# Better prediction by use of co-data: Adaptive group-regularized ridge regression

arXiv: https://arxiv.org/abs/1411.3496 · HTML: https://mlsanity.com/paper/1411.3496/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2014.

## Built on by (most cited first, 18 of 18)

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- [An Uncertainty-Aware Dynamic Decision Framework for Progressive Multi-Omics Integration in Classification Tasks](https://mlsanity.com/paper/2507.01032/) (2025)
- [ProMUSE: Progressive Multi-modal Uncertainty-guided Staged Evidential Alzheimer Disease Classification](https://mlsanity.com/paper/2606.19371/) (2026)
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- [Penalised regression with multiple sources of prior effects](https://mlsanity.com/paper/2212.08581/) (2022)
- [Co-data Learning for Bayesian Additive Regression Trees](https://mlsanity.com/paper/2311.09997/) (2023)
- [Guiding adaptive shrinkage by co-data to improve regression-based prediction and feature selection](https://mlsanity.com/paper/2405.04917/) (2024)
- [SDM-Q: Cost-Aware Staged Decision-Making for Multi-Omics Classification with Deep Q-Learning](https://mlsanity.com/paper/2605.31014/) (2026)
- [Adaptive Confidence-weighted Expansion for Trustworthy Multi-Omics Multimodal Fusion](https://mlsanity.com/paper/2607.20742/) (2026)

## Abstract (arXiv)

For many high-dimensional studies, additional information on the variables, like (genomic) annotation or external p-values, is available. In the context of binary and continuous prediction, we develop a method for adaptive group-regularized (logistic) ridge regression, which makes structural use of such 'co-data'. Here, 'groups' refer to a partition of the variables according to the co-data. We derive empirical Bayes estimates of group-specific penalties, which possess several nice properties: i) they are analytical; ii) they adapt to the informativeness of the co-data for the data at hand; iii) only one global penalty parameter requires tuning by cross-validation. In addition, the method allows use of multiple types of co-data at little extra computational effort. We show that the group-specific penalties may lead to a larger distinction between `near-zero' and relatively large regression parameters, which facilitates post-hoc variable selection. The method, termed GRridge, is implemented in an easy-to-use R-package. It is demonstrated on two cancer genomics studies, which both concern the discrimination of precancerous cervical lesions from normal cervix tissues using methylation microarray data. For both examples, GRridge clearly improves the predictive performances of ordinary logistic ridge regression and the group lasso. In addition, we show that for the second study the relatively good predictive performance is maintained when selecting only 42 variables.