Tuning parameter calibration for $\ell_1$-regularized logistic regression
This addresses the challenge of calibrating tuning parameters for feature selection in logistic regression, which lacks finite sample guarantees, offering a solution with practical benefits for statistical modeling in high-dimensional data.
The paper tackles the problem of tuning parameter calibration for ℓ1-regularized logistic regression in high-dimensional classification, introducing a novel scheme based on simple tests along the tuning parameter path that provides optimal guarantees for feature selection and outperforms existing methods in simulations and real data.
Feature selection is a standard approach to understanding and modeling high-dimensional classification data, but the corresponding statistical methods hinge on tuning parameters that are difficult to calibrate. In particular, existing calibration schemes in the logistic regression framework lack any finite sample guarantees. In this paper, we introduce a novel calibration scheme for $\ell_1$-penalized logistic regression. It is based on simple tests along the tuning parameter path and is equipped with optimal guarantees for feature selection. It is also amenable to easy and efficient implementations, and it rivals or outmatches existing methods in simulations and real data applications.