Abstract

For high-dimensional settings, we show how one can use empirical Bayes (EB) principles to estimate penalties that may differ across groups of variables. These groups are predefined using co-data, which is auxiliary information available on the variables (e.g. genomic annotation or external p-values). Due to the adaptive character of the penalties, the group-wise penalties may improve predictions when the groups are indeed informative, while not deteriorating those when this is not the case. We provide an implementation in a classical logistic ridge regression setting. However, we will also discuss extension of the framework to a Bayesian ridge regression setting. The latter is particularly useful for obtaining credibility intervals on the predicted event probabilities. In particular a hybrid EB-Full Bayes approach in combination with highest-probability density intervals seem to have good coverage properties when the number of variables is not extremely large. Finally, the potential for better variable selection, either by post-hoc selection or by sparse regression, will be shortly considered. Several real data examples will be discussed, in particular on cancer diagnostics using a variety of molecular data types, such as methylation, RNAseq and microRNAs.