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Run the BART algorithm for supervised learning.

Source: R/bart.R
bart.Rd

Run the BART algorithm for supervised learning.

Usage

bart(
  X_train,
  y_train,
  leaf_basis_train = NULL,
  rfx_group_ids_train = NULL,
  rfx_basis_train = NULL,
  X_test = NULL,
  leaf_basis_test = NULL,
  rfx_group_ids_test = NULL,
  rfx_basis_test = NULL,
  num_gfr = 5,
  num_burnin = 0,
  num_mcmc = 100,
  previous_model_json = NULL,
  previous_model_warmstart_sample_num = NULL,
  general_params = list(),
  mean_forest_params = list(),
  variance_forest_params = list(),
  random_effects_params = list()
)

Arguments

X_train

Covariates used to split trees in the ensemble. May be provided either as a dataframe or a matrix. Matrix covariates will be assumed to be all numeric. Covariates passed as a dataframe will be preprocessed based on the variable types (e.g. categorical columns stored as unordered factors will be one-hot encoded, categorical columns stored as ordered factors will passed as integers to the core algorithm, along with the metadata that the column is ordered categorical).

y_train

Outcome to be modeled by the ensemble.

leaf_basis_train

(Optional) Bases used to define a regression model y ~ W in each leaf of each regression tree. By default, BART assumes constant leaf node parameters, implicitly regressing on a constant basis of ones (i.e. y ~ 1).

rfx_group_ids_train

(Optional) Group labels used for an additive random effects model.

rfx_basis_train

(Optional) Basis for "random-slope" regression in an additive random effects model. If rfx_group_ids_train is provided with a regression basis, an intercept-only random effects model will be estimated.

X_test

(Optional) Test set of covariates used to define "out of sample" evaluation data. May be provided either as a dataframe or a matrix, but the format of X_test must be consistent with that of X_train.

leaf_basis_test

(Optional) Test set of bases used to define "out of sample" evaluation data. While a test set is optional, the structure of any provided test set must match that of the training set (i.e. if both X_train and leaf_basis_train are provided, then a test set must consist of X_test and leaf_basis_test with the same number of columns).

rfx_group_ids_test

(Optional) Test set group labels used for an additive random effects model. We do not currently support (but plan to in the near future), test set evaluation for group labels that were not in the training set.

rfx_basis_test

(Optional) Test set basis for "random-slope" regression in additive random effects model.

num_gfr

Number of "warm-start" iterations run using the grow-from-root algorithm (He and Hahn, 2021). Default: 5.

num_burnin

Number of "burn-in" iterations of the MCMC sampler. Default: 0.

num_mcmc

Number of "retained" iterations of the MCMC sampler. Default: 100.

previous_model_json

(Optional) JSON string containing a previous BART model. This can be used to "continue" a sampler interactively after inspecting the samples or to run parallel chains "warm-started" from existing forest samples. Default: NULL.

previous_model_warmstart_sample_num

(Optional) Sample number from previous_model_json that will be used to warmstart this BART sampler. One-indexed (so that the first sample is used for warm-start by setting previous_model_warmstart_sample_num = 1). Default: NULL.

general_params

(Optional) A list of general (non-forest-specific) model parameters, each of which has a default value processed internally, so this argument list is optional.

  • cutpoint_grid_size Maximum size of the "grid" of potential cutpoints to consider in the GFR algorithm. Default: 100.

  • standardize Whether or not to standardize the outcome (and store the offset / scale in the model object). Default: TRUE.

  • sample_sigma2_global Whether or not to update the sigma^2 global error variance parameter based on IG(sigma2_global_shape, sigma2_global_scale). Default: TRUE.

  • sigma2_global_init Starting value of global error variance parameter. Calibrated internally as 1.0*var(y_train), where y_train is the possibly standardized outcome, if not set.

  • sigma2_global_shape Shape parameter in the IG(sigma2_global_shape, sigma2_global_scale) global error variance model. Default: 0.

  • sigma2_global_scale Scale parameter in the IG(sigma2_global_shape, sigma2_global_scale) global error variance model. Default: 0.

  • variable_weights Numeric weights reflecting the relative probability of splitting on each variable. Does not need to sum to 1 but cannot be negative. Defaults to rep(1/ncol(X_train), ncol(X_train)) if not set here. Note that if the propensity score is included as a covariate in either forest, its weight will default to 1/ncol(X_train).

  • random_seed Integer parameterizing the C++ random number generator. If not specified, the C++ random number generator is seeded according to std::random_device.

  • keep_burnin Whether or not "burnin" samples should be included in the stored samples of forests and other parameters. Default FALSE. Ignored if num_mcmc = 0.

  • keep_gfr Whether or not "grow-from-root" samples should be included in the stored samples of forests and other parameters. Default FALSE. Ignored if num_mcmc = 0.

  • keep_every How many iterations of the burned-in MCMC sampler should be run before forests and parameters are retained. Default 1. Setting keep_every <- k for some k > 1 will "thin" the MCMC samples by retaining every k-th sample, rather than simply every sample. This can reduce the autocorrelation of the MCMC samples.

  • num_chains How many independent MCMC chains should be sampled. If num_mcmc = 0, this is ignored. If num_gfr = 0, then each chain is run from root for num_mcmc * keep_every + num_burnin iterations, with num_mcmc samples retained. If num_gfr > 0, each MCMC chain will be initialized from a separate GFR ensemble, with the requirement that num_gfr >= num_chains. Default: 1.

  • verbose Whether or not to print progress during the sampling loops. Default: FALSE.

  • probit_outcome_model Whether or not the outcome should be modeled as explicitly binary via a probit link. If TRUE, y must only contain the values 0 and 1. Default: FALSE.

  • num_threads Number of threads to use in the GFR and MCMC algorithms, as well as prediction. If OpenMP is not available on a user's setup, this will default to 1, otherwise to the maximum number of available threads.

mean_forest_params

(Optional) A list of mean forest model parameters, each of which has a default value processed internally, so this argument list is optional.

  • num_trees Number of trees in the ensemble for the conditional mean model. Default: 200. If num_trees = 0, the conditional mean will not be modeled using a forest, and the function will only proceed if num_trees > 0 for the variance forest.

  • alpha Prior probability of splitting for a tree of depth 0 in the mean model. Tree split prior combines alpha and beta via alpha*(1+node_depth)^-beta. Default: 0.95.

  • beta Exponent that decreases split probabilities for nodes of depth > 0 in the mean model. Tree split prior combines alpha and beta via alpha*(1+node_depth)^-beta. Default: 2.

  • min_samples_leaf Minimum allowable size of a leaf, in terms of training samples, in the mean model. Default: 5.

  • max_depth Maximum depth of any tree in the ensemble in the mean model. Default: 10. Can be overridden with -1 which does not enforce any depth limits on trees.

  • sample_sigma2_leaf Whether or not to update the leaf scale variance parameter based on IG(sigma2_leaf_shape, sigma2_leaf_scale). Cannot (currently) be set to true if ncol(leaf_basis_train)>1. Default: FALSE.

  • sigma2_leaf_init Starting value of leaf node scale parameter. Calibrated internally as 1/num_trees if not set here.

  • sigma2_leaf_shape Shape parameter in the IG(sigma2_leaf_shape, sigma2_leaf_scale) leaf node parameter variance model. Default: 3.

  • sigma2_leaf_scale Scale parameter in the IG(sigma2_leaf_shape, sigma2_leaf_scale) leaf node parameter variance model. Calibrated internally as 0.5/num_trees if not set here.

  • keep_vars Vector of variable names or column indices denoting variables that should be included in the forest. Default: NULL.

  • drop_vars Vector of variable names or column indices denoting variables that should be excluded from the forest. Default: NULL. If both drop_vars and keep_vars are set, drop_vars will be ignored.

  • num_features_subsample How many features to subsample when growing each tree for the GFR algorithm. Defaults to the number of features in the training dataset.

variance_forest_params

(Optional) A list of variance forest model parameters, each of which has a default value processed internally, so this argument list is optional.

  • num_trees Number of trees in the ensemble for the conditional variance model. Default: 0. Variance is only modeled using a tree / forest if num_trees > 0.

  • alpha Prior probability of splitting for a tree of depth 0 in the variance model. Tree split prior combines alpha and beta via alpha*(1+node_depth)^-beta. Default: 0.95.

  • beta Exponent that decreases split probabilities for nodes of depth > 0 in the variance model. Tree split prior combines alpha and beta via alpha*(1+node_depth)^-beta. Default: 2.

  • min_samples_leaf Minimum allowable size of a leaf, in terms of training samples, in the variance model. Default: 5.

  • max_depth Maximum depth of any tree in the ensemble in the variance model. Default: 10. Can be overridden with -1 which does not enforce any depth limits on trees.

  • leaf_prior_calibration_param Hyperparameter used to calibrate the IG(var_forest_prior_shape, var_forest_prior_scale) conditional error variance model. If var_forest_prior_shape and var_forest_prior_scale are not set below, this calibration parameter is used to set these values to num_trees / leaf_prior_calibration_param^2 + 0.5 and num_trees / leaf_prior_calibration_param^2, respectively. Default: 1.5.

  • var_forest_leaf_init Starting value of root forest prediction in conditional (heteroskedastic) error variance model. Calibrated internally as log(0.6*var(y_train))/num_trees, where y_train is the possibly standardized outcome, if not set.

  • var_forest_prior_shape Shape parameter in the IG(var_forest_prior_shape, var_forest_prior_scale) conditional error variance model (which is only sampled if num_trees > 0). Calibrated internally as num_trees / leaf_prior_calibration_param^2 + 0.5 if not set.

  • var_forest_prior_scale Scale parameter in the IG(var_forest_prior_shape, var_forest_prior_scale) conditional error variance model (which is only sampled if num_trees > 0). Calibrated internally as num_trees / leaf_prior_calibration_param^2 if not set.

  • keep_vars Vector of variable names or column indices denoting variables that should be included in the forest. Default: NULL.

  • drop_vars Vector of variable names or column indices denoting variables that should be excluded from the forest. Default: NULL. If both drop_vars and keep_vars are set, drop_vars will be ignored.

  • num_features_subsample How many features to subsample when growing each tree for the GFR algorithm. Defaults to the number of features in the training dataset.

random_effects_params

(Optional) A list of random effects model parameters, each of which has a default value processed internally, so this argument list is optional.

  • model_spec Specification of the random effects model. Options are "custom" and "intercept_only". If "custom" is specified, then a user-provided basis must be passed through rfx_basis_train. If "intercept_only" is specified, a random effects basis of all ones will be dispatched internally at sampling and prediction time. If "intercept_plus_treatment" is specified, a random effects basis that combines an "intercept" basis of all ones with the treatment variable (Z_train) will be dispatched internally at sampling and prediction time. Default: "custom". If "intercept_only" is specified, rfx_basis_train and rfx_basis_test (if provided) will be ignored.

  • working_parameter_prior_mean Prior mean for the random effects "working parameter". Default: NULL. Must be a vector whose dimension matches the number of random effects bases, or a scalar value that will be expanded to a vector.

  • group_parameters_prior_mean Prior mean for the random effects "group parameters." Default: NULL. Must be a vector whose dimension matches the number of random effects bases, or a scalar value that will be expanded to a vector.

  • working_parameter_prior_cov Prior covariance matrix for the random effects "working parameter." Default: NULL. Must be a square matrix whose dimension matches the number of random effects bases, or a scalar value that will be expanded to a diagonal matrix.

  • group_parameter_prior_cov Prior covariance matrix for the random effects "group parameters." Default: NULL. Must be a square matrix whose dimension matches the number of random effects bases, or a scalar value that will be expanded to a diagonal matrix.

  • variance_prior_shape Shape parameter for the inverse gamma prior on the variance of the random effects "group parameter." Default: 1.

  • variance_prior_scale Scale parameter for the inverse gamma prior on the variance of the random effects "group parameter." Default: 1.

Value

List of sampling outputs and a wrapper around the sampled forests (which can be used for in-memory prediction on new data, or serialized to JSON on disk).

Examples

n <- 100
p <- 5
X <- matrix(runif(n*p), ncol = p)
f_XW <- (
    ((0 <= X[,1]) & (0.25 > X[,1])) * (-7.5) +
    ((0.25 <= X[,1]) & (0.5 > X[,1])) * (-2.5) +
    ((0.5 <= X[,1]) & (0.75 > X[,1])) * (2.5) +
    ((0.75 <= X[,1]) & (1 > X[,1])) * (7.5)
)
noise_sd <- 1
y <- f_XW + rnorm(n, 0, noise_sd)
test_set_pct <- 0.2
n_test <- round(test_set_pct*n)
n_train <- n - n_test
test_inds <- sort(sample(1:n, n_test, replace = FALSE))
train_inds <- (1:n)[!((1:n) %in% test_inds)]
X_test <- X[test_inds,]
X_train <- X[train_inds,]
y_test <- y[test_inds]
y_train <- y[train_inds]

bart_model <- bart(X_train = X_train, y_train = y_train, X_test = X_test,
                   num_gfr = 10, num_burnin = 0, num_mcmc = 10)