Generalized Bayesian Additive Regression Trees Models: Beyond Conditional Conjugacy
This work expands BART's applicability to a broader class of models, addressing a bottleneck for researchers and practitioners in fields like survival analysis and regression.
The authors tackled the limitation of Bayesian additive regression trees (BART) to conditionally conjugate models by developing a reversible jump MCMC algorithm, enabling application to generalized BART models such as survival analysis and heteroskedastic regression without tuning parameters.
Bayesian additive regression trees have seen increased interest in recent years due to their ability to combine machine learning techniques with principled uncertainty quantification. The Bayesian backfitting algorithm used to fit BART models, however, limits their application to a small class of models for which conditional conjugacy exists. In this article, we greatly expand the domain of applicability of BART to arbitrary \emph{generalized BART} models by introducing a very simple, tuning-parameter-free, reversible jump Markov chain Monte Carlo algorithm. Our algorithm requires only that the user be able to compute the likelihood and (optionally) its gradient and Fisher information. The potential applications are very broad; we consider examples in survival analysis, structured heteroskedastic regression, and gamma shape regression.