# Incorporating prior information and borrowing information in high-dimensional sparse regression using the horseshoe and variational Bayes

## TL;DR

This paper presents a novel high-dimensional sparse regression method that integrates prior knowledge and information across multiple datasets using horseshoe priors and variational Bayes, enhancing analysis of complex biological data.

## Contribution

It introduces a new framework combining horseshoe priors with empirical Bayes and variational Bayes for efficient, prior-informed, multi-dataset sparse regression.

## Key findings

- Effective in gene regulatory network reconstruction
- Improves eQTL mapping accuracy
- Handles complex dependence structures

## Abstract

We introduce a sparse high-dimensional regression approach that can incorporate prior information on the regression parameters and can borrow information across a set of similar datasets. Prior information may for instance come from previous studies or genomic databases, and information borrowed across a set of genes or genomic networks. The approach is based on prior modelling of the regression parameters using the horseshoe prior, with a prior on the sparsity index that depends on external information. Multiple datasets are integrated by applying an empirical Bayes strategy on hyperparameters. For computational efficiency we approximate the posterior distribution using a variational Bayes method. The proposed framework is useful for analysing large-scale data sets with complex dependence structures. We illustrate this by applications to the reconstruction of gene regulatory networks and to eQTL mapping.