drf {drf}

Distributional Random Forests

Description

Trains a distributional random forest that can be used to estimate statistical functional F(P(Y | X)) for possibly multivariate response Y.

Usage

drf(
  X,
  Y,
  num.trees = 500,
  splitting.rule = "FourierMMD",
  num.features = 10,
  bandwidth = NULL,
  response.scaling = TRUE,
  node.scaling = FALSE,
  sample.weights = NULL,
  clusters = NULL,
  equalize.cluster.weights = FALSE,
  sample.fraction = 0.5,
  mtry = min(ceiling(sqrt(ncol(X)) + 20), ncol(X)),
  min.node.size = 15,
  honesty = TRUE,
  honesty.fraction = 0.5,
  honesty.prune.leaves = TRUE,
  alpha = 0.05,
  imbalance.penalty = 0,
  ci.group.size = 2,
  compute.oob.predictions = TRUE,
  num.threads = NULL,
  seed = stats::runif(1, 0, .Machine$integer.max),
  compute.variable.importance = FALSE
)

Arguments

X

The covariates used in the regression. Can be either a matrix of numerical values, or a data.frame with characters and factors. In the latter case, one-hot-encoding will be implicitely used.

Y

The (multivariate) outcome. A matrix or data.frame of numeric values.

num.trees

Number of trees grown in the forest. Default is 500.

splitting.rule

a character value. The type of splitting rule used, can be either "CART" or "FourierMMD".

num.features

a numeric value, in case of "FourierMMD", the number of random features to sample.

bandwidth

a numeric value, the bandwidth of the Gaussian kernel used in case of "FourierMMD", by default the value is NULL and the median heuristic is used.

response.scaling

a boolean value, should the reponses be globally scaled at first.

node.scaling

a boolean value, should the responses be scaled or not by node.

sample.weights

(experimental) Weights given to an observation in estimation. If NULL, each observation is given the same weight. Default is NULL.

clusters

Vector of integers or factors specifying which cluster each observation corresponds to. Default is NULL (ignored).

equalize.cluster.weights

If FALSE, each unit is given the same weight (so that bigger clusters get more weight). If TRUE, each cluster is given equal weight in the forest. In this case, during training, each tree uses the same number of observations from each drawn cluster: If the smallest cluster has K units, then when we sample a cluster during training, we only give a random K elements of the cluster to the tree-growing procedure. When estimating average treatment effects, each observation is given weight 1/cluster size, so that the total weight of each cluster is the same. Note that, if this argument is FALSE, sample weights may also be directly adjusted via the sample.weights argument. If this argument is TRUE, sample.weights must be set to NULL. Default is FALSE.

sample.fraction

Fraction of the data used to build each tree. Note: If honesty = TRUE, these subsamples will further be cut by a factor of honesty.fraction. Default is 0.5.

mtry

Number of variables tried for each split. Default is \sqrt p + 20 where p is the number of variables.

min.node.size

A target for the minimum number of observations in each tree leaf. Note that nodes with size smaller than min.node.size can occur, as in the original randomForest package. Default is 5.

honesty

Whether to use honest splitting (i.e., sub-sample splitting). Default is TRUE. For a detailed description of honesty, honesty.fraction, honesty.prune.leaves, and recommendations for parameter tuning, see the grf reference for more information (initial source) algorithm reference.

honesty.fraction

The fraction of data that will be used for determining splits if honesty = TRUE. Corresponds to set J1 in the notation of the paper. Default is 0.5 (i.e. half of the data is used for determining splits).

honesty.prune.leaves

If TRUE, prunes the estimation sample tree such that no leaves are empty. If FALSE, keep the same tree as determined in the splits sample (if an empty leave is encountered, that tree is skipped and does not contribute to the estimate). Setting this to FALSE may improve performance on small/marginally powered data, but requires more trees (note: tuning does not adjust the number of trees). Only applies if honesty is enabled. Default is TRUE.

alpha

A tuning parameter that controls the maximum imbalance of a split. Default is 0.05.

imbalance.penalty

A tuning parameter that controls how harshly imbalanced splits are penalized. Default is 0.

ci.group.size

The forest will grow ci.group.size trees on each subsample. In order to provide confidence intervals, ci.group.size must be at least 2. Default is 2.

compute.oob.predictions

Whether OOB predictions on training set should be precomputed. Default is TRUE.

num.threads

Number of threads used in training. By default, the number of threads is set to the maximum hardware concurrency.

seed

The seed of the C++ random number generator.

compute.variable.importance

boolean, should the variable importance be computed in the object.

Value

A trained distributional random forest object.

Examples

# Train a distributional random forest with CART splitting rule.
n <- 100
p <- 2
X <- matrix(rnorm(n * p), n, p)
Y <- X + matrix(rnorm(n * p), ncol=p)
drf.forest <- drf(X = X, Y = Y)

# Predict conditional correlation.
X.test <- matrix(0, 101, p)
X.test[, 1] <- seq(-2, 2, length.out = 101)
cor.pred <- predict(drf.forest, X.test, functional = "cor")

# Predict on out-of-bag training samples.
cor.oob.pred <- predict(drf.forest,  functional = "cor")

# Train a distributional random forest with "FourierMMD" splitting rule.
n <- 100
p <- 2
X <- matrix(rnorm(n * p), n, p)
Y <- X + matrix(rnorm(n * p), ncol=p)
drf.forest <- drf(X = X, Y = Y, splitting.rule = "FourierMMD", num.features = 10)

# Predict conditional correlation.
X.test <- matrix(0, 101, p)
X.test[, 1] <- seq(-2, 2, length.out = 101)
cor.pred <- predict(drf.forest, X.test, functional = "cor")

# Predict on out-of-bag training samples.
cor.oob.pred <- predict(drf.forest,  functional = "cor")