# Bayesian Regularization for Graphical Models with Unequal Shrinkage

arXiv: https://arxiv.org/abs/1805.02257 · HTML: https://mlsanity.com/paper/1805.02257/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2018.

## Built on by (most cited first, 5 of 5)

- [Concentration of a sparse Bayesian model with Horseshoe prior in estimating high-dimensional precision matrix](https://mlsanity.com/paper/2406.14269/) (2024)
- [Scalable Bayesian Structure Learning for Gaussian Graphical Models Using Marginal Pseudo-likelihood](https://mlsanity.com/paper/2307.00127/) (2023)
- [Bayesian Approach to Linear Bayesian Networks](https://mlsanity.com/paper/2311.15610/) (2023)
- [A Novel approach to portfolio construction](https://mlsanity.com/paper/2602.03325/) (2026)
- [Sparse Bayesian Deep Functional Learning with Structured Region Selection](https://mlsanity.com/paper/2602.20651/) (2026)

## Abstract (arXiv)

We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian standpoint, we investigate the MAP (maximum a posteriori) estimator from a penalized likelihood perspective that gives rise to a new non-convex penalty approximating the ℓ0 penalty. Optimal error rates for estimation consistency in terms of various matrix norms along with selection consistency for sparse structure recovery are shown for the unique MAP estimator under mild conditions. For fast and efficient computation, an EM algorithm is proposed to compute the MAP estimator of the precision matrix and (approximate) posterior probabilities on the edges of the underlying sparse structure. Through extensive simulation studies and a real application to a call center data, we have demonstrated the fine performance of our method compared with existing alternatives.