Informative co-data learning for high-dimensional Horseshoe regression

TL;DR

This paper introduces a Bayesian regression model that incorporates prior knowledge (co-data) to enhance variable selection and prediction in high-dimensional genomics data, using both Gibbs sampling and Variational methods.

Contribution

The paper proposes a novel Bayesian framework, infHS, for integrating co-data into high-dimensional regression, improving predictive accuracy and variable selection.

Findings

infHS outperforms competing methods in genomics applications.

Gibbs sampler suitable for moderate dimensions with posterior inference.

Variational algorithm enables handling very large variable sets.

Abstract

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.