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Activity Number: 189 - SBSS Student Paper Competition I
Type: Topic Contributed
Date/Time: Monday, August 8, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #323416
Title: Density Regression with Bayesian Additive Regression Trees
Author(s): Vittorio Orlandi* and Jared S Murray and Antonio R. Linero and Alex Volfovsky
Companies: Duke University and The University of Texas McCombs School of Business and University of Texas at Austin and Duke University
Keywords: Bayesian Nonparametrics; Heteroscedasticity; Latent Variables; Conditional Density Estimation; Posterior Concentration

Flexibly modeling how a density changes with covariates is an important but challenging generalization of mean and quantile regression. While existing methods for density regression primarily consist of covariate-dependent discrete mixture models, we consider a continuous latent variable model in general covariate spaces, which we call DR-BART. The prior mapping the latent variable to the data is constructed via a novel application of BART. We prove that the posterior induced by our model concentrates quickly around true generative functions that are sufficiently smooth. We also analyze DR-BART's performance on a set of challenging simulated examples, where it outperforms various other methods for Bayesian density regression. Lastly, we apply DR-BART to a U.S. census dataset to study returns to education. Our proposed sampler is efficient and allows one to take advantage of BART’s flexibility in many applied settings where the entire response distribution is of interest. Furthermore, our scheme for splitting on latent variables within BART facilitates its application to other models that can be described via latent variables, such as those involving hierarchical or network data.

Authors who are presenting talks have a * after their name.

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