Statistics and Data Science Seminar: Towards a more flexible BART

Abstract: Bayesian Additive Regression Trees have become ubiquitous across Bayesian statistics in the last decade. Leveraging a sum-of-trees approach, BART is able to flexibly model or approximate E[Y|x], without too much concern for overfitting. Recent advances in BART have seen its extension to binary outcomes, variance regression and to survival analysis. In this work we provide a natural extension of the BART framework to incorporating latent variables and demonstrate how this allows us to study density regression problems and to capture potentially hierarchical structure in our data. For our Density Regression BART (DR-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. We conclude by demonstrating our generalized Latent Variable BART (LV-BART) framework in the context of hierarchical modeling and sensitivity analysis to unobserved confounding in observational studies.

Host: Robert Lunde