Tuning Parameter Calibration in High-dimensional Logistic Regression With Theoretical Guarantees
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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 penalized logistic regression. It is based on simple tests along the tuning parameter path and satisfies optimal finite sample bounds. It is also amenable to easy and efficient implementations, and it rivals or outmatches existing methods in simulations and real data applications.
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