Log-Linear Bayesian Additive Regression Trees for Multinomial Logistic and Count Regression Models

• 成果类型: Article
• 署名作者: Murray, Jared S.
• 署名单位: University of Texas System; University of Texas Austin; University of Texas System; University of Texas Austin
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1813587
• 发表日期: 2021
• 页码: 756-769
• 关键词: Cart; inference; selection; binary; bart

摘要

We introduce Bayesian additive regression trees (BART) for log-linear models including multinomial logistic regression and count regression with zero-inflation and overdispersion. BART has been applied to nonparametric mean regression and binary classification problems in a range of settings. However, existing applications of BART have been mostly limited to models for Gaussian data, either observed or latent. This is primarily because efficient MCMC algorithms are available for Gaussian likelihoods. But while many useful models are naturally cast in terms of latent Gaussian variables, many others are not-including models considered in this article. We develop new data augmentation strategies and carefully specified prior distributions for these new models. Like the original BART prior, the new prior distributions are carefully constructed and calibrated to be flexible while guarding against overfitting. Together the new priors and data augmentation schemes allow us to implement an efficient MCMC sampler outside the context of Gaussian models. The utility of these new methods is illustrated with examples and an application to a previously published dataset. for this article are available online.