# Empirical Bayes posterior concentration in sparse high-dimensional linear models

arXiv: https://arxiv.org/abs/1406.7718 · HTML: https://mlsanity.com/paper/1406.7718/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2014.

## Built on by (most cited first, 10 of 10)

- [Performance of Bayesian linear regression in a model with mismatch](https://mlsanity.com/paper/2107.06936/) (2021)
- [High-dimensional Bayesian Tobit regression for censored response with Horseshoe prior](https://mlsanity.com/paper/2505.08288/) (2025)
- [Spike and slab Bayesian sparse principal component analysis](https://mlsanity.com/paper/2102.00305/) (2021)
- [Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm](https://mlsanity.com/paper/2209.08139/) (2022)
- [Handling bounded response in high dimensions: a Horseshoe prior Bayesian Beta regression approach](https://mlsanity.com/paper/2505.22211/) (2025)
- [Adaptive posterior concentration rates for sparse high-dimensional linear regression with random design and unknown error variance](https://mlsanity.com/paper/2405.19016/) (2024)
- [Bayesian Analysis for Over-parameterized Linear Model via Effective Spectra](https://mlsanity.com/paper/2305.15754/) (2023)
- [Variational empirical Bayes variable selection in high-dimensional logistic regression](https://mlsanity.com/paper/2502.10532/) (2025)
- [Leveraging heterogeneity for identifiability: Bayesian order-based learning of multiple DAGs](https://mlsanity.com/paper/2605.15639/) (2026)
- [Joint Model and Data Sparsification via the Marginal Likelihood](https://mlsanity.com/paper/2605.29908/) (2026)

## Abstract (arXiv)

We propose a new empirical Bayes approach for inference in the p gg n normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a variety of concentration rate results for the empirical Bayes posterior distribution, relevant for both estimation and model selection. Computation is straightforward and fast, and simulation results demonstrate the strong finite-sample performance of the empirical Bayes model selection procedure.