Tuning-free ridge estimators for high-dimensional generalized linear models

TL;DR

This paper introduces tuning-free ridge estimators for high-dimensional generalized linear models, eliminating the need for parameter calibration and improving prediction accuracy with theoretical guarantees.

Contribution

It proposes modified ridge estimators that do not require tuning parameters, enhancing practical usability and predictive performance.

Findings

Tuning-free ridge estimators outperform standard methods with cross-validation.

Theoretical guarantees support the effectiveness of the modified estimators.

Empirical results show improved prediction accuracy.

Abstract

Ridge estimators regularize the squared Euclidean lengths of parameters. Such estimators are mathematically and computationally attractive but involve tuning parameters that can be difficult to calibrate. In this paper, we show that ridge estimators can be modified such that tuning parameters can be avoided altogether. We also show that these modified versions can improve on the empirical prediction accuracies of standard ridge estimators combined with cross-validation, and we provide first theoretical guarantees.