# Bayesian Global-Local Regularization

arXiv: https://arxiv.org/abs/2512.13992 · HTML: https://mlsanity.com/paper/2512.13992/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2025.

## Built on by (most cited first, 1 of 1)

- [Generative Bayesian Hyperparameter Tuning](https://mlsanity.com/paper/2512.20051/) (2025)

## Abstract (arXiv)

We propose a unified framework for global-local regularization that bridges the gap between classical techniques -- such as ridge regression and the nonnegative garotte -- and modern Bayesian hierarchical modeling. By estimating local regularization strengths via marginal likelihood under order constraints, our approach generalizes Stein's positive-part estimator and provides a principled mechanism for adaptive shrinkage in high-dimensional settings. We establish that this isotonic empirical Bayes estimator achieves near-minimax risk (up to logarithmic factors) over sparse ordered model classes, constituting a significant advance in high-dimensional statistical inference. Applications to orthogonal polynomial regression demonstrate the methodology's flexibility, while our theoretical results clarify the connections between empirical Bayes, shape-constrained estimation, and degrees-of-freedom adjustments.