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Build a BART Model

Source: R/bartMachine.R, R/bart_package_builders.R
bartMachine.Rd

Builds a BART model for regression or classification.

Usage

bartMachine(
  X = NULL,
  y = NULL,
  Xy = NULL,
  num_trees = 50,
  num_burn_in = 250,
  num_iterations_after_burn_in = 1000,
  alpha = 0.95,
  beta = 2,
  k = 2,
  q = 0.9,
  nu = 3,
  prob_rule_class = 0.5,
  mh_prob_steps = c(2.5, 2.5, 4)/9,
  debug_log = FALSE,
  run_in_sample = TRUE,
  s_sq_y = "mse",
  sig_sq_est = NULL,
  print_tree_illustrations = FALSE,
  cov_prior_vec = NULL,
  interaction_constraints = NULL,
  use_missing_data = FALSE,
  covariates_to_permute = NULL,
  num_rand_samps_in_library = 10000,
  use_missing_data_dummies_as_covars = FALSE,
  replace_missing_data_with_x_j_bar = FALSE,
  impute_missingness_with_rf_impute = FALSE,
  impute_missingness_with_x_j_bar_for_lm = TRUE,
  mem_cache_for_speed = TRUE,
  flush_indices_to_save_RAM = TRUE,
  serialize = FALSE,
  seed = NULL,
  use_xoshiro = FALSE,
  verbose = TRUE
)

build_bart_machine(
  X = NULL,
  y = NULL,
  Xy = NULL,
  num_trees = 50,
  num_burn_in = 250,
  num_iterations_after_burn_in = 1000,
  alpha = 0.95,
  beta = 2,
  k = 2,
  q = 0.9,
  nu = 3,
  prob_rule_class = 0.5,
  mh_prob_steps = c(2.5, 2.5, 4)/9,
  debug_log = FALSE,
  run_in_sample = TRUE,
  s_sq_y = "mse",
  sig_sq_est = NULL,
  print_tree_illustrations = FALSE,
  cov_prior_vec = NULL,
  interaction_constraints = NULL,
  use_missing_data = FALSE,
  covariates_to_permute = NULL,
  num_rand_samps_in_library = 10000,
  use_missing_data_dummies_as_covars = FALSE,
  replace_missing_data_with_x_j_bar = FALSE,
  impute_missingness_with_rf_impute = FALSE,
  impute_missingness_with_x_j_bar_for_lm = TRUE,
  mem_cache_for_speed = TRUE,
  flush_indices_to_save_RAM = TRUE,
  serialize = FALSE,
  seed = NULL,
  use_xoshiro = FALSE,
  verbose = TRUE
)

Arguments

X

Data frame of predictors. Factors are automatically converted to dummies internally.

y

Vector of response variable. If y is numeric or integer, a BART model for regression is built. If y is a factor with two levels, a BART model for classification is built.

Xy

A data frame of predictors and the response. The response column must be named “y”.

num_trees

The number of trees to be grown in the sum-of-trees model.

num_burn_in

Number of MCMC samples to be discarded as “burn-in”.

num_iterations_after_burn_in

Number of MCMC samples to draw from the posterior distribution of \(\hat{f}(x)\).

alpha

Base hyperparameter in tree prior for whether a node is nonterminal or not.

beta

Power hyperparameter in tree prior for whether a node is nonterminal or not.

k

For regression, k determines the prior probability that \(E(Y|X)\) is contained in the interval \((y_{min}, y_{max})\), based on a normal distribution. For example, when \(k=2\), the prior probability is 95%. For classification, k determines the prior probability that \(E(Y|X)\) is between \((-3,3)\). Note that a larger value of k results in more shrinkage and a more conservative fit.

q

Quantile of the prior on the error variance at which the data-based estimate is placed. Note that the larger the value of q, the more aggressive the fit as you are placing more prior weight on values lower than the data-based estimate. Not used for classification.

nu

Degrees of freedom for the inverse \(\chi^2\) prior. Not used for classification.

prob_rule_class

Threshold for classification. Any observation with a conditional probability greater than prob_class_rule is assigned the “positive” outcome. Note that the first level of the response is treated as the “positive” outcome and the second is treated as the “negative” outcome.

mh_prob_steps

Vector of prior probabilities for proposing changes to the tree structures: (GROW, PRUNE, CHANGE)

debug_log

If TRUE, additional information about the model construction are printed to a file in the working directory.

run_in_sample

If TRUE, in-sample statistics such as \(\hat{f}(x)\), Pseudo-\(R^2\), and RMSE are computed. Setting this to FALSE when not needed can decrease computation time.

s_sq_y

If “mse”, a data-based estimated of the error variance is computed as the MSE from ordinary least squares regression. If “var”., the data-based estimate is computed as the variance of the response. Not used in classification.

sig_sq_est

Pass in an estimate of the maximum sig_sq of the model. This is useful to cache somewhere and then pass in during cross-validation since the default method of estimation is a linear model. In large dimensions, linear model estimation is slow.

print_tree_illustrations

For every Gibbs iteration, print out an illustration of the trees side-by-side. This is excruciatingly SLOW!

cov_prior_vec

Vector assigning relative weights to how often a particular variable should be proposed as a candidate for a split. The vector is internally normalized so that the weights sum to 1. Note that the length of this vector must equal the length of the design matrix after dummification and augmentation of indicators of missingness (if used). To see what the dummified matrix looks like, use dummify_data. See Bleich et al. (2013) for more details on when this feature is most appropriate.

interaction_constraints

A list of vectors indicating where the vectors are sets of elements allowed to interact with one another. The elements in each vector correspond to features in the data frame X specified by either the column number as a numeric value or the column name as a string e.g. list(c(1, 2), c("nox", "rm")). The elements of the vectors can be reused among components for any level of interaction complexity you wish. Default is NULL which corresponds to the vanilla modeling procedure where all interactions are legal. For a pure generalized added model, use as.list(seq(1 : p)) where p is the number of columns in the design matrix X.

use_missing_data

If TRUE, the missing data feature is used to automatically handle missing data without imputation. See Kapelner and Bleich (2013) for details.

covariates_to_permute

Private argument for cov_importance_test. Not needed by user.

num_rand_samps_in_library

Before building a BART model, samples from the Standard Normal and \(\chi^2(\nu)\) are drawn to be used in the MCMC steps. This parameter determines the number of samples to be taken.

use_missing_data_dummies_as_covars

If TRUE, additional indicator variables for whether or not an observation in a particular column is missing are included. See Kapelner and Bleich (2013) for details.

replace_missing_data_with_x_j_bar

If TRUE ,missing entries in X are imputed with average value or modal category.

impute_missingness_with_rf_impute

If TRUE, missing entries are filled in using the rf.impute() function from the randomForest library.

impute_missingness_with_x_j_bar_for_lm

If TRUE, when computing the data-based estimate of \(\sigma^2\), missing entries are imputed with average value or modal category.

mem_cache_for_speed

Speed enhancement that caches the predictors and the split values that are available at each node for selecting new rules. If the number of predictors is large, the memory requirements become large. We recommend keeping this on (default) and turning it off if you experience out-of-memory errors.

flush_indices_to_save_RAM

Setting this flag to TRUE saves memory with the downside that you cannot use the functions node_prediction_training_data_indices nor get_projection_weights.

serialize

Setting this option to TRUE will allow serialization of bartMachine objects which allows for persistence between R sessions if the object is saved and reloaded. Note that serialized objects can take up a large amount of memory. Thus, the default is FALSE.

seed

Optional: sets the seed in both R and Java. Default is NULL which does not set the seed in R nor Java. Setting the seed enforces deterministic behavior only in the case when one core is used (the default before set_bart_machine_num_cores() was invoked.

use_xoshiro

if TRUE, use the Xoshiro256PlusPlus random number generator; if FALSE, use the legacy MersenneTwister random number generator (default is FALSE)

verbose

Prints information about progress of the algorithm to the screen.

Value

Returns an object of class “bartMachine”. The “bartMachine” object contains a list of the following components:

java_bart_machine

A pointer to the BART Java object.

train_data_features

The names of the variables used in the training data.

training_data_features_with_missing_features.

The names of the variables used in the training data. If use_missing_data_dummies_as_covars = TRUE, this also includes dummies for any predictors that contain at least one missing entry (named “M_<feature>”).

y

The values of the response for the training data.

y_levels

The levels of the response (for classification only).

pred_type

Whether the model was build for regression of classification.

model_matrix_training_data

The training data with factors converted to dummies.

num_cores

The number of cores used to build the BART model.

sig_sq_est

The data-based estimate of \(\sigma^2\) used to create the prior on the error variance for the BART model.

time_to_build

Total time to build the BART model.

y_hat_train

The posterior means of \(\hat{f}(x)\) for each observation. Only returned if run_in_sample = TRUE.

residuals

The model residuals given by y - y_hat_train. Only returned if run_in_sample = TRUE.

L1_err_train

L1 error on the training set. Only returned if run_in_sample = TRUE.

L2_err_train

L2 error on the training set. Only returned if run_in_sample = TRUE.

PseudoRsq

Calculated as 1 - SSE / SST where SSE is the sum of square errors in the training data and SST is the sample variance of the response times \(n-1\). Only returned if run_in_sample = TRUE.

rmse_train

Root mean square error on the training set. Only returned if run_in_sample = TRUE.

Additionally, the parameters passed to the function bartMachine are also components of the list.

Note

This function is parallelized by the number of cores set by set_bart_machine_num_cores. Each core will create an independent MCMC chain of size
num_burn_in \(+\) num_iterations_after_burn_in / bart_machine_num_cores.

References

Adam Kapelner, Justin Bleich (2016). bartMachine: Machine Learning with Bayesian Additive Regression Trees. Journal of Statistical Software, 70(4), 1-40. doi:10.18637/jss.v070.i04

HA Chipman, EI George, and RE McCulloch. BART: Bayesian Additive Regressive Trees. The Annals of Applied Statistics, 4(1): 266–298, 2010.

A Kapelner and J Bleich. Prediction with Missing Data via Bayesian Additive Regression Trees. Canadian Journal of Statistics, 43(2): 224-239, 2015

J Bleich, A Kapelner, ST Jensen, and EI George. Variable Selection Inference for Bayesian Additive Regression Trees. ArXiv e-prints, 2013.

See also

bartMachineCV

Author

Adam Kapelner and Justin Bleich

Examples

if (FALSE) { # \dontrun{
##regression example

##generate Friedman data
set.seed(11)
n  = 200
p = 5
X = data.frame(matrix(runif(n * p), ncol = p))
y = 10 * sin(pi* X[ ,1] * X[,2]) +20 * (X[,3] -.5)^2 + 10 * X[ ,4] + 5 * X[,5] + rnorm(n)

##build BART regression model
bart_machine = bartMachine(X, y)
summary(bart_machine)

##Build another BART regression model
bart_machine = bartMachine(X,y, num_trees = 200, num_burn_in = 500,
num_iterations_after_burn_in = 1000)

##Classification example

#get data and only use 2 factors
data(iris)
iris2 = iris[51:150,]
iris2$Species = factor(iris2$Species)

#build BART classification model
bart_machine = build_bart_machine(iris2[ ,1:4], iris2$Species)

##get estimated probabilities
phat = bart_machine$p_hat_train
##look at in-sample confusion matrix
bart_machine$confusion_matrix
} # }