Robust and sparse logistic regression

Dries Cornilly, Lise Tubex, Stefan Van Aelst and Tim Verdonck ()
Additional contact information
Dries Cornilly: KU Leuven
Lise Tubex: University of Antwerp - imec
Stefan Van Aelst: KU Leuven
Tim Verdonck: KU Leuven

Advances in Data Analysis and Classification, 2024, vol. 18, issue 3, No 6, 663-679

Abstract: Abstract Logistic regression is one of the most popular statistical techniques for solving (binary) classification problems in various applications (e.g. credit scoring, cancer detection, ad click predictions and churn classification). Typically, the maximum likelihood estimator is used, which is very sensitive to outlying observations. In this paper, we propose a robust and sparse logistic regression estimator where robustness is achieved by means of the $$\gamma$$ γ -divergence. An elastic net penalty ensures sparsity in the regression coefficients such that the model is more stable and interpretable. We show that the influence function is bounded and demonstrate its robustness properties in simulations. The good performance of the proposed estimator is also illustrated in an empirical application that deals with classifying the type of fuel used by cars.

Keywords: Elastic net; $$\gamma$$ γ -divergence; Logistic regression; Robustness; Sparsity; 62F35; 62J12 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11634-023-00572-4

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