Last chance! 50% off unlimited learning
Sale ends in
Fast OpenMP parallel computing of random forests (Breiman 2001) for regression, classification, survival analysis (Ishwaran 2008), competing risks (Ishwaran 2012), multivariate (Segal and Xiao 2011), unsupervised (Mantero and Ishwaran 2020), quantile regression (Meinhausen 2006, Zhang et al. 2019), and class imbalanced q-classification (O'Brien and Ishwaran 2019). Different splitting rules invoked under deterministic or random splitting (Geurts et al. 2006, Ishwaran 2015) are available for all families. Variable importance (VIMP), and holdout VIMP, as well as confidence regions (Ishwaran and Lu 2019) can be calculated for single and grouped variables. Fast interface for missing data imputation using a variety of different random forest methods (Tang and Ishwaran 2017).
Key items users should be aware of:
Visualize trees on your Safari or Google Chrome browser (works
for all families). See get.tree
.
sidClustering (see sidClustering
) for
unsupervised data analysis.
Fast hold out VIMP (see holdout.vimp
).
Can be conservative but has good false discovery properties
unlike Breiman-Cutler VIMP (see vimp
).
VIMP confidence intervals using subsampling (see
subsample
).
q-classifier for class imbalanced data, including G-mean
VIMP which is superior to Breiman-Cutler
(see imbalanced
).
Fast imputation using on the fly imputation,
missForest and multivariate missForest (see
impute
).
Fast random forests using subsampling (see rfsrc.fast
).
This is the main entry point to the randomForestSRC
package. For more information about this package and OpenMP parallel
processing, use the command package?randomForestSRC
.
rfsrc(formula, data, ntree = 500,
mtry = NULL, ytry = NULL,
nodesize = NULL, nodedepth = NULL,
splitrule = NULL, nsplit = 10,
importance = c(FALSE, TRUE, "none", "permute", "random", "anti"),
block.size = if (any(is.element(as.character(importance),
c("none", "FALSE")))) NULL else 10,
ensemble = c("all", "oob", "inbag"),
bootstrap = c("by.root", "none", "by.user"),
samptype = c("swor", "swr"), samp = NULL, membership = FALSE,
sampsize = if (samptype == "swor") function(x){x * .632} else function(x){x},
na.action = c("na.omit", "na.impute"), nimpute = 1,
ntime = 250, cause,
proximity = FALSE, distance = FALSE, forest.wt = FALSE,
xvar.wt = NULL, yvar.wt = NULL, split.wt = NULL, case.wt = NULL,
forest = TRUE,
var.used = c(FALSE, "all.trees", "by.tree"),
split.depth = c(FALSE, "all.trees", "by.tree"),
seed = NULL,
do.trace = FALSE,
statistics = FALSE,
...)## convenient interface for growing a CART tree
rfsrc.cart(formula, data, ntree = 1, mtry = ncol(data), bootstrap = "none", ...)
A symbolic description of the model to be fit. If missing, unsupervised splitting is implemented.
Data frame containing the y-outcome and x-variables.
Number of trees.
Number of variables randomly selected as candidates for
splitting a node. The default is p
/3 for regression,
where p
equals the number of variables. For all
other families (including unsupervised settings), the default is
sqrt(p
). Values are always rounded up.
For unsupervised forests, sets the number of randomly
selected pseudo-responses (see below for more details).
The default is ytry
=1, which selects one pseudo-response.
Minumum size of terminal node.
The defaults are: survival (15), competing risk
(15), regression (5), classification (1), mixed outcomes (3),
unsupervised (3). It is recommended to experiment with different
nodesize
values.
Maximum depth to which a tree should be grown. The default behaviour is that this parameter is ignored.
Splitting rule (see below).
Non-negative integer value for number of random splits to consider for each candidate splitting variable. This significantly increases speed. When zero or NULL, uses much slower deterministic splitting where all possible splits considered.
Method for computing variable importance (VIMP); see
below. Default action is importance="none"
but VIMP can
always be recovered later using vimp
or
predict
.
Should the cumulative error rate be calculated on
every tree? When NULL
, it will only be calculated on the
last tree and the plot of the cumulative error rate will result in a
flat line. To view the cumulative error rate on every nth tree, set
the value to an integer between 1
and ntree
. As an
intended side effect, if importance is requested, VIMP is
calculated in "blocks" of size equal to block.size
, thus
resulting in a useful compromise between ensemble and permutation
VIMP. The default action is to use 10 trees.
Specifies the type of ensemble. By default both out-of-bag (OOB) and inbag ensembles are returned. Always use OOB values for inference on the training data.
Bootstrap protocol. The default is by.root
which bootstraps the data by sampling with or without replacement
(by default sampling is without replacement; see the option
samptype
below). If none
is chosen, the data is not
bootstrapped at all. If by.user
is choosen, the bootstrap
specified by samp
is used. It is not possible to return OOB
ensembles or prediction error if none
is in effect.
Type of bootstrap when by.root
is in effect.
Choices are swor
(sampling without replacement) and
swr
(sampling with replacement). Unlike Breiman's random
forests, the default action here is sampling without replacement.
Thus out-of-bag (OOB) technically means out-of-sample, but for
legacy reasons we retain the term OOB.
Bootstrap specification when by.user
is in
effect. Array of dim n x ntree
specifying how many
times each record appears inbag in the bootstrap for each tree.
Should terminal node membership and inbag information be returned?
Function specifying size of bootstrap data when
by.root
is in effect. For sampling without replacement, it is
the requested size of the sample, which by default is .632 times the
sample size. For sampling with replacement, it is the sample size.
Can also be specified by using a number.
Action taken if the data contains NA
's.
Possible values are na.omit
or na.impute
.
The default na.omit
removes the entire record if
even one of its entries is NA
(for x-variables this applies only
to those specifically listed in 'formula'). Selecting
na.impute
imputes the data. Also see the function
impute
for fast direct imputation.
Number of iterations of the missing data algorithm.
Performance measures such as out-of-bag (OOB) error rates tend to
become optimistic if nimpute
is greater than 1.
Integer value used for survival to constrain ensemble
calculations to an ntime
grid of time points over the
observed event times. Alternatively if a vector of values of length
greater than one is supplied, it is assumed these are the time
points to be used to constrain the calculations (note that the
constrained time points used will be the observed event times
closest to the user supplied time points). Setting ntime
to
zero (or NULL) uses all observed event times.
Integer value between 1 and J
indicating the event
of interest for splitting a node for competing risks, where J
is the number of event types. If not specified, the default is to
use a composite splitting rule that averages over all event types.
Can also be a vector of non-negative weights of length J
specifying weights for each event (for example, passing a vector of
ones reverts to the default composite split statistic). Finally,
regardless of how cause
is specified, the returned forest
object always provides estimates for all event types.
Proximity of cases as measured by the frequency of
sharing the same terminal node. This is an n
xn
matrix, which can be large. Choices are inbag
, oob
,
all
, TRUE
, or FALSE
. Setting proximity =
TRUE
is equivalent to proximity = "inbag"
.
Distance between cases as measured by the ratio of the
sum of the count of edges from each case to their immediate common
ancestor node to the sum of the count of edges from each case to the
root node. If the cases are co-terminal for a tree, this measure is
zero and reduces to 1 - the proximity measure for these cases in a
tree. This is an n
xn
matrix, which can be large.
Choices are inbag
, oob
, all
, TRUE
,
or FALSE
. Setting distance = TRUE
is equivalent to
distance = "inbag"
.
Should the forest weight matrix be
calculated? Creates an n
xn
matrix which can be
used for prediction and constructing customized estimators. Choices
are similar to proximity: inbag
, oob
, all
,
TRUE
, or FALSE
. The default is TRUE
which
is equivalent to inbag
.
Vector of non-negative weights (does not have to sum to 1) representing the probability of selecting a variable for splitting. Default is to use uniform weights.
NOT YET IMPLEMENTED: Vector of non-negative weights (does not have to sum to 1) representing the probability of selecting a response as a candidate for the split statistic in unsupervised settings. Default is to use uniform weights.
Vector of non-negative weights used for multiplying the split statistic for a variable. A large value encourages the node to split on a specific variable. Default is to use uniform weights.
Vector of non-negative weights (does not have to sum to 1) for sampling cases. Observations with larger weights will be selected with higher probability in the bootstrap (or subsampled) samples. It is generally better to use real weights rather than integers. See the example below for the breast data set for an illustration of its use for class imbalanced data.
Should the forest object be returned? Used for prediction on new data and required by many of the package functions.
Return variables used for splitting? Default is
FALSE
. Possible values are all.trees
which returns a
vector of the number of times a split occurred on a variable, and
by.tree
which returns a matrix recording the number of times
a split occurred on a variable in a specific tree.
Records the minimal depth for each variable.
Default is FALSE
. Possible values are all.trees
which
returns a matrix of the average minimal depth for a variable
(columns) for a specific case (rows), and by.tree
which
returns a three-dimensional array recording minimal depth for a
specific case (first dimension) for a variable (second dimension)
for a specific tree (third dimension).
Negative integer specifying seed for the random number generator.
Number of seconds between updates to the user on approximate time to completion.
Should split statistics be returned? Values can be
parsed using stat.split
.
Further arguments passed to or from other methods.
An object of class (rfsrc, grow)
with the following
components:
The original call to rfsrc
.
The family used in the analysis.
Sample size of the data (depends upon NA
's, see na.action
).
Number of trees grown.
Number of variables randomly selected for splitting at each node.
Minimum size of terminal nodes.
Maximum depth allowed for a tree.
Splitting rule used.
Number of randomly selected split points.
y-outcome values.
A character vector of the y-outcome names.
Data frame of x-variables.
A character vector of the x-variable names.
Vector of non-negative weights specifying the probability used to select a variable for splitting a node.
Vector of non-negative weights specifying multiplier by which the split statistic for a covariate is adjusted.
Vector of weights used for the composite competing risk splitting rule.
Number of terminal nodes for each tree in the
forest. Vector of length ntree
. A value of zero indicates
a rejected tree (can occur when imputing missing data).
Values of one indicate tree stumps.
Proximity matrix recording the frequency of pairs of data points occur within the same terminal node.
If forest=TRUE
, the forest object is returned.
This object is used for prediction with new test data
sets and is required for other R-wrappers.
Forest weight matrix.
Matrix recording terminal node membership where each column records node mebership for a case for a tree (rows).
Splitting rule used.
Matrix recording inbag membership where each column contains the number of times that a case appears in the bootstrap sample for a tree (rows).
Count of the number of times a variable is used in growing the forest.
Vector of indices for cases with missing values.
Data frame of the imputed data. The first column(s) are reserved for the y-responses, after which the x-variables are listed.
Matrix [i][j] or array [i][j][k] recording the minimal depth for variable [j] for case [i], either averaged over the forest, or by tree [k].
Split statistics returned when
statistics=TRUE
which can be parsed using stat.split
.
Tree cumulative OOB error rate.
When importance=TRUE
, vector of the
cumulative error rate for each ensemble block comprised of
block.size
trees. So with block.size = 10
, entries are
the cumulative error rate for the first 10 trees, the first 20 trees,
30 trees, and so on. As another exmple, if block.size = 1
,
entries are the error rate for each tree.
Variable importance (VIMP) for each x-variable.
In-bag predicted value.
OOB predicted value.
for classification settings, additionally ++++++++
In-bag predicted class labels.
OOB predicted class labels.
for multivariate settings, additionally ++++++++
List containing performance values for multivariate regression responses (applies only in multivariate settings).
List containing performance values for multivariate categorical (factor) responses (applies only in multivariate settings).
for survival settings, additionally ++++++++
In-bag survival function.
OOB survival function.
In-bag cumulative hazard function (CHF).
OOB CHF.
Ordered unique death times.
Number of deaths.
for competing risks, additionally ++++++++
In-bag cause-specific cumulative hazard function (CSCHF) for each event.
OOB CSCHF.
In-bag cumulative incidence function (CIF) for each event.
OOB CIF.
Ordered unique event times.
Number of events.
Types of forests
There is no need to set the type of forest as the package automagically determines the underlying random forest requested from the type of response and the formula supplied. There are several possible scenarios:
Regression forests for continuous responses.
Classification forests for factor responses.
Multivariate forests for continuous and/or factor responses and for mixed (both type) of responses.
Unsupervised forests when there is no response.
Survival forests for right-censored survival.
Competing risk survival forests for competing risk.
Splitting
Splitting rules are specified by the option splitrule
.
For all families, pure random splitting can be invoked by setting
splitrule
="random".
For all families, computational speed can be increased using
randomized splitting invoked by the option nsplit
.
See Improving Computational Speed.
Available splitting rules
Regression analysis:
mse
: default split rule implements weighted
mean-squared error splitting (Breiman et al. 1984, Chapter 8.4).
quantile.regr
: quantile regression splitting via
the "check-loss" function. Requires specifying the target
quantiles. See quantreg.rfsrc
for further details.
la.quantile.regr
: local adaptive quantile
regression splitting. See quantreg.rfsrc
.
Classification analysis:
gini
: default splitrule implements Gini index
splitting (Breiman et al. 1984, Chapter 4.3).
auc
: AUC (area under the ROC curve) splitting
for both two-class and multiclass setttings. AUC splitting is
appropriate for imbalanced data. See imbalanced
for
more information.
entropy
: entropy splitting (Breiman et
al. 1984, Chapter 2.5, 4.3).
Survival analysis:
logrank
: default splitrule implements
log-rank splitting (Segal, 1988; Leblanc and Crowley, 1993).
bs.gradient
: gradient-based (global non-quantile)
brier score splitting. The time horizon used for the Brier
score is set to the 90th percentile of the observed event times.
This can be over-ridden by the option prob
, which must be
a value between 0 and 1 (set to .90 by default).
logrankscore
: log-rank score splitting (Hothorn and
Lausen, 2003).
Competing risk analysis (for details see Ishwaran et al., 2014):
logrankCR
: default splitrule implements a modified
weighted log-rank splitting rule modeled after Gray's test
(Gray, 1988). Use this to find *all* variables
that are informative and when the goal is long term
prediction.
logrank
: weighted log-rank splitting where each
event type is treated as the event of interest and all
other events are treated as censored. The split rule is
the weighted value of each of log-rank statistics,
standardized by the variance. Use this to find variables
that affect a *specific* cause of interest and when
the goal is a targeted analysis of a specific cause.
However in order for this to be effective, remember to set
the cause
option to the targeted cause of interest.
See examples below.
Multivariate analysis: When one or both regression and classification responses are detected, a multivariate normalized composite split rule of mean-squared error and Gini index splitting is invoked. See Tang and Ishwaran (2017) for details on this splitting rule. This splitting rule is different than Segal and Xiao (2011) who use Mahalanobis distance splitting.
Unsupervised analysis: In settings where there is no
outcome, unsupervised splitting is invoked. In this case,
the mixed outcome splitting rule (above) is applied. Also
see sidClustering
for a more sophisticated method for
unsupervised analysis (Mantero and Ishwaran, 2020).
Custom splitting: All families except unsupervised are
available for user defined custom splitting. Some basic
C-programming skills are required. The harness for defining
these rules is in splitCustom.c
. In this file we
give examples of how to code rules for regression,
classification, survival, and competing risk. Each family
can support up to sixteen custom split rules. Specifying
splitrule="custom"
or splitrule="custom1"
will
trigger the first split rule for the family defined by the
training data set. Multivariate families will need a custom
split rule for both regression and classification. In the
examples, we demonstrate how the user is presented with the
node specific membership. The task is then to define a
split statistic based on that membership. Take note of the
instructions in splitCustom.c
on how to
register the custom split rules. It is suggested
that the existing custom split rules be kept in place for
reference and that the user proceed to develop
splitrule="custom2"
and so on. The package must be
recompiled and installed for the custom split rules to
become available.
Improving computational speed
See the function rfsrc.fast
for a fast
implementation of rfsrc
. In general, the key methods for
increasing speed are as follows:
Randomized splitting rules
Computational speed can be significantly improved with randomized
splitting invoked by the option nsplit
. When nsplit
is set to a non-zero positive integer, a maximum of nsplit
split points are chosen randomly for each of the candidate
splitting variables when splitting a tree node, thus significantly
reducing the cost from having to consider all possible split-values.
To revert to traditional deterministic splitting (all split
values considered) use nsplit
=0.
Randomized splitting for trees has a long history. See for
example, Loh and Shih (1997), Dietterich (2000), and Lin and Jeon
(2006). Geurts et al. (2006) recently introduced extremely
randomized trees using what they call the extra-trees algorithm.
We can see that this algorithm essentially corresponds to
randomized splitting with nsplit
=1. In our experience
however this is not always the optimal value for nsplit
and
may often be too low. See Ishwaran (2015).
Finally, for completely randomized (pure random) splitting use
splitrule
="random". In pure splitting, nodes are split by
randomly selecting a variable and randomly selecting its split
point (Cutler and Zhao, 2001).
Subsampling
Subsampling can be used to reduce the size of the in-sample data
used to grow a tree and therefore can greatly reduce computational
load. Subsampling is implemented using options sampsize
and samptype
. See rfsrc.fast
for a fast forest
implementation using subsampling.
Unique time points
Setting ntime
to a reasonably small value such as 100 or
250 (the default) constrains survival ensemble calculations to a
restricted grid of time points and significantly improves
computational times.
Large number of variables
The default setting importance="none"
turns off variable
importance (VIMP) calculations and considerably reduces
computational times. Variable importance can always
be recovered later using functions vimp
or
predict
. Also consider using max.subtree
which calculates minimal depth, a measure of the depth that a
variable splits, and yields fast variable selection (Ishwaran,
2010).
Prediction Error
Prediction error is calculated using OOB data. Performance is
measured in terms of mean-squared-error for regression, and
misclassification error for classification. A normalized Brier
score (relative to a coin-toss) and the AUC (area under the ROC
curve) is also provided upon printing a classification forest.
Performance for Brier score can be specified using
perf.type="brier"
. G-mean performance is also available, see
the function imbalanced
for more details.
For survival, prediction error is measured by 1-C, where C is Harrell's (Harrell et al., 1982) concordance index. Prediction error is between 0 and 1, and measures how well the predictor correctly ranks (classifies) two random individuals in terms of survival. A value of 0.5 is no better than random guessing. A value of 0 is perfect.
When bootstrapping is by none
, a coherent OOB subset is not
available to assess prediction error. Thus, all outputs dependent
on this are suppressed. In such cases, prediction error is only
available via classical cross-validation (the user will need to use
the predict.rfsrc
function).
Variable Importance (VIMP)
To obtain VIMP use the option importance
. Setting this to
"permute" or "TRUE" returns permutation VIMP from permuting OOB
cases. Choosing "random" replaces permutation with random
assignment. Thus when an OOB case is dropped down a tree, the case
goes left or right randomly whenever a split is encountered
for the target variable. If "anti" is specified, the case is
assigned to the opposite split. By default importance
="FALSE"
and VIMP is not requested.
VIMP depends upon block.size
, an integer value between 1 and
ntree
, specifying the number of trees in a block used to
determine VIMP. When block.size
=1, VIMP is calculated by
tree. The difference between prediction error under the perturbed
predictor and the original predictor is calculated for each tree and
averaged over the forest. This yields Breiman-Cutler VIMP (Breiman
2001).
When block.size
="ntree", VIMP is calculated across the forest
by comparing the perturbed OOB forest ensemble (using all trees) to the
unperturbed OOB forest ensemble (using all trees). Unlike
Breiman-Cutler VIMP, ensemble VIMP does not measure the tree average
effect of x, but rather its overall forest effect. This is
called Ishwaran-Kogalur VIMP (Ishwaran et al. 2008).
A useful compromise between Breiman-Cutler (BC) and Ishwaran-Kogalur
(IK) VIMP can be obtained by setting block.size
to a value
between 1 and ntree
. Smaller values are closer to BC and
larger values closer to IK. Smaller generally gives better
accuracy, however computational times will be higher because VIMP is
calculated over more blocks. Also see imbalanced
for
imbalanced classification data where a larger block.size
works better (O'Brien and Ishwaran, 2019).
See vimp
for a user interface for extracting VIMP and
subsampling
for calculating confidence intervals for VIMP.
Also see holdout.vimp
for holdout VIMP, which calculates
importance by holding out variables. This leads to a more
conservative procedure but with good false discovery properties.
Note that for classification, VIMP is returned as a matrix with with J+1 columns where J is the number of classes. The first column "all" is the unconditional VIMP, while the remaining columns are VIMP conditioned on cases corresponding to that class label.
Multivariate Forests
Multivariate forests can be specified in two ways:
rfsrc(Multivar(y1, y2, ..., yd) ~ . , my.data, ...)
rfsrc(cbind(y1, y2, ..., yd) ~ . , my.data, ...)
A multivariate normalized composite splitting rule is used to split nodes. The nature of the outcomes will inform the code as to the type of multivariate forest to be grown; i.e. whether it is real-valued, categorical, or a combination of both (mixed). Note that performance measures (when requested) are returned for all outcomes.
Unsupervised Forests and sidClustering
See sidClustering sidClustering
for a more sophisticated
method for unsupervised analysis.
Otherwise a more direct (but naive) way to proceed is to use the unsupervised splitting rule. The following are equivalent ways to grow an unsupervised forest via unsupervised splitting:
rfsrc(data = my.data)
rfsrc(Unsupervised() ~ ., data = my.data)
In unsupervised mode, features take turns acting as target
y-outcomes and x-variables for splitting. Specifically, mtry
x-variables are randomly selected for splitting the node. Then for
each mtry
feature, ytry
variables are selected
from the remaining features to act as the target pseduo-responses.
Splitting uses the multivariate normalized composite splitting rule.
The default value of ytry
is 1 but can be increased. As
illustration, the following equivalent unsupervised calls set
mtry=10
and ytry
=5:
rfsrc(data = my.data, ytry = 5, mtry = 10)
rfsrc(Unsupervised(5) ~ ., my.data, mtry = 10)
Note that all performance values (error rates, VIMP, prediction) are turned off in unsupervised mode.
Survival, Competing Risks
Survival settings require a time and censoring variable which
should be identifed in the formula as the response using the standard
Surv
formula specification. A typical formula call looks like:
Surv(my.time, my.status) ~ .
where my.time
and my.status
are the variables names for
the event time and status variable in the users data set.
For survival forests (Ishwaran et al. 2008), the censoring variable must be coded as a non-negative integer with 0 reserved for censoring and (usually) 1=death (event).
For competing risk forests (Ishwaran et al., 2013), the implementation is similar to survival, but with the following caveats:
Censoring must be coded as a non-negative integer, where 0 indicates right-censoring, and non-zero values indicate different event types. While 0,1,2,..,J is standard, and recommended, events can be coded non-sequentially, although 0 must always be used for censoring.
Setting the splitting rule to logrankscore
will result
in a survival analysis in which all events are treated as if they
are the same type (indeed, they will coerced as such).
Generally, competing risks requires a larger nodesize
than
survival settings.
Missing data imputation
Set na.action="na.impute"
to impute missing data (both x and
y-variables) using the missing data algorithm of Ishwaran et
al. (2008). However, see the function impute
for an
alternate way to do fast and accurate imputation.
The missing data algorithm can be iterated by setting nimpute
to a positive integer greater than 1. When iterated, at the
completion of each iteration, missing data is imputed using OOB
non-missing terminal node data which is then used as input to grow a
new forest. A side effect of iteration is that missing values in
the returned objects xvar
, yvar
are replaced by
imputed values. In other words the incoming data is overlaid with
the missing data. Also, performance measures such as error rates
and VIMP become optimistically biased.
Records in which all outcome and x-variable information are missing are removed from the forest analysis. Variables having all missing values are also removed.
Allowable data types and factors
Data types must be real valued, integer, factor or logical --
however all except factors are coerced and treated as if real
valued. For ordered x-variable factors, splits are similar to real
valued variables. For unordered factors, a split will move a subset
of the levels in the parent node to the left daughter, and the
complementary subset to the right daughter. All possible
complementary pairs are considered and apply to factors with an
unlimited number of levels. However, there is an optimization check
to ensure number of splits attempted is not greater than number of
cases in a node or the value of nsplit
.
For coherence, an immutable map is applied to each factor that ensures factor levels in the training data are consistent with the factor levels in any subsequent test data. This map is applied to each factor before and after the native C library is executed. Because of this, if all x-variables all factors, then computational time will be long in high dimensional problems. Consider converting factors to real if this is the case.
Breiman L., Friedman J.H., Olshen R.A. and Stone C.J. (1984). Classification and Regression Trees, Belmont, California.
Breiman L. (2001). Random forests, Machine Learning, 45:5-32.
Cutler A. and Zhao G. (2001). PERT-Perfect random tree ensembles. Comp. Sci. Statist., 33: 490-497.
Dietterich, T. G. (2000). An experimental comparison of three methods for constructing ensembles of decision trees: bagging, boosting, and randomization. Machine Learning, 40, 139-157.
Gray R.J. (1988). A class of k-sample tests for comparing the cumulative incidence of a competing risk, Ann. Statist., 16: 1141-1154.
Geurts, P., Ernst, D. and Wehenkel, L., (2006). Extremely randomized trees. Machine learning, 63(1):3-42.
Harrell et al. F.E. (1982). Evaluating the yield of medical tests, J. Amer. Med. Assoc., 247:2543-2546.
Hothorn T. and Lausen B. (2003). On the exact distribution of maximally selected rank statistics, Comp. Statist. Data Anal., 43:121-137.
Ishwaran H. (2007). Variable importance in binary regression trees and forests, Electronic J. Statist., 1:519-537.
Ishwaran H. and Kogalur U.B. (2007). Random survival forests for R, Rnews, 7(2):25-31.
Ishwaran H., Kogalur U.B., Blackstone E.H. and Lauer M.S. (2008). Random survival forests, Ann. App. Statist., 2:841-860.
Ishwaran H., Kogalur U.B., Gorodeski E.Z, Minn A.J. and Lauer M.S. (2010). High-dimensional variable selection for survival data. J. Amer. Statist. Assoc., 105:205-217.
Ishwaran H., Kogalur U.B., Chen X. and Minn A.J. (2011). Random survival forests for high-dimensional data. Stat. Anal. Data Mining, 4:115-132
Ishwaran H., Gerds T.A., Kogalur U.B., Moore R.D., Gange S.J. and Lau B.M. (2014). Random survival forests for competing risks. Biostatistics, 15(4):757-773.
Ishwaran H. and Malley J.D. (2014). Synthetic learning machines. BioData Mining, 7:28.
Ishwaran H. (2015). The effect of splitting on random forests. Machine Learning, 99:75-118.
Lin, Y. and Jeon, Y. (2006). Random forests and adaptive nearest neighbors. J. Amer. Statist. Assoc., 101(474), 578-590.
Lu M., Sadiq S., Feaster D.J. and Ishwaran H. (2018). Estimating individual treatment effect in observational data using random forest methods. J. Comp. Graph. Statist, 27(1), 209-219
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.
LeBlanc M. and Crowley J. (1993). Survival trees by goodness of split, J. Amer. Statist. Assoc., 88:457-467.
Loh W.-Y and Shih Y.-S (1997). Split selection methods for classification trees, Statist. Sinica, 7:815-840.
Mantero A. and Ishwaran H. (2020). Unsupervised random forests. To appear in Statistical Analysis and Data Mining.
Meinshausen N. (2006) Quantile regression forests, Journal of Machine Learning Research, 7:983-999.
Mogensen, U.B, Ishwaran H. and Gerds T.A. (2012). Evaluating random forests for survival analysis using prediction error curves, J. Statist. Software, 50(11): 1-23.
O'Brien R. and Ishwaran H. (2019). A random forests quantile classifier for class imbalanced data. Pattern Recognition, 90, 232-249
Segal M.R. (1988). Regression trees for censored data, Biometrics, 44:35-47.
Segal M.R. and Xiao Y. Multivariate random forests. (2011). Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery. 1(1):80-87.
Tang F. and Ishwaran H. (2017). Random forest missing data algorithms. Statistical Analysis and Data Mining, 10:363-377.
Zhang H., Zimmerman J., Nettleton D. and Nordman D.J. (2019). Random forest prediction intervals. The American Statistician. 4:1-5.
imbalanced.rfsrc
,
impute.rfsrc
,
partial.rfsrc
,
plot.competing.risk.rfsrc
,
plot.rfsrc
,
plot.survival.rfsrc
,
plot.variable.rfsrc
,
predict.rfsrc
,
print.rfsrc
,
# NOT RUN {
##------------------------------------------------------------
## survival analysis
##------------------------------------------------------------
## veteran data
## randomized trial of two treatment regimens for lung cancer
data(veteran, package = "randomForestSRC")
v.obj <- rfsrc(Surv(time, status) ~ ., data = veteran,
ntree = 100, block.size = 1)
## print tree number 3
plot(get.tree(v.obj, 3))
## print the grow object and plot various useful details
print(v.obj)
plot(v.obj)
## plot survival curves for first 10 individuals -- direct way
matplot(v.obj$time.interest, 100 * t(v.obj$survival.oob[1:10, ]),
xlab = "Time", ylab = "Survival", type = "l", lty = 1)
## plot survival curves for first 10 individuals
## using function "plot.survival"
plot.survival(v.obj, subset = 1:10)
# }
# NOT RUN {
## fast nodesize optimization for veteran data
## optimal nodesize in survival is larger than other families
## see the function "tune" for more examples
tune.nodesize(Surv(time,status) ~ ., veteran)
## Primary biliary cirrhosis (PBC) of the liver
data(pbc, package = "randomForestSRC")
pbc.obj <- rfsrc(Surv(days, status) ~ ., pbc)
print(pbc.obj)
##------------------------------------------------------------
## trees can be plotted for any family
## see get.tree for details and more examples
##------------------------------------------------------------
## survival where factors have many levels
data(veteran, package = "randomForestSRC")
vd <- veteran
vd$celltype=factor(vd$celltype)
vd$diagtime=factor(vd$diagtime)
vd.obj <- rfsrc(Surv(time,status)~., vd, ntree = 100, nodesize = 5)
plot(get.tree(vd.obj, 3))
## classification
iris.obj <- rfsrc(Species ~., data = iris)
plot(get.tree(iris.obj, 25, class.type = "bayes"))
plot(get.tree(iris.obj, 25, target = "setosa"))
plot(get.tree(iris.obj, 25, target = "versicolor"))
plot(get.tree(iris.obj, 25, target = "virginica"))
## ------------------------------------------------------------
## simple example of VIMP using iris classification
## ------------------------------------------------------------
## directly from grow call
print(rfsrc(Species~.,iris,importance=TRUE)$importance)
## note by default VIMP (and performance) uses misclassification error,
## but brier prediction error can be specified
print(rfsrc(Species~.,iris,importance=TRUE,perf.type="brier")$importance)
## using vimp function (see vimp help file for details)
iris.obj <- rfsrc(Species ~., data = iris)
print(vimp(iris.obj)$importance)
print(vimp(iris.obj,perf.type="brier")$importance)
## hold out vimp (see holdout.vimp help file for details)
print(holdout.vimp(Species~.,iris)$importance)
print(holdout.vimp(Species~.,iris,perf.type="brier")$importance)
## ------------------------------------------------------------
## confidence interval for vimp using subsampling
## compare with holdout vimp
## ------------------------------------------------------------
## new York air quality measurements
o <- rfsrc(Ozone ~ ., data = airquality)
so <- subsample(o)
plot(so)
## compare with holdout vimp
print(holdout.vimp(Ozone ~ ., data = airquality)$importance)
##------------------------------------------------------------
## example of imputation in survival analysis
##------------------------------------------------------------
data(pbc, package = "randomForestSRC")
pbc.obj2 <- rfsrc(Surv(days, status) ~ ., pbc,
nsplit = 10, na.action = "na.impute")
## same as above but we iterate the missing data algorithm
pbc.obj3 <- rfsrc(Surv(days, status) ~ ., pbc,
na.action = "na.impute", nimpute = 3)
## fast way to impute the data (no inference is done)
## see impute for more details
pbc.imp <- impute(Surv(days, status) ~ ., pbc, splitrule = "random")
##------------------------------------------------------------
## compare RF-SRC to Cox regression
## Illustrates C-index and Brier score measures of performance
## assumes "pec" and "survival" libraries are loaded
##------------------------------------------------------------
if (library("survival", logical.return = TRUE)
& library("pec", logical.return = TRUE)
& library("prodlim", logical.return = TRUE))
{
##prediction function required for pec
predictSurvProb.rfsrc <- function(object, newdata, times, ...){
ptemp <- predict(object,newdata=newdata,...)$survival
pos <- sindex(jump.times = object$time.interest, eval.times = times)
p <- cbind(1,ptemp)[, pos + 1]
if (NROW(p) != NROW(newdata) || NCOL(p) != length(times))
stop("Prediction failed")
p
}
## data, formula specifications
data(pbc, package = "randomForestSRC")
pbc.na <- na.omit(pbc) ##remove NA's
surv.f <- as.formula(Surv(days, status) ~ .)
pec.f <- as.formula(Hist(days,status) ~ 1)
## run cox/rfsrc models
## for illustration we use a small number of trees
cox.obj <- coxph(surv.f, data = pbc.na, x = TRUE)
rfsrc.obj <- rfsrc(surv.f, pbc.na, ntree = 150)
## compute bootstrap cross-validation estimate of expected Brier score
## see Mogensen, Ishwaran and Gerds (2012) Journal of Statistical Software
set.seed(17743)
prederror.pbc <- pec(list(cox.obj,rfsrc.obj), data = pbc.na, formula = pec.f,
splitMethod = "bootcv", B = 50)
print(prederror.pbc)
plot(prederror.pbc)
## compute out-of-bag C-index for cox regression and compare to rfsrc
rfsrc.obj <- rfsrc(surv.f, pbc.na)
cat("out-of-bag Cox Analysis ...", "\n")
cox.err <- sapply(1:100, function(b) {
if (b%%10 == 0) cat("cox bootstrap:", b, "\n")
train <- sample(1:nrow(pbc.na), nrow(pbc.na), replace = TRUE)
cox.obj <- tryCatch({coxph(surv.f, pbc.na[train, ])}, error=function(ex){NULL})
if (!is.null(cox.obj)) {
get.cindex(pbc.na$days[-train], pbc.na$status[-train], predict(cox.obj, pbc.na[-train, ]))
} else NA
})
cat("\n\tOOB error rates\n\n")
cat("\tRSF : ", rfsrc.obj$err.rate[rfsrc.obj$ntree], "\n")
cat("\tCox regression : ", mean(cox.err, na.rm = TRUE), "\n")
}
##------------------------------------------------------------
## competing risks
##------------------------------------------------------------
## WIHS analysis
## cumulative incidence function (CIF) for HAART and AIDS stratified by IDU
data(wihs, package = "randomForestSRC")
wihs.obj <- rfsrc(Surv(time, status) ~ ., wihs, nsplit = 3, ntree = 100)
plot.competing.risk(wihs.obj)
cif <- wihs.obj$cif.oob
Time <- wihs.obj$time.interest
idu <- wihs$idu
cif.haart <- cbind(apply(cif[,,1][idu == 0,], 2, mean),
apply(cif[,,1][idu == 1,], 2, mean))
cif.aids <- cbind(apply(cif[,,2][idu == 0,], 2, mean),
apply(cif[,,2][idu == 1,], 2, mean))
matplot(Time, cbind(cif.haart, cif.aids), type = "l",
lty = c(1,2,1,2), col = c(4, 4, 2, 2), lwd = 3,
ylab = "Cumulative Incidence")
legend("topleft",
legend = c("HAART (Non-IDU)", "HAART (IDU)", "AIDS (Non-IDU)", "AIDS (IDU)"),
lty = c(1,2,1,2), col = c(4, 4, 2, 2), lwd = 3, cex = 1.5)
## illustrates the various splitting rules
## illustrates event specific and non-event specific variable selection
if (library("survival", logical.return = TRUE)) {
## use the pbc data from the survival package
## events are transplant (1) and death (2)
data(pbc, package = "survival")
pbc$id <- NULL
## modified Gray's weighted log-rank splitting
## (equivalent to cause=c(1,1) and splitrule="logrankCR")
pbc.cr <- rfsrc(Surv(time, status) ~ ., pbc)
## log-rank cause-1 specific splitting and targeted VIMP for cause 1
pbc.log1 <- rfsrc(Surv(time, status) ~ ., pbc,
splitrule = "logrank", cause = c(1,0), importance = TRUE)
## log-rank cause-2 specific splitting and targeted VIMP for cause 2
pbc.log2 <- rfsrc(Surv(time, status) ~ ., pbc,
splitrule = "logrank", cause = c(0,1), importance = TRUE)
## extract VIMP from the log-rank forests: event-specific
## extract minimal depth from the Gray log-rank forest: non-event specific
var.perf <- data.frame(md = max.subtree(pbc.cr)$order[, 1],
vimp1 = 100 * pbc.log1$importance[ ,1],
vimp2 = 100 * pbc.log2$importance[ ,2])
print(var.perf[order(var.perf$md), ], digits = 2)
}
## ------------------------------------------------------------
## regression analysis
## ------------------------------------------------------------
## new York air quality measurements
airq.obj <- rfsrc(Ozone ~ ., data = airquality, na.action = "na.impute")
# partial plot of variables (see plot.variable for more details)
plot.variable(airq.obj, partial = TRUE, smooth.lines = TRUE)
## motor trend cars
mtcars.obj <- rfsrc(mpg ~ ., data = mtcars)
## ------------------------------------------------------------
## regression with custom bootstrap
## ------------------------------------------------------------
ntree <- 25
n <- nrow(mtcars)
s.size <- n / 2
swr <- TRUE
samp <- randomForestSRC:::make.sample(ntree, n, s.size, swr)
o <- rfsrc(mpg ~ ., mtcars, bootstrap = "by.user", samp = samp)
## ------------------------------------------------------------
## classification analysis
## ------------------------------------------------------------
## iris data
iris.obj <- rfsrc(Species ~., data = iris)
## wisconsin prognostic breast cancer data
data(breast, package = "randomForestSRC")
breast.obj <- rfsrc(status ~ ., data = breast, block.size=1)
plot(breast.obj)
## ------------------------------------------------------------
## big data set, reduce number of variables using simple method
## ------------------------------------------------------------
## use Iowa housing data set
data(housing, package = "randomForestSRC")
## original data contains lots of missing data, use fast imputation
## however see impute for other methods
housing2 <- impute(data = housing, fast = TRUE)
## run shallow trees to find variables that split any tree
xvar.used <- rfsrc(SalePrice ~., housing2, ntree = 250, nodedepth = 4,
var.used="all.trees", mtry = Inf, nsplit = 100)$var.used
## now fit forest using filtered variables
xvar.keep <- names(xvar.used)[xvar.used >= 1]
o <- rfsrc(SalePrice~., housing2[, c("SalePrice", xvar.keep)])
print(o)
## ------------------------------------------------------------
## imbalanced classification data
## see the "imbalanced" function for further details
##
## a) use balanced random forests with undersampling of the majority class
## Specifically let n0, n1 be sample sizes for majority, minority
## cases. We sample 2 x n1 cases with majority, minority cases chosen
## with probabilities n1/n, n0/n where n=n0+n1
##
## b) balanced random forests using "imbalanced"
##
## c) q-classifier (RFQ) using "imbalanced"
##
## ------------------------------------------------------------
## Wisconsin breast cancer example
data(breast, package = "randomForestSRC")
breast <- na.omit(breast)
## balanced random forests - brute force
y <- breast$status
obdirect <- rfsrc(status ~ ., data = breast, nsplit = 10,
case.wt = randomForestSRC:::make.wt(y),
sampsize = randomForestSRC:::make.size(y))
print(obdirect)
print(get.imbalanced.performance(obdirect))
## balanced random forests - using "imbalanced"
ob <- imbalanced(status ~ ., data = breast, method = "brf")
print(ob)
print(get.imbalanced.performance(ob))
## q-classifier (RFQ) - using "imbalanced"
oq <- imbalanced(status ~ ., data = breast)
print(oq)
print(get.imbalanced.performance(oq))
## q-classifier (RFQ) - with auc splitting
oqauc <- imbalanced(status ~ ., data = breast, splitrule = "auc")
print(oqauc)
print(get.imbalanced.performance(oqauc))
## ------------------------------------------------------------
## unsupervised analysis
## ------------------------------------------------------------
## two equivalent ways to implement unsupervised forests
mtcars.unspv <- rfsrc(Unsupervised() ~., data = mtcars)
mtcars2.unspv <- rfsrc(data = mtcars)
## illustration of sidClustering for the mtcars data
## see sidClustering for more details
mtcars.sid <- sidClustering(mtcars, k = 1:10)
print(split(mtcars, mtcars.sid$cl[, 3]))
print(split(mtcars, mtcars.sid$cl[, 10]))
## ------------------------------------------------------------
## multivariate regression analysis
## ------------------------------------------------------------
mtcars.mreg <- rfsrc(Multivar(mpg, cyl) ~., data = mtcars,
block.size=1, importance = TRUE)
## extract error rates, vimp, and OOB predicted values for all targets
err <- get.mv.error(mtcars.mreg)
vmp <- get.mv.vimp(mtcars.mreg)
pred <- get.mv.predicted(mtcars.mreg)
## standardized error and vimp
err.std <- get.mv.error(mtcars.mreg, standardize = TRUE)
vmp.std <- get.mv.vimp(mtcars.mreg, standardize = TRUE)
## ------------------------------------------------------------
## multivariate mixed forests (nutrigenomic study)
## study effects of diet, lipids and gene expression for mice
## diet, genotype and lipids used as the multivariate y
## genes used for the x features
## ------------------------------------------------------------
## load the data (data is a list)
data(nutrigenomic, package = "randomForestSRC")
## assemble the multivariate y data
ydta <- data.frame(diet = nutrigenomic$diet,
genotype = nutrigenomic$genotype,
nutrigenomic$lipids)
## multivariate mixed forest call
## uses "get.mv.formula" for conveniently setting formula
mv.obj <- rfsrc(get.mv.formula(colnames(ydta)),
data.frame(do.call(cbind, nutrigenomic)),
importance=TRUE, nsplit = 10)
## print results for diet and genotype y values
print(mv.obj, outcome.target = "diet")
print(mv.obj, outcome.target = "genotype")
## extract standardized VIMP
svimp <- get.mv.vimp(mv.obj, standardize = TRUE)
## plot standardized VIMP for diet, genotype and lipid for each gene
boxplot(t(svimp), col = "bisque", cex.axis = .7, las = 2,
outline = FALSE,
ylab = "standardized VIMP",
main = "diet/genotype/lipid VIMP for each gene")
## ------------------------------------------------------------
## custom splitting using the pre-coded examples
## ------------------------------------------------------------
## motor trend cars
mtcars.obj <- rfsrc(mpg ~ ., data = mtcars, splitrule = "custom")
## iris analysis
iris.obj <- rfsrc(Species ~., data = iris, splitrule = "custom1")
## WIHS analysis
wihs.obj <- rfsrc(Surv(time, status) ~ ., wihs, nsplit = 3,
ntree = 100, splitrule = "custom1")
# }
Run the code above in your browser using DataLab