Informative Co‐Data Learning for High‐Dimensional Horseshoe Regression

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 by incorporating information about the predictors obtained from existing 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, termed 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 latter's computational efficiency allows handling a very large number of variables. We show the benefits of including co-data through a simulation study. Lastly, we demonstrate that infHS outperforms competing approaches in two genomics applications.