11. BART

This submodule contains a class to set up a Gaussian process regression with the BART kernel. See the bart and barteasy examples.

class lsqfitgp.bayestree.bart(x_train, y_train, *, x_test=None, fitkw={}, kernelkw={})

GP version of BART.

Evaluate a Gaussian process regression with a kernel which accurately approximates the infinite trees limit of BART. The hyperparameters are optimized to their marginal MAP.

Parameters:

x_train(n, p) array or dataframe

Observed covariates.

y_train(n,) array

Observed outcomes.

x_test(n*, p) array or dataframe, optional

Covariates of outcomes to be imputed.

fitkwdict

Additional arguments passed to empbayes_fit, overrides the defaults.

kernelkwdict

Additional arguments passed to BART, overrides the defaults.

See also

lsqfitgp.BART

Notes

The tree splitting grid is set using quantiles of the observed covariates. This corresponds to settings usequants=True, numcut=inf in the R packages BayesTree and BART.

Attributes:

yhat_train_mean(n,) array

The posterior mean of the latent regression function at the observed covariates.

yhat_train_var(n,) array

The posterior variance of the latent regression function at the observed covariates.

yhat_test_mean(n*,) array

The posterior mean of the latent regression function at the covariates of imputed outcomes.

yhat_test_var(n*,) array

The posterior variance of the latent regression function at the covariates of imputed outcomes.

sigmagvar

The error term standard deviation.

alphagvar

The numerator of the tree spawn probability (named base in BayesTree and BART).

betagvar

The depth exponent of the tree spawn probability (named power in BayesTree and BART).

meansdevgvar

The prior standard deviation of the latent regression function.

fitempbayes_fit

The hyperparameters fit object.

gpGP

The centered Gaussian process object constructed at the hyperparameters MAP. Its keys are ‘trainmean’ and ‘testmean’.

muscalar

The prior mean.