GHS: The Graphical Horseshoe Estimator for Inverse Covariance Matrices. 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 this http URL. The graphical horseshoe estimator compares favorably to existing techniques in simulations and in a human gene network data analysis.
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References in zbMATH (referenced in 7 articles )
Showing results 1 to 7 of 7.
- Bhadra, Anindya (ed.): Discussion to: Bayesian graphical models for modern biological applications by Y. Ni, V. Baladandayuthapani, M. Vannucci and F.C. Stingo (2022)
- Li, Yunfan; Datta, Jyotishka; Craig, Bruce A.; Bhadra, Anindya: Joint mean-covariance estimation via the horseshoe (2021)
- Lukemire, Joshua; Kundu, Suprateek; Pagnoni, Giuseppe; Guo, Ying: Bayesian joint modeling of multiple brain functional networks (2021)
- Li, Zehang Richard; McComick, Tyler H.; Clark, Samuel J.: Using Bayesian latent Gaussian graphical models to infer symptom associations in verbal autopsies (2020)
- Williams, Donald R.; Mulder, Joris: Bayesian hypothesis testing for Gaussian graphical models: conditional independence and order constraints (2020)
- Bhadra, Anindya; Datta, Jyotishka; Polson, Nicholas G.; Willard, Brandon: Lasso meets horseshoe: a survey (2019)
- Li, Yunfan; Craig, Bruce A.; Bhadra, Anindya: The graphical horseshoe estimator for inverse covariance matrices (2019)