bases (version 0.2.0)

b_bart: Bayesian Additive Regression Tree (BART) features

Description

Generates random features from a BART prior on symmetric trees. Equivalently, the features are the interaction of a small number of indicator functions. The number of interacted indicators is the depth of the symmetric tree, and is drawn from a prior on the tree depth which is calibrated to match the traditional BART prior of Chipman et al. (2010). The variable at each tree node is selected uniformly, and thresholds are selected uniformly from the range of each variable.

Usage

b_bart(
  ...,
  trees = 100,
  depths = bart_depth_prior()(trees),
  vars = NULL,
  thresh = NULL,
  drop = NULL,
  min_drop = 0L,
  ranges = NULL
)
bart_depth_prior(mean_depth = 1.25)

Value

A matrix of indicator variables encoding the random features.

Arguments

...

The variable(s) to build features for. A single data frame or matrix may be provided as well. Missing values are not allowed.

trees

The number of trees to sample.

depths

The depths of each tree. By default, these are drawn from a Poisson distribution calibrated to produce trees with around 2.5 leaves, on average, matching the traditional BART prior.

vars

Integer indices of the variables to use for each tree. If provided, overrides those generated automatically by sampling uniformly from the available input features. Provided in flat form, so should have length equal to sum(depths).

thresh

The thresholds for each variable. If provided, overrides those generated automatically by sampling uniformly from ranges, which defaults to the range of each input feature. Provided in flat form, so should have length equal to sum(depths).

drop

Columns in the calculated indicator matrix to drop. By default, any leaves which match zero input rows are dropped. If provided, overrides this default.

min_drop

Controls the default dropping of columns. Leaves which match min_drop or fewer input rows are dropped. Defaults to 0, so only empty leaves are dropped.

ranges

The range of the input features, provided as a matrix with two rows and a column for each input feature. The first row is the minimum and the second row is the maximum.

mean_depth

The mean prior depth of each tree, where a single node has depth zero and a two-leaf tree has depth 1. This value minus one becomes the rate parameter of a Poisson distribution, whose samples are then shifted up by one. In this way, no zero-depth trees (which produce trivial features) are sampled.

Functions

• bart_depth_prior(): Poisson depth prior for random trees, parametrized in terms of mean tree depth. Returns a function which generates samples from the prior with argument giving the number of samples. The default prior closely matches the average number of leaves in the original (asymmetric) BART prior.

References

Hugh A. Chipman. Edward I. George. Robert E. McCulloch. "BART: Bayesian additive regression trees." Ann. Appl. Stat. 4 (1) 266 - 298, March 2010. https://doi.org/10.1214/09-AOAS285

Examples

X = with(mtcars, b_bart(cyl, disp, hp, drat, wt, trees = 50))
all(colSums(X) > 0) # TRUE; empty leaves are pruned away
# each row belongs to 1 leaf node per tree; some trees pruned away
all(rowSums(X) == rowSums(X)[1]) # TRUE
all(rowSums(X) <= 50) # TRUE

x = 1:150
y = as.numeric(BJsales)
m = ridge(y ~ b_bart(x, trees=25))
plot(x, y)
lines(x, fitted(m), type="s", col="blue")