dorsal/arxiv
View SchemaCensored Graphical Horseshoe: Bayesian sparse precision matrix estimation with censored and missing data
| Authors | The Tien Mai, Sayantan Banerjee |
|---|---|
| Categories | |
| ArXiv ID | 2601.06671vv1 |
| URL | https://arxiv.org/abs/2601.06671 |
| License | http://creativecommons.org/licenses/by-nc-sa/4.0/ |
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 .
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"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 .",
"arxiv_id": "2601.06671",
"authors": [
"The Tien Mai",
"Sayantan Banerjee"
],
"categories": [
"stat.ME",
"math.ST",
"stat.CO",
"stat.TH"
],
"license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
"title": "Censored Graphical Horseshoe: Bayesian sparse precision matrix estimation with censored and missing data",
"url": "https://arxiv.org/abs/2601.06671",
"version": "v1"
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