Crossvalidation For Bayesian Additive Regression Trees
Fits the BART model against varying k, power, base, and ntree parameters using K-fold or repeated random subsampling crossvalidation, sharing burn-in between parameter settings. Results are given an array of evalulations of a loss functions on the held-out sets.
xbart(formula, data, subset, weights, offset, verbose = FALSE, n.samples = 200L,
method = c("k-fold", "random subsample"), n.test = c(5, 0.2),
n.reps = 40L, n.burn = c(200L, 150L, 50L),
loss = c("rmse", "log", "mcr"), n.threads = guessNumCores(), n.trees = 75L,
k = NULL, power = 2, base = 0.95, drop = TRUE,
resid.prior = chisq, control = dbartsControl(), sigma = NA_real_)formula |
An object of class |
data |
An optional data frame, list, or environment containing predictors to be used with the
model. For backwards compatibility, can also be the |
subset |
An optional vector specifying a subset of observations to be used in the fitting process. |
weights |
An optional vector of weights to be used in the fitting process. When present, BART fits a model with observations y | x ~ N(f(x), σ^2 / w), where f(x) is the unknown function. |
offset |
An optional vector specifying an offset from 0 for the relationship between the underyling function, f(x), and the response y. Only is useful for binary responses, in which case the model fit is to assume P(Y = 1 | X = x) = Φ(f(x) + offset), where Φ is the standard normal cumulative distribution function. |
verbose |
A logical determining if additional output is printed to the console. |
n.samples |
A positive integer, setting the number of posterior samples drawn for each fit of training data and used by the loss function. |
method |
Character string, either |
n.test |
For each fit, the test sample size or proportion. For method |
n.reps |
A positive integer setting the number of cross validation steps that will be taken. For |
n.burn |
Between one and three positive integers, specifying the 1) initial burn-in, 2) burn-in when moving from
one parameter setting to another, and 3) the burn-in between each random subsample replication. The third
parameter is also the burn in when moving between folds in |
loss |
Either a one of the pre-set loss functions as character-strings ( |
n.threads |
Across different sets of parameters ( |
n.trees |
A vector of positive integers setting the BART hyperparameter for the number of trees in the
sum-of-trees formulation. See |
k |
A vector of positive real numbers, setting the BART hyperparameter for the node-mean prior standard
deviation. If |
power |
A vector of real numbers greater than one, setting the BART hyperparameter for the tree prior's growth probability, given by {base} / (1 + depth)^{power}. |
base |
A vector of real numbers in (0, 1), setting the BART hyperparameter for the tree prior's growth probability. |
drop |
Logical, determining if dimensions with a single value are dropped from the result. |
resid.prior |
An expression of the form |
control |
An object inheriting from |
sigma |
A positive numeric estimate of the residual standard deviation. If |
Crossvalidates n.reps replications against the crossproduct of given hyperparameter vectors
n.trees * k * power * base.
For each fit, either one fold is withheld as test data and n.test - 1 folds are used as
training data or n * n.test observations are withheld as test data and n * (1 - n.test)
used as training. A replication corresponds to fitting all K folds in "k-fold" crossvalidation
or a single fit with "random subsample". The training data is used to fit a model and make
predictions on the test data which are used together with the test data itself to evaluate the loss
function.
loss functions are either the default of average negative log-loss for binary outcomes and
root-mean-squared error for continuous outcomes, missclassification rates for binary outcomes, or a
function with arguments y.test and y.test.hat. y.test.hat is of dimensions
equal to length(y.test) * n.samples. A third option is to pass a list of
list(function, evaluationEnvironment), so as to provide default bindings. RMSE is a monotonic
transformation of the average log-loss for continuous outcomes, so specifying log-loss in that case
calculates RMSE instead.
An array of dimensions n.reps * length(n.trees) *
length(k) * length(power) * length(base).
If drop is TRUE, dimensions of length 1 are omitted. If all hyperparameters
are of length 1, then the result will be a vector of length n.reps. When the result is an
array, the dimnames of the result shall be set to the corresponding hyperparameters.
For method "k-fold", each element is an average across the K fits. For
"random subsample", each element represents a single fit.
Vincent Dorie: vdorie@gmail.com
f <- function(x) {
10 * sin(pi * x[,1] * x[,2]) + 20 * (x[,3] - 0.5)^2 +
10 * x[,4] + 5 * x[,5]
}
set.seed(99)
sigma <- 1.0
n <- 100
x <- matrix(runif(n * 10), n, 10)
Ey <- f(x)
y <- rnorm(n, Ey, sigma)
mad <- function(y.train, y.train.hat)
mean(abs(y.train - apply(y.train.hat, 1L, mean)))
## low iteration numbers to to run quickly
xval <- xbart(x, y, n.samples = 15L, n.reps = 4L, n.burn = c(10L, 3L, 1L),
n.trees = c(5L, 7L),
k = c(1, 2, 4),
power = c(1.5, 2),
base = c(0.75, 0.8, 0.95), n.threads = 1L,
loss = mad)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.