# The Graphical Horseshoe Estimator for Inverse Covariance Matrices

arXiv: https://arxiv.org/abs/1707.06661 · HTML: https://mlsanity.com/paper/1707.06661/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2017.

## Built on by (most cited first, 9 of 9)

- [Concentration of a sparse Bayesian model with Horseshoe prior in estimating high-dimensional precision matrix](https://mlsanity.com/paper/2406.14269/) (2024)
- [Conditional Matrix Flows for Gaussian Graphical Models](https://mlsanity.com/paper/2306.07255/) (2023)
- [Network reconstruction via the minimum description length principle](https://mlsanity.com/paper/2405.01015/) (2024)
- [Efficient Network Automatic Relevance Determination](https://mlsanity.com/paper/2506.12352/) (2025)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [Bayesian Regularization for Functional Graphical Models with Applications to Neuroimaging](https://mlsanity.com/paper/2110.05575/) (2021)
- [Scalable Bayesian Structure Learning for Gaussian Graphical Models Using Marginal Pseudo-likelihood](https://mlsanity.com/paper/2307.00127/) (2023)
- [A Bayesian Methodology for Estimation for Sparse Canonical Correlation](https://mlsanity.com/paper/2310.19621/) (2023)
- [Graph-dependent shrinkage priors for Bayesian trend filtering](https://mlsanity.com/paper/2608.23802/) (2026)

## Abstract (arXiv)

We develop a new estimator of the inverse covariance matrix for high-dimensional multivariate normal data using the horseshoe prior. The proposed graphical horseshoe estimator has attractive properties compared to other popular estimators, such as the graphical lasso and graphical Smoothly Clipped Absolute Deviation (SCAD). The most prominent benefit is that when the true inverse covariance matrix is sparse, the graphical horseshoe provides estimates with small information divergence from the true sampling distribution. The posterior mean under the graphical horseshoe prior can also be almost unbiased under certain conditions. In addition to these theoretical results, we also provide a full Gibbs sampler for implementing our estimator. MATLAB code is available for download from github at http://github.com/liyf1988/GHS. The graphical horseshoe estimator compares favorably to existing techniques in simulations and in a human gene network data analysis.