Generalized Bayesian Additive Regression Trees Models: Beyond Conditional Conjugacy
本文提出一种无需调参的可逆跳跃马尔可夫链蒙特卡洛算法，将贝叶斯加性回归树的应用范围从条件共轭模型扩展到任意广义模型，适用于生存分析、异方差回归等场景。
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 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.