Title: Log-linear Bayesian additive regression trees for multinomial logistic and count regression
Authors: Jared Murray - University of Texas at Austin (United States) [presenting]
Abstract: Bayesian additive regression trees (BART) have been applied to nonparametric mean regression and binary classification problems in a range of applied areas. To date BART models have been limited to models for Gaussian ``data'', either observed or latent, and with good reason - the Bayesian backfitting MCMC algorithm for BART is remarkably efficient in Gaussian models. But while many useful models are naturally cast in terms of observed or latent Gaussian variables, many others are not. We extend BART to a range of log-linear models including multinomial logistic regression and count regression models with zero-inflation and overdispersion. Extending to these non-Gaussian settings requires a novel prior distribution over BART's parameters. Like the original BART prior, this new prior distribution is carefully constructed and calibrated to be flexible while avoiding overfitting. With this new prior distribution and some data augmentation techniques we are able to implement an efficient generalization of the Bayesian backfitting algorithm for MCMC in log-linear BART models. We demonstrate the utility of these new methods with several examples and applications.