BCF

stochtree.bcf.BCFModel

Class that handles sampling, storage, and serialization of stochastic forest models for causal effect estimation. The class takes its name from Bayesian Causal Forests, an MCMC sampler originally developed in Hahn, Murray, Carvalho (2020), but supports several sampling algorithms:

• MCMC: The "classic" sampler defined in Hahn, Murray, Carvalho (2020). In order to run the MCMC sampler, set num_gfr = 0 (explained below) and then define a sampler according to several parameters:
  • num_burnin: the number of iterations to run before "retaining" samples for further analysis. These "burned in" samples are helpful for allowing a sampler to converge before retaining samples.
  • num_chains: the number of independent sequences of MCMC samples to generate (typically referred to in the literature as "chains")
  • num_mcmc: the number of "retained" samples of the posterior distribution
  • keep_every: after a sampler has "burned in", we will run the sampler for keep_every * num_mcmc iterations, retaining one of each keep_every iteration in a chain.
• GFR (Grow-From-Root): A fast, greedy approximation of the BART MCMC sampling algorithm introduced in Krantsevich, He, and Hahn (2023). GFR sampler iterations are governed by the num_gfr parameter, and there are two primary ways to use this sampler:
  • Standalone: setting num_gfr > 0 and both num_burnin = 0 and num_mcmc = 0 will only run and retain GFR samples of the posterior. This is typically referred to as "XBART" (accelerated BART).
  • Initializer for MCMC: setting num_gfr > 0 and num_mcmc > 0 will use ensembles from the GFR algorithm to initialize num_chains independent MCMC BART samplers, which are run for num_mcmc iterations. This is typically referred to as "warm start BART".

In addition to enabling multiple samplers, we support a broad set of models. First, note that the original BCF model of Hahn, Murray, Carvalho (2020) is

\[\begin{equation*} \begin{aligned} y &= a(X) + b_z(X) + \epsilon\\ b_z(X) &= (b_1 Z + b_0 (1-Z)) t(X)\\ b_0, b_1 &\sim N(0, \frac{1}{2})\\\\ a(X) &\sim \text{BART}()\\ t(X) &\sim \text{BART}()\\ \epsilon &\sim N(0, \sigma^2)\\ \sigma^2 &\sim IG(a, b) \end{aligned} \end{equation*}\]

for continuous outcome \(y\), binary treatment \(Z\), and covariates \(X\).

In words, there are two nonparametric mean functions -- a "prognostic" function and a "treatment effect" function -- governed by tree ensembles with BART priors and an additive (mean-zero) Gaussian error term, whose variance is parameterized with an inverse gamma prior.

The BCFModel class supports the following extensions of this model:

• Continuous Treatment: If \(Z\) is continuous rather than binary, we define \(b_z(X) = \tau(X, Z) = Z \tau(X)\), where the "leaf model" for the \(\tau\) forest is essentially a regression on continuous \(Z\).
• Heteroskedasticity: Rather than define \(\epsilon\) parameterically, we can let a forest \(\sigma^2(X)\) model a conditional error variance function. This can be done by setting num_trees_variance > 0 in the params dictionary passed to the sample method.

sample(X_train, Z_train, y_train, pi_train=None, X_test=None, Z_test=None, pi_test=None, num_gfr=5, num_burnin=0, num_mcmc=100, params=None)

Runs a BCF sampler on provided training set. Outcome predictions and estimates of the prognostic and treatment effect functions will be cached for the training set and (if provided) the test set.

Parameters:

Name	Type	Description	Default
X_train	array or DataFrame	Covariates used to split trees in the ensemble. Can be passed as either a matrix or dataframe.	required
Z_train	array	Array of (continuous or binary; univariate or multivariate) treatment assignments.	required
y_train	array	Outcome to be modeled by the ensemble.	required
pi_train	array	Optional vector of propensity scores. If not provided, this will be estimated from the data.	None
X_test	array	Optional test set of covariates used to define "out of sample" evaluation data.	None
Z_test	array	Optional test set of (continuous or binary) treatment assignments. Must be provided if X_test is provided.	None
pi_test	array	Optional test set vector of propensity scores. If not provided (but X_test and Z_test are), this will be estimated from the data.	None
num_gfr	int	Number of "warm-start" iterations run using the grow-from-root algorithm (He and Hahn, 2021). Defaults to 5.	5
num_burnin	int	Number of "burn-in" iterations of the MCMC sampler. Defaults to 0. Ignored if num_gfr > 0.	0
num_mcmc	int	Number of "retained" iterations of the MCMC sampler. Defaults to 100. If this is set to 0, GFR (XBART) samples will be retained.	100
params	dict	Dictionary of model parameters, each of which has a default value. cutpoint_grid_size (int): Maximum number of cutpoints to consider for each feature. Defaults to 100. sigma_leaf_mu (float): Starting value of leaf node scale parameter for the prognostic forest. Calibrated internally as 2/num_trees_mu if not set here. sigma_leaf_tau (float or np.array): Starting value of leaf node scale parameter for the treatment effect forest. When treatment (Z_train) is multivariate, this can be either a float or a square 2-dimensional np.array with sigma_leaf_tau.shape[0] == Z_train.shape[1] and sigma_leaf_tau.shape[1] == Z_train.shape[1]. If sigma_leaf_tau is provided as a float for multivariate treatment, the leaf scale term will be set as a diagonal matrix with sigma_leaf_tau on every diagonal. If not passed as an argument, this parameter is calibrated internally as 1/num_trees_tau (and propagated to a diagonal matrix if necessary). alpha_mu (float): Prior probability of splitting for a tree of depth 0 for the prognostic forest. Tree split prior combines alpha and beta via alpha*(1+node_depth)^-beta. alpha_tau (float): Prior probability of splitting for a tree of depth 0 for the treatment effect forest. Tree split prior combines alpha and beta via alpha*(1+node_depth)^-beta. alpha_variance (float): Prior probability of splitting for a tree of depth 0 in the conditional variance model. Tree split prior combines alpha_variance and beta_variance via alpha_variance*(1+node_depth)^-beta_variance. beta_mu (float): Exponent that decreases split probabilities for nodes of depth > 0 for the prognostic forest. Tree split prior combines alpha and beta via alpha*(1+node_depth)^-beta. beta_tau (float): Exponent that decreases split probabilities for nodes of depth > 0 for the treatment effect forest. Tree split prior combines alpha and beta via alpha*(1+node_depth)^-beta. beta_variance (float): Exponent that decreases split probabilities for nodes of depth > 0 in the conditional variance model. Tree split prior combines alpha_variance and beta_variance via alpha_variance*(1+node_depth)^-beta_variance. min_samples_leaf_mu (int): Minimum allowable size of a leaf, in terms of training samples, for the prognostic forest. Defaults to 5. min_samples_leaf_tau (int): Minimum allowable size of a leaf, in terms of training samples, for the treatment effect forest. Defaults to 5. min_samples_leaf_variance (int): Minimum allowable size of a leaf, in terms of training samples in the conditional variance model. Defaults to 5. max_depth_mu (int): Maximum depth of any tree in the mu ensemble. Defaults to 10. Can be overriden with -1 which does not enforce any depth limits on trees. max_depth_tau (int): Maximum depth of any tree in the tau ensemble. Defaults to 5. Can be overriden with -1 which does not enforce any depth limits on trees. max_depth_variance (int): Maximum depth of any tree in the ensemble in the conditional variance model. Defaults to 10. Can be overriden with -1 which does not enforce any depth limits on trees. a_global (float): Shape parameter in the IG(a_global, b_global) global error variance model. Defaults to 0. b_global (float): Component of the scale parameter in the IG(a_global, b_global) global error variance prior. Defaults to 0. a_leaf_mu (float): Shape parameter in the IG(a_leaf, b_leaf) leaf node parameter variance model for the prognostic forest. Defaults to 3. a_leaf_tau (float): Shape parameter in the IG(a_leaf, b_leaf) leaf node parameter variance model for the treatment effect forest. Defaults to 3. b_leaf_mu (float): Scale parameter in the IG(a_leaf, b_leaf) leaf node parameter variance model for the prognostic forest. Calibrated internally as 0.5/num_trees if not set here. b_leaf_tau (float): Scale parameter in the IG(a_leaf, b_leaf) leaf node parameter variance model for the treatment effect forest. Calibrated internally as 0.5/num_trees if not set here. sigma2_init (float): Starting value of global variance parameter. Calibrated internally as in Sparapani et al (2021) if not set here. variance_forest_leaf_init (float): Starting value of root forest prediction in conditional (heteroskedastic) error variance model. Calibrated internally as np.log(pct_var_variance_forest_init*np.var((y-np.mean(y))/np.std(y)))/num_trees_variance if not set. pct_var_sigma2_init (float): Percentage of standardized outcome variance used to initialize global error variance parameter. Superseded by sigma2. Defaults to 0.25. pct_var_variance_forest_init (float): Percentage of standardized outcome variance used to initialize global error variance parameter. Default: 1. Superseded by variance_forest_init. variable_weights_mean (np.array): Numeric weights reflecting the relative probability of splitting on each variable in the prognostic and treatment effect forests. Does not need to sum to 1 but cannot be negative. Defaults tonp.repeat(1/X_train.shape[1], X_train.shape[1])if not set here. Note that if the propensity score is included as a covariate in either forest, its weight will default to1/X_train.shape[1]. A workaround if you wish to provide a custom weight for the propensity score is to include it as a column inX_trainand then setpropensity_covariateto'none'and adjustkeep_vars_muandkeep_vars_tau` accordingly. variable_weights_variance (np.array): Numeric weights reflecting the relative probability of splitting on each variable in the variance forest. Does not need to sum to 1 but cannot be negative. Defaults to uniform over the columns of X_train if not provided. keep_vars_mu (list or np.array): Vector of variable names or column indices denoting variables that should be included in the prognostic (mu(X)) forest. Defaults to None. drop_vars_mu (list or np.array): Vector of variable names or column indices denoting variables that should be excluded from the prognostic (mu(X)) forest. Defaults to None. If both drop_vars_mu and keep_vars_mu are set, drop_vars_mu will be ignored. drop_vars_variance (list or np.array): Vector of variable names or column indices denoting variables that should be excluded from the variance (sigma^2(X)) forest. Defaults to None. If both drop_vars_variance and keep_vars_variance are set, drop_vars_variance will be ignored. keep_vars_tau (list or np.array): Vector of variable names or column indices denoting variables that should be included in the treatment effect (tau(X)) forest. Defaults to None. drop_vars_tau (list or np.array): Vector of variable names or column indices denoting variables that should be excluded from the treatment effect (tau(X)) forest. Defaults to None. If both drop_vars_tau and keep_vars_tau are set, drop_vars_tau will be ignored. drop_vars_variance (list or np.array): Vector of variable names or column indices denoting variables that should be excluded from the variance (sigma^2(X)) forest. Defaults to None. If both drop_vars_variance and keep_vars_variance are set, drop_vars_variance will be ignored. keep_vars_variance (list or np.array): Vector of variable names or column indices denoting variables that should be included in the variance (sigma^2(X)) forest. Defaults to None. num_trees_mu (int): Number of trees in the prognostic forest. Defaults to 200. num_trees_tau (int): Number of trees in the treatment effect forest. Defaults to 50. num_trees_variance (int): Number of trees in the ensemble for the conditional variance model. Defaults to 0. Variance is only modeled using a tree / forest if num_trees_variance > 0. sample_sigma_global (bool): Whether or not to update the sigma^2 global error variance parameter based on IG(a_global, b_global). Defaults to True. sample_sigma_leaf_mu (bool): Whether or not to update the tau leaf scale variance parameter based on IG(a_leaf, b_leaf) for the prognostic forest. Cannot (currently) be set to true if basis_train has more than one column. Defaults to True. sample_sigma_leaf_tau (bool): Whether or not to update the tau leaf scale variance parameter based on IG(a_leaf, b_leaf) for the treatment effect forest. Cannot (currently) be set to true if basis_train has more than one column. Defaults to True. propensity_covariate (str): Whether to include the propensity score as a covariate in either or both of the forests. Enter "none" for neither, "mu" for the prognostic forest, "tau" for the treatment forest, and "both" for both forests. If this is not "none" and a propensity score is not provided, it will be estimated from (X_train, Z_train) using BARTModel. Defaults to "mu". adaptive_coding (bool): Whether or not to use an "adaptive coding" scheme in which a binary treatment variable is not coded manually as (0,1) or (-1,1) but learned via parameters b_0 and b_1 that attach to the outcome model [b_0 (1-Z) + b_1 Z] tau(X). This is ignored when Z is not binary. Defaults to True. b_0 (float): Initial value of the "control" group coding parameter. This is ignored when Z is not binary. Default: -0.5. b_1 (float): Initial value of the "treated" group coding parameter. This is ignored when Z is not binary. Default: 0.5. random_seed (int): Integer parameterizing the C++ random number generator. If not specified, the C++ random number generator is seeded according to std::random_device. keep_burnin (bool): Whether or not "burnin" samples should be included in predictions. Defaults to False. Ignored if num_mcmc == 0. keep_gfr (bool): Whether or not "warm-start" / grow-from-root samples should be included in predictions. Defaults to False. Ignored if num_mcmc == 0. keep_every (int): How many iterations of the burned-in MCMC sampler should be run before forests and parameters are retained. Defaults to 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.	None

predict_tau(X, Z, propensity=None)

Predict CATE function for every provided observation.

Parameters:

Name	Type	Description	Default
X	array or DataFrame	Test set covariates.	required
Z	array	Test set treatment indicators.	required
propensity	array	Optional test set propensities. Must be provided if propensities were provided when the model was sampled.	None

Returns:

Type	Description
array	Array with as many rows as in X and as many columns as retained samples of the algorithm.

predict_variance(covariates, propensity=None)

Predict expected conditional variance from a BART model.

Parameters:

Name	Type	Description	Default
covariates	array	Test set covariates.	required
propensity	array	Test set propensity scores. Optional (not currently used in variance forests).	None

Returns:

Type	Description
array	Array of predictions corresponding to the variance forest. Each array will contain as many rows as in covariates and as many columns as retained samples of the algorithm.

predict(X, Z, propensity=None)

Predict outcome model components (CATE function and prognostic function) as well as overall outcome for every provided observation. Predicted outcomes are computed as yhat = mu_x + Z*tau_x where mu_x is a sample of the prognostic function and tau_x is a sample of the treatment effect (CATE) function.

Parameters:

Name	Type	Description	Default
X	array or DataFrame	Test set covariates.	required
Z	array	Test set treatment indicators.	required
propensity	`np.array`	Optional test set propensities. Must be provided if propensities were provided when the model was sampled.	None

Returns:

Name	Type	Description
tau_x	array	Conditional average treatment effect (CATE) samples for every observation provided.
mu_x	array	Prognostic effect samples for every observation provided.
yhat_x	array	Outcome prediction samples for every observation provided.
sigma2_x	(array, optional)	Variance forest samples for every observation provided. Only returned if the model includes a heteroskedasticity forest.

to_json()

Converts a sampled BART model to JSON string representation (which can then be saved to a file or processed using the json library)

Returns:

Type	Description
str	JSON string representing model metadata (hyperparameters), sampled parameters, and sampled forests

from_json(json_string)

Converts a JSON string to an in-memory BART model.

Parameters:

Name	Type	Description	Default
json_string	str	JSON string representing model metadata (hyperparameters), sampled parameters, and sampled forests	required

is_sampled()

Whether or not a BCF model has been sampled.

Returns:

Type	Description
bool	True if a BCF model has been sampled, False otherwise