Robust logistic regression modelling via the elastic net-type regularization and tuning parameter selection

Abstract

The penalized logistic regression is a useful tool for classifying samples and feature selection. Although the methodology has been widely used in various fields of research, their performance takes a sudden turn for the worst in the presence of outlier, since the logistic regression is based on the maximum log-likelihood method which is sensitive to outliers. It implies that we cannot accurately classify samples and find important factors having crucial information for classification. To overcome the problem, we propose a robust penalized logistic regression based on a weighted likelihood methodology. We also derive an information criterion for choosing the tuning parameters, which is a vital matter in robust penalized logistic regression modelling in line with generalized information criteria. We demonstrate through Monte Carlo simulations and real-world example that the proposed robust modelling strategies perform well for sparse logistic regression modelling even in the presence of outliers.

Keywords:

• high-dimensional data
• information criteria
• L${}_1$-type regularization
• robust logisticregression
• tuning parameter selection

AMS Subject Classification:

• 62J
• 62H

Acknowledgements

The authors would like to thank the associate editor and anonymous reviewers for the constructive and valuable comments that improved the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.