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Abstract:
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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.
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