Censored Graphical Horseshoe: Bayesian sparse precision matrix estimation with censored and missing data

TL;DR

The paper introduces CGHS, a Bayesian method extending the Graphical Horseshoe to handle censored and missing Gaussian data, improving sparse precision matrix estimation in incomplete datasets.

Contribution

It develops a novel Bayesian framework with latent variables for censored/missing data, providing efficient Gibbs sampling and theoretical insights.

Findings

CGHS outperforms penalized likelihood methods in simulations.

The method effectively handles incomplete data in Gaussian graphical models.

Theoretical results on posterior behavior under censoring are established.

Abstract

Gaussian graphical models provide a powerful framework for studying conditional dependencies in multivariate data, with widespread applications spanning biomedical, environmental sciences, and other data-rich scientific domains. While the Graphical Horseshoe (GHS) method has emerged as a state-of-the-art Bayesian method for sparse precision matrix estimation, existing approaches assume fully observed data and thus fail in the presence of censoring or missingness, which are pervasive in real-world studies. In this paper, we develop the Censored Graphical Horseshoe (CGHS), a novel Bayesian framework that extends the GHS to censored and arbitrarily missing Gaussian data. By introducing a latent-variable representation, CGHS accommodates incomplete observations while retaining the adaptive global-local shrinkage properties of the Horseshoe prior. We derive efficient Gibbs samplers for posterior computation and establish new theoretical results on posterior behavior under censoring and missingness, filling a gap not addressed by frequentist Lasso-based methods. Through extensive simulations, we demonstrate that CGHS consistently improves estimation accuracy compared to penalized likelihood approaches. Our methods are implemented in the package GHScenmis available on Github: https://github.com/tienmt/ghscenmis .