The Graphical Horseshoe Estimator for Inverse Covariance Matrices

2017/07/20 by Yunfan Li, Bruce Α. Craig, Li, Yunfan +3 · 5 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Computer and information sciences #Gene expression and cancer classification #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1707.06661

openalex publication_date 2017/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

<b>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 the graphical smoothly clipped absolute deviation. 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 sampling model. 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</b>http://github.com/liyf1988/GHS<b>. The graphical horseshoe estimator compares favorably to existing techniques in simulations and in a human gene network data analysis. Supplementary materials for this article are available online.</b>

Citations

• The horseshoe estimator for sparse signals

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