Semiparametric Mixed-Scale Models Using Shared Bayesian Forests

TL;DR

This paper introduces a Bayesian nonparametric approach using shared forests for multivariate and semi-continuous regression, improving inference by sharing information across model components, especially in high-dimensional sparse settings.

Contribution

It develops novel shared Bayesian forest models for multivariate and semi-continuous responses, enabling nonparametric information sharing across components, and applies these to complex medical expenditure data.

Findings

Sharing information improves model performance in high-dimensional settings.

The proposed models effectively analyze heteroscedastic and semi-continuous data.

Application to MEPS data demonstrates practical utility and interpretability.

Abstract

This paper demonstrates the advantages of sharing information about unknown features of covariates across multiple model components in various nonparametric regression problems including multivariate, heteroscedastic, and semi-continuous responses. In this paper, we present methodology which allows for information to be shared nonparametrically across various model components using Bayesian sum-of-tree models. Our simulation results demonstrate that sharing of information across related model components is often very beneficial, particularly in sparse high-dimensional problems in which variable selection must be conducted. We illustrate our methodology by analyzing medical expenditure data from the Medical Expenditure Panel Survey (MEPS). To facilitate the Bayesian nonparametric regression analysis, we develop two novel models for analyzing the MEPS data using Bayesian additive regression trees - a heteroskedastic log-normal hurdle model with a "shrink-towards-homoskedasticity" prior, and a gamma hurdle model.