# Bayesian inference in high-dimensional linear models using an empirical correlation-adaptive prior

arXiv: https://arxiv.org/abs/1810.00739 · HTML: https://mlsanity.com/paper/1810.00739/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2018.

## Built on by (most cited first, 2 of 2)

- [Concentration of a sparse Bayesian model with Horseshoe prior in estimating high-dimensional precision matrix](https://mlsanity.com/paper/2406.14269/) (2024)
- [Adaptive posterior concentration rates for sparse high-dimensional linear regression with random design and unknown error variance](https://mlsanity.com/paper/2405.19016/) (2024)

## Abstract (arXiv)

In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity, determining if parameters associated with correlated predictors should be shrunk together or kept apart. Under suitable conditions, we prove that this empirical Bayes posterior concentrates around the true sparse parameter at the optimal rate asymptotically. A simplified version of a shotgun stochastic search algorithm is employed to implement the variable selection procedure, and we show, via simulation experiments across different settings and a real-data application, the favorable performance of the proposed method compared to existing methods.