# Fast marginal likelihood estimation of penalties for group-adaptive elastic net

arXiv: https://arxiv.org/abs/2101.03875 · HTML: https://mlsanity.com/paper/2101.03875/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 35 references that are in the map.
- First posted on arXiv 11 Jan 2021.

## Builds on (most cited first, 7 of 7)

- [Better prediction by use of co-data: Adaptive group-regularized ridge regression](https://mlsanity.com/paper/1411.3496/) (2014)
- [Feature-weighted elastic net: using "features of features" for better prediction](https://mlsanity.com/paper/2006.01395/) (2020)
- [Adaptive penalization in high-dimensional regression and classification with external covariates using variational Bayes](https://mlsanity.com/paper/1811.02962/) (2018)
- [Flexible co-data learning for high-dimensional prediction](https://mlsanity.com/paper/2005.04010/) (2020)
- [Adaptive group-regularized logistic elastic net regression](https://mlsanity.com/paper/1805.00389/) (2018)
- [Improving the INLA approach for approximate Bayesian inference for latent Gaussian models](https://mlsanity.com/paper/1503.07307/) (2015)
- [Fast cross-validation for multi-penalty ridge regression](https://mlsanity.com/paper/2005.09301/) (2020)

## Built on by (most cited first, 4 of 4)

- [ecpc: An R-package for generic co-data models for high-dimensional prediction](https://mlsanity.com/paper/2205.07640/) (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)
- [pared: Model selection using multi-objective optimization](https://mlsanity.com/paper/2505.21730/) (2025)

## Abstract (arXiv)

Nowadays, clinical research routinely uses omics data, such as gene expression, for predicting clinical outcomes or selecting markers. Additionally, so-called co-data are often available, providing complementary information on the covariates, like p-values from previously published studies or groups of genes corresponding to pathways. Elastic net penalisation is widely used for prediction and covariate selection. Group-adaptive elastic net penalisation learns from co-data to improve the prediction and covariate selection, by penalising important groups of covariates less than other groups. Existing methods are, however, computationally expensive. Here we present a fast method for marginal likelihood estimation of group-adaptive elastic net penalties for generalised linear models. We first derive a low-dimensional representation of the Taylor approximation of the marginal likelihood and its first derivative for group-adaptive ridge penalties, to efficiently estimate these penalties. Then we show by using asymptotic normality of the linear predictors that the marginal likelihood for elastic net models may be approximated well by the marginal likelihood for ridge models. The ridge group penalties are then transformed to elastic net group penalties by using the variance function. The method allows for overlapping groups and unpenalised variables. We demonstrate the method in a model-based simulation study and an application to cancer genomics. The method substantially decreases computation time and outperforms or matches other methods by learning from co-data.