Bayesian Additive Regression Trees (BART) is a nonparametric Bayesian regression technique that becomes equivalent to Gaussian process (GP) regression in the limit of infinite trees.
The exact BART prior covariance function has been derived and computed for the first time in this study, allowing implementation of the infinite trees limit of BART as GP regression.
Empirical tests show that the GP regression obtained from BART's infinite trees limit, when tuned appropriately, can be competitive with standard BART after tuning hyperparameters.
Using a GP surrogate of BART simplifies model building and avoids the complex BART MCMC algorithm, offering new insights into the development of both BART and GP regression.