Adaptive group-regularized logistic elastic net regression

Author:

Münch Magnus M1,Peeters Carel F W2,Van Der Vaart Aad W3,Van De Wiel Mark A4

Affiliation:

1. Department of Epidemiology & Biostatistics, Amsterdam Public Health Research Institute, Amsterdam University Medical Centers, PO Box 7057, 1007 MB Amsterdam, The Netherlands and Mathematical Institute, Leiden University, PO Box 9512, 2300 RA Leiden, The Netherlands

2. Department of Epidemiology & Biostatistics, Amsterdam Public Health Research Institute, Amsterdam University Medical Centers, PO Box 7057, 1007 MB Amsterdam, The Netherlands

3. Mathematical Institute, Leiden University, PO Box 9512, 2300 RA Leiden, The Netherlands

4. Department of Epidemiology & Biostatistics, Amsterdam Public Health Research Institute, Amsterdam University Medical Centers, PO Box 7057, 1007 MB Amsterdam, The Netherlands and MRC Biostatistics Unit, University of Cambridge, Cambridge CB2 0SR, UK

Abstract

Summary In high-dimensional data settings, additional information on the features is often available. Examples of such external information in omics research are: (i) $p$-values from a previous study and (ii) omics annotation. The inclusion of this information in the analysis may enhance classification performance and feature selection but is not straightforward. We propose a group-regularized (logistic) elastic net regression method, where each penalty parameter corresponds to a group of features based on the external information. The method, termed gren, makes use of the Bayesian formulation of logistic elastic net regression to estimate both the model and penalty parameters in an approximate empirical–variational Bayes framework. Simulations and applications to three cancer genomics studies and one Alzheimer metabolomics study show that, if the partitioning of the features is informative, classification performance, and feature selection are indeed enhanced.

Funder

European Research Council

Publisher

Oxford University Press (OUP)

Subject

Statistics, Probability and Uncertainty,General Medicine,Statistics and Probability

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