mlsanityData to 14 Oct 2026

Concentration of a sparse Bayesian model with Horseshoe prior in estimating high-dimensional precision matrix

arXiv 2406.14269 ↗First posted 20 Jun 2024math.ST stat.ML stat.THcited by 8

Not on the map. Why?

Abstract (arXiv)

Precision matrices are crucial in many fields such as social networks, neuroscience, and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off-diagonal position of the precision matrix indicates conditional independence between nodes. In high-dimensional settings where the dimension of the precision matrix ( p ) exceeds the sample size ( n ) and the matrix is sparse, methods like graphical Lasso, graphical SCAD, and CLIME are popular for estimating GGMs. While frequentist methods are well-studied, Bayesian approaches for (unstructured) sparse precision matrices are less explored. The graphical horseshoe estimate by citeli2019graphical, applying the global-local horseshoe prior, shows superior empirical performance, but theoretical work for sparse precision matrix estimations using shrinkage priors is limited. This paper addresses these gaps by providing concentration results for the tempered posterior with the fully specified horseshoe prior in high-dimensional settings. Moreover, we also provide novel theoretical results for model misspecification, offering a general oracle inequality for the posterior. A concise set of simulations is performed to validate our theoretical findings.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 18 of its 45 references that are in the map. First posted on arXiv 20 Jun 2024.

Builds on

18 of 45 references.

References · 18

  1. 2013A General Framework for Updating Belief Distributionscited by 175
  2. 2014Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing Itcited by 95
  3. 2017Concentration of tempered posteriors and of their variational approximationscited by 66
  4. 2017General Bayesian Updating and the Loss-Likelihood Bootstrapcited by 34
  5. 2015Calibrating general posterior credible regionscited by 27
  6. 2020A comparison of learning rate selection methods in generalized Bayesian inferencecited by 23
  7. 2015An Overview on the Estimation of Large Covariance and Precision Matricescited by 21
  8. 2021On the Robustness to Misspecification of α-Posteriors and Their Variational Approximationscited by 15
  9. 2017The Graphical Horseshoe Estimator for Inverse Covariance Matricescited by 9
  10. 2021Adaptation of the Tuning Parameter in General Bayesian Inference with Robust Divergencecited by 7
  11. 2016Bayesian sparse multiple regression for simultaneous rank reduction and variable selectioncited by 6
  12. 2014PAC-Bayesian AUC classification and scoringcited by 5
6 more
  1. 2018Bayesian Regularization for Graphical Models with Unequal Shrinkagecited by 5
  2. 2017α-Variational Inference with Statistical Guaranteescited by 4
  3. 2021Precision Matrix Estimation under the Horseshoe-like Prior-Penalty Dualcited by 4
  4. 2023Semiparametric inference using fractional posteriorscited by 4
  5. 2018Bayesian inference in high-dimensional linear models using an empirical correlation-adaptive priorcited by 2
  6. 2021Contraction of a quasi-Bayesian model with shrinkage priors in precision matrix estimationcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 6; 2026: 2.

8 papers.

  1. 2025High-dimensional Bayesian Tobit regression for censored response with Horseshoe priorcited by 4
  2. 2025Handling bounded response in high dimensions: a Horseshoe prior Bayesian Beta regression approachcited by 2
  3. 2025Heavy Lasso: sparse penalized regression under heavy-tailed noise via data-augmented soft-thresholdingcited by 2
  4. 2025Bayesian Pliable Lasso with Horseshoe Prior for Interaction Effects in GLMs with Missing Responsescited by 1
  5. 2025Kullback-Leibler excess risk bounds for exponential weighted aggregation in Generalized linear modelscited by 0
  6. 2025Sparse classification with positive-confidence data in high dimensionscited by 0
  7. 2026Robust low-rank estimation with multiple binary responses using pairwise AUC losscited by 0
  8. 2026Mixture-of-experts Wishart model for covariance matrices with an application to Cancer drug screeningcited by 0