Research Paper#Bayesian Statistics, Elastic Net, Regression, Machine Learning🔬 ResearchAnalyzed: Jan 3, 2026 06:12
Bayesian Elastic Net with Structured Prior Dependence
Published:Dec 31, 2025 18:41
•1 min read
•ArXiv
Analysis
This paper addresses a limitation in Bayesian regression models, specifically the assumption of independent regression coefficients. By introducing the orthant normal distribution, the authors enable structured prior dependence in the Bayesian elastic net, offering greater modeling flexibility. The paper's contribution lies in providing a new link between penalized optimization and regression priors, and in developing a computationally efficient Gibbs sampling method to overcome the challenge of an intractable normalizing constant. The paper demonstrates the benefits of this approach through simulations and a real-world data example.
Key Takeaways
- •Addresses the limitation of independent regression coefficients in Bayesian regression.
- •Introduces the orthant normal distribution to enable structured prior dependence.
- •Provides a new link between penalized optimization and regression priors.
- •Develops a computationally efficient Gibbs sampling method.
- •Demonstrates benefits through simulation and a real-world example.
Reference
“The paper introduces the orthant normal distribution in its general form and shows how it can be used to structure prior dependence in the Bayesian elastic net regression model.”