Interface

Implement a user interface that mimics the R BART package.

class bartz.BART.gbart(x_train, y_train, *, x_test=None, type='wbart', usequants=False, sigest=None, sigdf=3, sigquant=0.9, k=2, power=2, base=0.95, lamda=None, tau_num=None, offset=None, w=None, ntree=200, numcut=255, ndpost=1000, nskip=100, keepevery=1, printevery=100, seed=0, maxdepth=6, init_kw=None, run_mcmc_kw=None)[source]

Nonparametric regression with Bayesian Additive Regression Trees (BART).

Regress y_train on x_train with a latent mean function represented as a sum of decision trees. The inference is carried out by sampling the posterior distribution of the tree ensemble with an MCMC.

Parameters:

  • x_train (array (p, n) or DataFrame) – The training predictors.

  • y_train (array (n,) or Series) – The training responses.

  • x_test (array (p, m) or DataFrame, optional) – The test predictors.

  • type (Literal['wbart', 'pbart'], default: 'wbart') – The type of regression. ‘wbart’ for continuous regression, ‘pbart’ for binary regression with probit link.

  • usequants (bool, default False) – Whether to use predictors quantiles instead of a uniform grid to bin predictors.

  • sigest (float, optional) – An estimate of the residual standard deviation on y_train, used to set lamda. If not specified, it is estimated by linear regression (with intercept, and without taking into account w). If y_train has less than two elements, it is set to 1. If n <= p, it is set to the standard deviation of y_train. Ignored if lamda is specified.

  • sigdf (int, default 3) – The degrees of freedom of the scaled inverse-chisquared prior on the noise variance.

  • sigquant (float, default 0.9) – The quantile of the prior on the noise variance that shall match sigest to set the scale of the prior. Ignored if lamda is specified.

  • k (float, default 2) – The inverse scale of the prior standard deviation on the latent mean function, relative to half the observed range of y_train. If y_train has less than two elements, k is ignored and the scale is set to 1.

  • power (float, default 2)

  • base (float, default 0.95) – Parameters of the prior on tree node generation. The probability that a node at depth d (0-based) is non-terminal is base / (1 + d) ** power.

  • lamda (float | Float[Any, ''] | None, default: None) – The prior harmonic mean of the error variance. (The harmonic mean of x is 1/mean(1/x).) If not specified, it is set based on sigest and sigquant.

  • tau_num (float | Float[Any, ''] | None, default: None) – The numerator in the expression that determines the prior standard deviation of leaves. If not specified, default to (max(y_train) - min(y_train)) / 2 (or 1 if y_train has less than two elements) for continuous regression, and 3 for binary regression.

  • offset (float | Float[Any, ''] | None, default: None) – The prior mean of the latent mean function. If not specified, it is set to the mean of y_train for continuous regression, and to Phi^-1(mean(y_train)) for binary regression. If y_train is empty, offset is set to 0.

  • w (array (n,), optional) – Coefficients that rescale the error standard deviation on each datapoint. Not specifying w is equivalent to setting it to 1 for all datapoints. Note: w is ignored in the automatic determination of sigest, so either the weights should be O(1), or sigest should be specified by the user.

  • ntree (int, default 200) – The number of trees used to represent the latent mean function.

  • numcut (int, default 255) –

    If usequants is False: the exact number of cutpoints used to bin the predictors, ranging between the minimum and maximum observed values (excluded).

    If usequants is True: the maximum number of cutpoints to use for binning the predictors. Each predictor is binned such that its distribution in x_train is approximately uniform across bins. The number of bins is at most the number of unique values appearing in x_train, or numcut + 1.

    Before running the algorithm, the predictors are compressed to the smallest integer type that fits the bin indices, so numcut is best set to the maximum value of an unsigned integer type.

  • ndpost (int, default 1000) – The number of MCMC samples to save, after burn-in.

  • nskip (int, default 100) – The number of initial MCMC samples to discard as burn-in.

  • keepevery (int, default 1) – The thinning factor for the MCMC samples, after burn-in.

  • printevery (int or None, default 100) –

    The number of iterations (including thinned-away ones) between each log line. Set to None to disable logging.

    printevery has a few unexpected side effects. On cpu, interrupting with ^C halts the MCMC only on the next log. And the total number of iterations is a multiple of printevery, so if nskip + keepevery * ndpost is not a multiple of printevery, some of the last iterations will not be saved.

  • seed (int or jax random key, default 0) – The seed for the random number generator.

  • maxdepth (int, default 6) – The maximum depth of the trees. This is 1-based, so with the default maxdepth=6, the depths of the levels range from 0 to 5.

  • init_kw (dict) – Additional arguments passed to mcmcstep.init.

  • run_mcmc_kw (dict) – Additional arguments passed to mcmcloop.run_mcmc.

Variables:

  • yhat_train (array (ndpost, n)) – The conditional posterior mean at x_train for each MCMC iteration.

  • yhat_train_mean (array (n,)) – The marginal posterior mean at x_train.

  • yhat_test (array (ndpost, m)) – The conditional posterior mean at x_test for each MCMC iteration.

  • yhat_test_mean (array (m,)) – The marginal posterior mean at x_test.

  • sigma (array (ndpost,)) – The standard deviation of the error.

  • first_sigma (array (nskip,)) – The standard deviation of the error in the burn-in phase.

  • offset (float) – The prior mean of the latent mean function.

  • sigest (float or None) – The estimated standard deviation of the error used to set lamda.

Notes

This interface imitates the function gbart from the R package BART, but with these differences:

  • If x_train and x_test are matrices, they have one predictor per row instead of per column.

  • If type is not specified, it is determined solely based on the data type of y_train, and not on whether it contains only two unique values.

  • If usequants=False, R BART switches to quantiles anyway if there are less predictor values than the required number of bins, while bartz always follows the specification.

  • The error variance parameter is called lamda instead of lambda.

  • rm_const is always False.

  • The default numcut is 255 instead of 100.

  • A lot of functionality is missing (e.g., variable selection).

  • There are some additional attributes, and some missing.

  • The trees have a maximum depth.

predict(x_test)[source]

Compute the posterior mean at x_test for each MCMC iteration.

Parameters:

x_test (array (p, m) or DataFrame) – The test predictors.

Returns:

yhat_test (array (ndpost, m)) – The conditional posterior mean at x_test for each MCMC iteration.

Raises:

ValueError – If x_test has a different format than x_train.