# Structured Shrinkage Priors

arXiv: https://arxiv.org/abs/1902.05106 · HTML: https://mlsanity.com/paper/1902.05106/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2019.

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

- [Feature Preserving Shrinkage on Bayesian Neural Networks via the R2D2 Prior](https://mlsanity.com/paper/2505.18280/) (2025)
- [Graph-dependent shrinkage priors for Bayesian trend filtering](https://mlsanity.com/paper/2608.23802/) (2026)

## Abstract (arXiv)

In many regression settings the unknown coefficients may have some known structure, for instance they may be ordered in space or correspond to a vectorized matrix or tensor. At the same time, the unknown coefficients may be sparse, with many nearly or exactly equal to zero. However, many commonly used priors and corresponding penalties for coefficients do not encourage simultaneously structured and sparse estimates. In this paper we develop structured shrinkage priors that generalize multivariate normal, Laplace, exponential power and normal-gamma priors. These priors allow the regression coefficients to be correlated a priori without sacrificing elementwise sparsity or shrinkage. The primary challenges in working with these structured shrinkage priors are computational, as the corresponding penalties are intractable integrals and the full conditional distributions that are needed to approximate the posterior mode or simulate from the posterior distribution may be non-standard. We overcome these issues using a flexible elliptical slice sampling procedure, and demonstrate that these priors can be used to introduce structure while preserving sparsity.