Fully Nonparametric Bayesian Additive Regression Trees

TL;DR

This paper extends Bayesian Additive Regression Trees (BART) by integrating a nonparametric error model using Dirichlet process mixtures, enhancing robustness to non-normal errors while maintaining BART's automatic modeling capabilities.

Contribution

It introduces a nonparametric error modeling approach into BART using DPM, allowing flexible error distribution modeling without losing the original method's advantages.

Findings

Improved robustness to non-normal error distributions.

Maintains BART's predictive performance with normal errors.

Demonstrates adaptability across various datasets.

Abstract

Bayesian Additive Regression Trees (BART) is a fully Bayesian approach to modeling with ensembles of trees. BART can uncover complex regression functions with high dimensional regressors in a fairly automatic way and provide Bayesian quantification of the uncertainty through the posterior. However, BART assumes IID normal errors. This strong parametric assumption can lead to misleading inference and uncertainty quantification. In this paper, we use the classic Dirichlet process mixture (DPM) mechanism to nonparametrically model the error distribution. A key strength of BART is that default prior settings work reasonably well in a variety of problems. The challenge in extending BART is to choose the parameters of the DPM so that the strengths of the standard BART approach is not lost when the errors are close to normal, but the DPM has the ability to adapt to non-normal errors.