# Handling bounded response in high dimensions: a Horseshoe prior Bayesian Beta regression approach

arXiv: https://arxiv.org/abs/2505.22211 · HTML: https://mlsanity.com/paper/2505.22211/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 50 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 12 of 12)

- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Concentration of tempered posteriors and of their variational approximations](https://mlsanity.com/paper/1706.09293/) (2017)
- [Sparsity information and regularization in the horseshoe and other shrinkage priors](https://mlsanity.com/paper/1707.01694/) (2017)
- [Bayesian linear regression with sparse priors](https://mlsanity.com/paper/1403.0735/) (2014)
- [A comparison of learning rate selection methods in generalized Bayesian inference](https://mlsanity.com/paper/2012.11349/) (2020)
- [Empirical Bayes posterior concentration in sparse high-dimensional linear models](https://mlsanity.com/paper/1406.7718/) (2014)
- [Concentration of a sparse Bayesian model with Horseshoe prior in estimating high-dimensional precision matrix](https://mlsanity.com/paper/2406.14269/) (2024)
- [Concentration properties of fractional posterior in 1-bit matrix completion](https://mlsanity.com/paper/2404.08969/) (2024)
- [Bayesian sparse multiple regression for simultaneous rank reduction and variable selection](https://mlsanity.com/paper/1612.00877/) (2016)
- [Empirical priors for prediction in sparse high-dimensional linear regression](https://mlsanity.com/paper/1903.00961/) (2019)
- [High-dimensional Bayesian Tobit regression for censored response with Horseshoe prior](https://mlsanity.com/paper/2505.08288/) (2025)
- [Optimal sparse phase retrieval via a quasi-Bayesian approach](https://mlsanity.com/paper/2504.09509/) (2025)

## Built on by (most cited first, 2 of 2)

- [Bayesian Pliable Lasso with Horseshoe Prior for Interaction Effects in GLMs with Missing Responses](https://mlsanity.com/paper/2509.07501/) (2025)
- [Mixture-of-experts Wishart model for covariance matrices with an application to Cancer drug screening](https://mlsanity.com/paper/2602.13888/) (2026)

## Abstract (arXiv)

Bounded continuous responses -- such as proportions -- arise frequently in diverse scientific fields including climatology, biostatistics, and finance. Beta regression is a widely adopted framework for modeling such data, due to the flexibility of the Beta distribution over the unit interval. While Bayesian extensions of Beta regression have shown promise, existing methods are limited to low-dimensional settings and lack theoretical guarantees. In this work, we propose a novel Bayesian approach for high-dimensional sparse Beta regression framework that employs a tempered posterior. Our method incorporates the Horseshoe prior for effective shrinkage and variable selection. Most notable, we propose a novel Gibbs sampling algorithm using P'olya-Gamma augmentation for efficient inference in Beta regression model. We also provide the first theoretical results establishing posterior consistency and convergence rates for Bayesian Beta regression. Through extensive simulation studies in both low- and high-dimensional scenarios, we demonstrate that our approach outperforms existing alternatives, offering improved estimation accuracy and model interpretability. Our method is implemented in the R package ``betaregbayes" available on Github.