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`

(defined via `cforest_control`

)
bootstrap samples of the learning sample. Most of the hyper parameters in
`cforest_control`

regulate the construction of the conditional inference trees.
Therefore you MUST NOT change anything you don't understand completely.

Hyper parameters you might want to change in `cforest_control`

are:

1. The number of randomly preselected variables `mtry`

, which is fixed
to the value 5 by default here for technical reasons, while in
`randomForest`

the default values for classification and regression
vary with 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) for a description.

Predictions can be computed using `predict`

. For observations
with zero weights, predictions are computed from the fitted tree
when `newdata = NULL`

. While `predict`

returns predictions
of the same type as the response in the data set by default (i.e., predicted class labels for factors),
`treeresponse`

returns the statistics of the conditional distribution of the response
(i.e., predicted class probabilities for factors). The same is done by `predict(..., type = "prob")`

.
Note that for multivariate responses `predict`

does not convert predictions to the type
of the response, i.e., `type = "prob"`

is used.

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., 2006a) or to
multivariate and ordered responses.

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).

The `proximity`

matrix is an \(n \times n\) matrix \(P\) with \(P_{ij}\)
equal to the fraction of trees where observations \(i\) and \(j\)
are element of the same terminal node (when both \(i\) and \(j\)
had non-zero weights in the same bootstrap sample).