# Informative co-data learning for high-dimensional Horseshoe regression

arXiv: https://arxiv.org/abs/2303.05898 · HTML: https://mlsanity.com/paper/2303.05898/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2023.

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

- [Linked shrinkage to improve estimation of interaction effects in regression models](https://mlsanity.com/paper/2309.13998/) (2023)
- [Guiding adaptive shrinkage by co-data to improve regression-based prediction and feature selection](https://mlsanity.com/paper/2405.04917/) (2024)

## Abstract (arXiv)

High-dimensional data often arise from clinical genomics research to infer relevant predictors of a particular trait. A way to improve the predictive performance is to include information on the predictors derived from prior knowledge or previous studies. Such information is also referred to as ``co-data''. To this aim, we develop a novel Bayesian model for including co-data in a high-dimensional regression framework, called Informative Horseshoe regression (infHS). The proposed approach regresses the prior variances of the regression parameters on the co-data variables, improving variable selection and prediction. We implement both a Gibbs sampler and a Variational approximation algorithm. The former is suited for applications of moderate dimensions which, besides prediction, target posterior inference, whereas the computational efficiency of the latter allows handling a very large number of variables. We show the benefits from including co-data with a simulation study. Eventually, we demonstrate that infHS outperforms competing approaches for two genomics applications.