-of-bag error rate estimator is not
available in this case. Double-bagging (Hothorn and Lausen,
2003) computes a LDA on the out-of-bag sample and uses the discriminant
variables as additional predictors for the classification trees. comb
is an optional list of lists with two elements model and predict.
model is a function with arguments formula and data.
predict is a function with arguments object, newdata only. If
the estimation of the covariance matrix in lda fails due to a
limited out-of-bag sample size, one can use slda instead.
See the example section for an example of double-bagging. The methodology is
not limited to a combination with LDA: bundling (Hothorn and Lausen, 2002b)
can be used with arbitrary classifiers.
NOTE: Up to ipred version 0.9-0, bagging was performed using a modified version of the original rpart function. Due to interface changes in rpart 3.1-55, the bagging function had to be rewritten. Results of previous version are not exactly reproducible.
The class of the object returned depends on class(y):
classbagg, regbagg and survbagg. Each is a list with elements
y |
the vector of responses. |
X |
the data frame of predictors. |
mtrees |
multiple trees: a list of length |
OOB |
logical whether the out-of-bag estimate should be computed. |
err |
if |
comb |
logical whether a combination of models was requested. |
For each class methods for the generics prune.rpart,
print, summary and predict are
available for inspection of the results and prediction, for example:
print.classbagg, summary.classbagg,
predict.classbagg and prune.classbagg for
classification problems.
Leo Breiman (1996a), Bagging Predictors. Machine Learning 24(2), 123–140.
Leo Breiman (1996b), Out-Of-Bag Estimation. Technical Report https://www.stat.berkeley.edu/~breiman/OOBestimation.pdf.
Leo Breiman (1998), Arcing Classifiers. The Annals of Statistics 26(3), 801–824.
Peter Buehlmann and Bin Yu (2002), Analyzing Bagging. The Annals of Statistics 30(4), 927–961.
Torsten Hothorn and Berthold Lausen (2003), Double-Bagging: Combining classifiers by bootstrap aggregation. Pattern Recognition, 36(6), 1303–1309.
Torsten Hothorn and Berthold Lausen (2005), Bundling Classifiers by Bagging Trees. Computational Statistics & Data Analysis, 49, 1068–1078.
Torsten Hothorn, Berthold Lausen, Axel Benner and Martin Radespiel-Troeger (2004), Bagging Survival Trees. Statistics in Medicine, 23(1), 77–91.
library("MASS")
library("survival")
# Classification: Breast Cancer data
data("BreastCancer", package = "mlbench")
# Test set error bagging (nbagg = 50): 3.7% (Breiman, 1998, Table 5)
mod <- bagging(Class ~ Cl.thickness + Cell.size
+ Cell.shape + Marg.adhesion
+ Epith.c.size + Bare.nuclei
+ Bl.cromatin + Normal.nucleoli
+ Mitoses, data=BreastCancer, coob=TRUE)
print(mod)
# Test set error bagging (nbagg=50): 7.9% (Breiman, 1996a, Table 2)
data("Ionosphere", package = "mlbench")
Ionosphere$V2 <- NULL # constant within groups
bagging(Class ~ ., data=Ionosphere, coob=TRUE)
# Double-Bagging: combine LDA and classification trees
# predict returns the linear discriminant values, i.e. linear combinations
# of the original predictors
comb.lda <- list(list(model=lda, predict=function(obj, newdata)
predict(obj, newdata)$x))
# Note: out-of-bag estimator is not available in this situation, use
# errorest
mod <- bagging(Class ~ ., data=Ionosphere, comb=comb.lda)
predict(mod, Ionosphere[1:10,])
# Regression:
data("BostonHousing", package = "mlbench")
# Test set error (nbagg=25, trees pruned): 3.41 (Breiman, 1996a, Table 8)
mod <- bagging(medv ~ ., data=BostonHousing, coob=TRUE)
print(mod)
library("mlbench")
learn <- as.data.frame(mlbench.friedman1(200))
# Test set error (nbagg=25, trees pruned): 2.47 (Breiman, 1996a, Table 8)
mod <- bagging(y ~ ., data=learn, coob=TRUE)
print(mod)
# Survival data
# Brier score for censored data estimated by
# 10 times 10-fold cross-validation: 0.2 (Hothorn et al,
# 2002)
data("DLBCL", package = "ipred")
mod <- bagging(Surv(time,cens) ~ MGEc.1 + MGEc.2 + MGEc.3 + MGEc.4 + MGEc.5 +
MGEc.6 + MGEc.7 + MGEc.8 + MGEc.9 +
MGEc.10 + IPI, data=DLBCL, coob=TRUE)
print(mod)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.