An implementation of the random forest and bagging ensemble algorithms utilizing conditional inference trees as base learners.
cforest(formula, data, weights, subset, offset, cluster, strata,
na.action = na.pass,
control = ctree_control(teststat = "quad", testtype = "Univ",
mincriterion = 0, saveinfo = FALSE, ...),
ytrafo = NULL, scores = NULL, ntree = 500L,
perturb = list(replace = FALSE, fraction = 0.632),
mtry = ceiling(sqrt(nvar)), applyfun = NULL, cores = NULL,
trace = FALSE, ...)
# S3 method for cforest
predict(object, newdata = NULL,
type = c("response", "prob", "weights", "node"),
OOB = FALSE, FUN = NULL, simplify = TRUE, scale = TRUE, ...)
# S3 method for cforest
gettree(object, tree = 1L, ...)An object of class cforest.
a symbolic description of the model to be fit.
a data frame containing the variables in the model.
an optional vector specifying a subset of observations to be used in the fitting process.
an optional vector of weights to be used in the fitting
process. Non-negative integer valued weights are
allowed as well as non-negative real weights.
Observations are sampled (with or without replacement)
according to probabilities weights / sum(weights).
The fraction of observations to be sampled (without replacement)
is computed based on the sum of the weights if all weights
are integer-valued and based on the number of weights greater zero
else. Alternatively, weights can be a double matrix defining
case weights for all ncol(weights) trees in the forest directly.
This requires more storage but gives the user more control.
an optional vector of offset values.
an optional factor indicating independent clusters. Highly experimental, use at your own risk.
an optional factor for stratified sampling.
a function which indicates what should happen when the data contain missing value.
a list with control parameters, see
ctree_control. The default values correspond to those
of the default values used by cforest from the
party package. saveinfo = FALSE leads to less
memory hungry representations of trees. Note that arguments
mtry, cores and applyfun in
ctree_control are ignored for cforest,
because they are already set.
an optional named list of functions to be applied to the response
variable(s) before testing their association with the explanatory
variables. Note that this transformation is only
performed once for the root node and does not take weights into account
(which means, the forest bootstrap or subsetting is ignored,
which is almost certainly not a good idea).
Alternatively, ytrafo can be a function of data and
weights. In this case, the transformation is computed for
every node and the corresponding weights. This feature is experimental
and the user interface likely to change.
an optional named list of scores to be attached to ordered factors.
Number of trees to grow for the forest.
a list with arguments replace and fraction determining which type of
resampling with replace = TRUE referring to the n-out-of-n bootstrap and
replace = FALSE to sample splitting.
fraction is the portion of observations to draw without
replacement. Honesty (experimental): If fraction has two elements, the
first fraction defines the portion of observations to be used for tree
induction, the second fraction defines the portion of observations used
for parameter estimation. The sum of both fractions can be smaller than
one but most not exceed one. Details can be found in Section 2.4 of
Wager and Athey (2018).
number of input variables randomly sampled as candidates
at each node for random forest like algorithms. Bagging, as special case
of a random forest without random input variable sampling, can
be performed by setting mtry either equal to Inf or
manually equal to the number of input variables.
an optional lapply-style function with arguments
function(X, FUN, ...). It is used for computing the variable selection criterion.
The default is to use the basic lapply
function unless the cores argument is specified (see below).
numeric. If set to an integer the applyfun is set to
mclapply with the desired number of cores.
a logical indicating if a progress bar shall be printed while the forest grows.
An object as returned by cforest
An optional data frame containing test data.
a character string denoting the type of predicted value
returned, ignored when argument FUN is given. For
"response", the mean of a numeric response, the predicted
class for a categorical response or the median survival time for a
censored response is returned. For "prob" the matrix of
conditional class probabilities (simplify = TRUE) or a list
with the conditional class probabilities for each observation
(simplify = FALSE) is returned for a categorical response.
For numeric and censored responses, a list with the empirical
cumulative distribution functions and empirical survivor functions
(Kaplan-Meier estimate) is returned when type = "prob".
"weights" returns an integer vector of prediction weights.
For type = "where", a list of terminal node ids for each of the
trees in the forest ist returned.
a logical defining out-of-bag predictions (only if newdata = NULL).
If the forest was fitted with honesty, this option is ignored.
a function to compute summary statistics. Predictions for each node have to be
computed based on arguments (y, w) where y is the response and
w are case weights.
a logical indicating whether the resulting list of predictions should be converted to a suitable vector or matrix (if possible).
a logical indicating scaling of the nearest neighbor weights by the sum of weights in the corresponding terminal node of each tree. In the simple regression forest, predicting the conditional mean by nearest neighbor weights will be equivalent to (but slower!) the aggregation of means.
an integer, the number of the tree to extract from the forest.
additional arguments.
This implementation of the random forest (and bagging) algorithm differs
from the reference implementation in randomForest
with respect to the base learners used and the aggregation scheme applied.
Conditional inference trees, see ctree, are fitted to each
of the ntree perturbed samples of the learning sample. Most of the hyper parameters in
ctree_control regulate the construction of the conditional inference trees.
Hyper parameters you might want to change are:
1. The number of randomly preselected variables mtry, which is fixed
to the square root of the number of input variables.
2. The number of trees ntree. Use more trees if you have more variables.
3. The depth of the trees, regulated by mincriterion. Usually unstopped and unpruned
trees are used in random forests. To grow large trees, set mincriterion to a small value.
The aggregation scheme works by averaging observation weights extracted
from each of the ntree trees and NOT by averaging predictions directly
as in randomForest.
See Hothorn et al. (2004) and Meinshausen (2006) for a description.
Predictions can be computed using predict. For observations
with zero weights, predictions are computed from the fitted tree
when newdata = NULL.
Ensembles of conditional inference trees have not yet been extensively
tested, so this routine is meant for the expert user only and its current
state is rather experimental. However, there are some things available
in cforest that can't be done with randomForest,
for example fitting forests to censored response variables (see Hothorn et al., 2004, 2006a) or to
multivariate and ordered responses. Using the rich partykit infrastructure allows
additional functionality in cforest, such as parallel tree growing and probabilistic
forecasting (for example via quantile regression forests). Also plotting of single trees from
a forest is much easier now.
Unlike cforest, cforest is entirely written in R which
makes customisation much easier at the price of longer computing times. However, trees
can be grown in parallel with this R only implemention which renders speed less of an issue.
Note that the default values are different from those used in package party, most
importantly the default for mtry is now data-dependent. predict(, type = "node") replaces
the where function and predict(, type = "prob") the
treeresponse function.
Moreover, when predictors vary in their scale of measurement of number
of categories, variable selection and computation of variable importance is biased
in favor of variables with many potential cutpoints in randomForest,
while in cforest unbiased trees and an adequate resampling scheme
are used by default. See Hothorn et al. (2006b) and Strobl et al. (2007)
as well as Strobl et al. (2009).
Breiman L (2001). Random Forests. Machine Learning, 45(1), 5--32.
Hothorn T, Lausen B, Benner A, Radespiel-Troeger M (2004). Bagging Survival Trees. Statistics in Medicine, 23(1), 77--91.
Hothorn T, Buehlmann P, Dudoit S, Molinaro A, Van der Laan MJ (2006a). Survival Ensembles. Biostatistics, 7(3), 355--373.
Hothorn T, Hornik K, Zeileis A (2006b). Unbiased Recursive Partitioning: A Conditional Inference Framework. Journal of Computational and Graphical Statistics, 15(3), 651--674.
Hothorn T, Zeileis A (2015). partykit: A Modular Toolkit for Recursive Partytioning in R. Journal of Machine Learning Research, 16, 3905--3909.
Meinshausen N (2006). Quantile Regression Forests. Journal of Machine Learning Research, 7, 983--999.
Strobl C, Boulesteix AL, Zeileis A, Hothorn T (2007). Bias in Random Forest Variable Importance Measures: Illustrations, Sources and a Solution. BMC Bioinformatics, 8, 25. tools:::Rd_expr_doi("10.1186/1471-2105-8-25")
Strobl C, Malley J, Tutz G (2009). An Introduction to Recursive Partitioning: Rationale, Application, and Characteristics of Classification and Regression Trees, Bagging, and Random Forests. Psychological Methods, 14(4), 323--348.
Stefan Wager & Susan Athey (2018). Estimation and Inference of Heterogeneous Treatment Effects using Random Forests. Journal of the American Statistical Association, 113(523), 1228--1242. tools:::Rd_expr_doi("10.1080/01621459.2017.1319839")
## basic example: conditional inference forest for cars data
cf <- cforest(dist ~ speed, data = cars)
## prediction of fitted mean and visualization
nd <- data.frame(speed = 4:25)
nd$mean <- predict(cf, newdata = nd, type = "response")
plot(dist ~ speed, data = cars)
lines(mean ~ speed, data = nd)
## predict quantiles (aka quantile regression forest)
## Note that this works for integer-valued weight w
## Other weights require weighted quantiles, see for example
## Hmisc::wtd.quantile(
myquantile <- function(y, w) quantile(rep(y, w), probs = c(0.1, 0.5, 0.9))
p <- predict(cf, newdata = nd, type = "response", FUN = myquantile)
colnames(p) <- c("lower", "median", "upper")
nd <- cbind(nd, p)
## visualization with conditional (on speed) prediction intervals
plot(dist ~ speed, data = cars, type = "n")
with(nd, polygon(c(speed, rev(speed)), c(lower, rev(upper)),
col = "lightgray", border = "transparent"))
points(dist ~ speed, data = cars)
lines(mean ~ speed, data = nd, lwd = 1.5)
lines(median ~ speed, data = nd, lty = 2, lwd = 1.5)
legend("topleft", c("mean", "median", "10% - 90% quantile"),
lwd = c(1.5, 1.5, 10), lty = c(1, 2, 1),
col = c("black", "black", "lightgray"), bty = "n")
if (FALSE) {
### honest (i.e., out-of-bag) cross-classification of
### true vs. predicted classes
data("mammoexp", package = "TH.data")
table(mammoexp$ME, predict(cforest(ME ~ ., data = mammoexp, ntree = 50),
OOB = TRUE, type = "response"))
### fit forest to censored response
if (require("TH.data") && require("survival")) {
data("GBSG2", package = "TH.data")
bst <- cforest(Surv(time, cens) ~ ., data = GBSG2, ntree = 50)
### estimate conditional Kaplan-Meier curves
print(predict(bst, newdata = GBSG2[1:2,], OOB = TRUE, type = "prob"))
print(gettree(bst))
}
}
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