SoftBART-CORM Models for Density Regression
Abstract
Flexible modelling of the conditional distribution of a response given predictors is important in many applications where nonlinear effects, heteroskedasticity, and multimodality may be present. We introduce the SoftBART-CoRM, a predictor-dependent infinite mixture model that combines the interpretable component structure of Compound Random Measures (CoRMs) with SoftBART priors on both mixture weights and component-specific parameters. The model flexibly captures complex distributional features, while global--local shrinkage and predictor-selection priors mitigate overfitting and identify the covariates driving component allocation and kernel parameters. Posterior inference is performed using an efficient Markov chain Monte Carlo algorithm that leverages existing \texttt{R} implementations of SoftBART. Through simulation studies and real-data applications, we show that the proposed approach can adaptively shrink towards simpler mixture representations, provide interpretable inference on the predictors governing different aspects of the conditional distribution, and achieve superior out-of-sample predictive performance relative to benchmark models.
Related
- Kernel Density Regression Estimation with Covariates on Riemannian Manifolds
- A note on distribution and density estimation as a regression problem of order statistics
- Logistic Gaussian process density regression: a generalized Bayesian approach
- Scalable Logistic Gaussian Process Density Regression with Kinetic Langevin Sampling
- Learning under Target Shift: Optimal Density Ratio Estimation and Importance-Weighted Regression
BibTeX
@misc{griffin2026softbartcorm,
title = {{SoftBART-CORM Models for Density Regression}},
author = {Jim E. Griffin and Maria Kalli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33669},
eprint = {2610.33669},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33669},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - SoftBART-CORM Models for Density Regression
AU - Jim E. Griffin
AU - Maria Kalli
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33669
UR - https://arxiv.org/abs/2610.33669
AB - Flexible modelling of the conditional distribution of a response given predictors is important in many applications where nonlinear effects, heteroskedasticity, and multimodality may be present. We introduce the SoftBART-CoRM, a predictor-dependent infinite mixture model that combines the interpretable component structure of Compound Random Measures (CoRMs) with SoftBART priors on both mixture weights and component-specific parameters. The model flexibly captures complex distributional features, while global--local shrinkage and predictor-selection priors mitigate overfitting and identify the covariates driving component allocation and kernel parameters. Posterior inference is performed using an efficient Markov chain Monte Carlo algorithm that leverages existing \texttt{R} implementations of SoftBART. Through simulation studies and real-data applications, we show that the proposed approach can adaptively shrink towards simpler mixture representations, provide interpretable inference on the predictors governing different aspects of the conditional distribution, and achieve superior out-of-sample predictive performance relative to benchmark models.
ER -