# Lasso Penalization for High-Dimensional Beta Regression Models: Computation, Analysis, and Inference

arXiv: https://arxiv.org/abs/2507.20079 · HTML: https://mlsanity.com/paper/2507.20079/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 53 references that are in the map.
- First posted on arXiv 26 Jul 2025.

## Builds on (most cited first, 8 of 8)

- [The Landscape of Empirical Risk for Non-convex Losses](https://mlsanity.com/paper/1607.06534/) (2016)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima](https://mlsanity.com/paper/1305.2436/) (2013)
- [False Discoveries Occur Early on the Lasso Path](https://mlsanity.com/paper/1511.01957/) (2015)
- [A Sparse Beta Regression Model for Network Analysis](https://mlsanity.com/paper/2010.13604/) (2020)
- [Bootstrap-based model selection criteria for beta regressions](https://mlsanity.com/paper/1405.4525/) (2014)
- [Shrinkage Estimators for Beta Regression Models](https://mlsanity.com/paper/2406.18047/) (2024)
- [Model selection criteria in beta regression with varying dispersion](https://mlsanity.com/paper/1405.3718/) (2014)

## Abstract (arXiv)

Beta regression is commonly employed when the outcome variable is a proportion. Since its conception, the approach has been widely used in applications spanning various scientific fields. A series of extensions have been proposed over time, several of which address variable selection and penalized estimation, e.g., with an ℓ1-penalty (LASSO). However, a theoretical analysis of this popular approach in the context of Beta regression with high-dimensional predictors is lacking. In this paper, we aim to close this gap. A particular challenge arises from the non-convexity of the associated negative log-likelihood, which we address by resorting to a framework for analyzing stationary points in a neighborhood of the target parameter. Leveraging this framework, we derive a non-asymptotic bound on the ℓ1-error of such stationary points. In addition, we propose a debiasing approach to construct confidence intervals for the regression parameters. A proximal gradient algorithm is devised for optimizing the resulting penalized negative log-likelihood function. Our theoretical analysis is corroborated via simulation studies, and a real data example concerning the prediction of county-level proportions of incarceration is presented to showcase the practical utility of our methodology.