VC-BART: Bayesian trees for varying coefficients

by   Sameer K. Deshpande, et al.

The linear varying coefficient (VC) model generalizes the conventional linear model by allowing the additive effect of each covariate on the outcome to vary as a function of additional effect modifiers. While there are many existing procedures for VC modeling with a single scalar effect modifier (often assumed to be time), there has, until recently, been comparatively less development for settings with multivariate modifiers. Unfortunately, existing state-of-the-art procedures that can accommodate multivariate modifiers typically make restrictive structural assumptions about the covariate effect functions or require intensive problem-specific hand-tuning that scales poorly to large datasets. In response, we propose VC-BART, which estimates the covariate effect functions in a VC model using Bayesian Additive Regression Trees (BART). On several synthetic and real-world data sets, we demonstrate that, with simple default hyperparameter settings, VC-BART displays covariate effect recovery performance superior to state-of-the-art VC modeling techniques and predictive performance on par with more flexible but less interpretable nonparametric regression procedures. We further demonstrate the theoretical near-optimality of VC-BART by synthesizing recent theoretical results about the VC model and BART to derive posterior concentration rates in settings with independent and correlated errors. An R package implementing VC-BART is available at



There are no comments yet.


page 1

page 2

page 3

page 4


On Soft Bayesian Additive Regression Trees and asynchronous longitudinal regression analysis

In many longitudinal studies, the covariate and response are often inter...

MPBART - Multinomial Probit Bayesian Additive Regression Trees

This article proposes Multinomial Probit Bayesian Additive Regression Tr...

Linear Aggregation in Tree-based Estimators

Regression trees and their ensemble methods are popular methods for non-...

Fully Nonparametric Bayesian Additive Regression Trees

Bayesian Additive Regression Trees (BART) is fully Bayesian approach to ...

Statistical Inference for Generalized Additive Partially Linear Model

The Generalized Additive Model (GAM) is a powerful tool and has been wel...

Active-set algorithms based statistical inference for shape-restricted generalized additive Cox regression models

Recently the shape-restricted inference has gained popularity in statist...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.